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<dd><a href="/zettels/multivariable_control/">Multivariable Control</a></dd>
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<dd><sup id="51789ae56fcd2284b8426153d90595c8"><a href="#albertos04_multiv_contr_system" title="Albertos \&amp; Antonio, Multivariable Control Systems: an Engineering Approach, Springer-Verlag (2004).">(Albertos &amp; Antonio, 2004)</a></sup></dd>
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<h1 id="bibliography">Bibliography</h1>
<p><a id="albertos04_multiv_contr_system"></a>Albertos, P., &amp; Antonio, S., <em>Multivariable control systems: an engineering approach</em> (2004), : Springer-Verlag. <a href="#51789ae56fcd2284b8426153d90595c8">↩</a></p>
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Bibliography Du, C., &amp;amp; Xie, L., Modeling and control of vibration in mechanical systems (2010), : CRC Press. ↩" />
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<dd><a href="/zettels/stewart_platforms/">Stewart Platforms</a>, <a href="/zettels/vibration_isolation/">Vibration Isolation</a></dd>
<dt>Reference</dt>
<dd><sup id="1d38bd128d92142dd456ab4e9bb4eb84"><a href="#du10_model_contr_vibrat_mechan_system" title="Chunling Du \&amp; Lihua Xie, Modeling and Control of Vibration in Mechanical Systems, CRC Press (2010).">(Chunling Du &amp; Lihua Xie, 2010)</a></sup></dd>
<dt>Author(s)</dt>
<dd>Du, C., &amp; Xie, L.</dd>
<dt>Year</dt>
<dd>2010</dd>
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<p>Read Chapter 1 and 3.</p>
<h1 id="bibliography">Bibliography</h1>
<p><a id="du10_model_contr_vibrat_mechan_system"></a>Du, C., &amp; Xie, L., <em>Modeling and control of vibration in mechanical systems</em> (2010), : CRC Press. <a href="#1d38bd128d92142dd456ab4e9bb4eb84">↩</a></p>
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Reference (Chunling Du &amp;amp; Chee Khiang Pang, 2019) Author(s) Du, C., &amp;amp; Pang, C. K. Year 2019 Mechanical Actuation Systems Introduction When high bandwidth, high position accuracy and long stroke are required simultaneously: dual-stage systems composed of a coarse (or primary) actuator and a fine actuator working together are used.
Popular choices for coarse actuator are:
DC motor Voice coil motor (VCM) Permanent magnet stepper motor Permanent magnet linear synchronous motor As fine actuators, most of the time piezoelectric actuator are used." />
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<p>Tags
:</p>
<dl>
<dt>Reference</dt>
<dd><sup id="28e6aa60b8446943c921ff0d6578ac85"><a href="#du19_multi_actuat_system_contr" title="Chunling Du \&amp; Chee Khiang Pang, Multi-stage Actuation Systems and Control, CRC Press (2019).">(Chunling Du &amp; Chee Khiang Pang, 2019)</a></sup></dd>
<dt>Author(s)</dt>
<dd>Du, C., &amp; Pang, C. K.</dd>
<dt>Year</dt>
<dd>2019</dd>
</dl>
<h2 id="mechanical-actuation-systems">Mechanical Actuation Systems</h2>
<h3 id="introduction">Introduction</h3>
<p>When high bandwidth, high position accuracy and long stroke are required simultaneously: dual-stage systems composed of a coarse (or primary) actuator and a fine actuator working together are used.</p>
<p>Popular choices for coarse actuator are:</p>
<ul>
<li>DC motor</li>
<li>Voice coil motor (VCM)</li>
<li>Permanent magnet stepper motor</li>
<li>Permanent magnet linear synchronous motor</li>
</ul>
<p>As fine actuators, most of the time piezoelectric actuator are used.</p>
<p>In order to overcome fine actuator stringent stroke limitation and increase control bandwidth, three-stage actuation systems are necessary in practical applications.</p>
<h3 id="actuators">Actuators</h3>
<h4 id="primary-actuator">Primary Actuator</h4>
<p>Without loss of generality, the VCM actuator is used as the primary actuator.
When current passes through the coil, a force is produced which accelerates the actuator radially.
The produced force is a function of the current \(i_c\):
\[ f_m = k_t i_c \]
where \(k_t\) is a linearized nominal value called the torque constant.</p>
<p>The resonance of the actuator is mainly due to the flexibility of the pivot bearing, arm, suspension.</p>
<p>Then the bandwidth of the control loop is low and the resonances are not a limiting factor of the control design, the actuator model can be considered as follows:
\[ P_v(s) = \frac{k_{vcm}}{s^2} \]</p>
<p>When the bandwidth is high, the actuator resonances have to be considered in the control design since the flexible resonance modes will reduce the system stability and affect the control performance. Then the actuator model becomes
\[ P_v(s) = \frac{k_{vcm}}{s^2} P_r(s) \]
which includes the resonance model
\[ P_r(s) = \Pi_{i=1}^{N} P_{ri}(s) \]
and the resonance \(P_{ri}(s)\) can be represented as one of the following forms</p>
<p>\begin{align*}
P_{ri}(s) &amp;= \frac{\omega_i^2}{s^2 + 2 \xi_i \omega_i s + \omega_i^2} \\\<br>
P_{ri}(s) &amp;= \frac{b_{1i} \omega_i s + b_{0i} \omega_i^2}{s^2 + 2 \xi_i \omega_i s + \omega_i^2} \\\<br>
P_{ri}(s) &amp;= \frac{b_{2i} s^2 + b_{1i} \omega_i s + b_{0i} \omega_i^2}{s^2 + 2 \xi_i \omega_i s + \omega_i^2}
\end{align*}</p>
<h4 id="secondary-actuators">Secondary Actuators</h4>
<p>We here consider two types of secondary actuators: the PZT milliactuator (figure <a href="#org53c168b">1</a>) and the microactuator.</p>
<p><a id="org53c168b"></a></p>
<figure>
<img src="/ox-hugo/du19_pzt_actuator.png"
alt="Figure 1: A PZT-actuator suspension"/> <figcaption>
<p>Figure 1: A PZT-actuator suspension</p>
</figcaption>
</figure>
<p>There are three popular types of micro-actuators: electrostatic moving-slider microactuator, PZT slider-driven microactuator and thermal microactuator.
There characteristics are shown on table <a href="#table--tab:microactuator">1</a>.</p>
<p><a id="table--tab:microactuator"></a></p>
<div class="table-caption">
<span class="table-number"><a href="#table--tab:microactuator">Table 1</a></span>:
Performance comparison of microactuators
</div>
<table>
<thead>
<tr>
<th></th>
<th>Elect.</th>
<th>PZT</th>
<th>Thermal</th>
</tr>
</thead>
<tbody>
<tr>
<td>TF</td>
<td>\(\frac{K}{s^2 + 2\xi\omega s + \omega^2}\)</td>
<td>\(\frac{K}{s^2 + 2\xi\omega s + \omega^2}\)</td>
<td>\(\frac{K}{\tau s + 1}\)</td>
</tr>
<tr>
<td>\(\tau\)</td>
<td>\(&lt;\SI{0.1}{ms}\)</td>
<td>\(&lt;\SI{0.05}{ms}\)</td>
<td>\(&gt;\SI{0.1}{ms}\)</td>
</tr>
<tr>
<td>\(omega\)</td>
<td>\(1-\SI{2}{kHz}\)</td>
<td>\(20-\SI{25}{kHz}\)</td>
<td>\(&gt;\SI{15}{kHz}\)</td>
</tr>
</tbody>
</table>
<h3 id="single-stage-actuation-systems">Single-Stage Actuation Systems</h3>
<p>A typical closed-loop control system is shown on figure <a href="#org5941a76">2</a>, where \(P_v(s)\) and \(C(z)\) represent the actuator system and its controller.</p>
<p><a id="org5941a76"></a></p>
<figure>
<img src="/ox-hugo/du19_single_stage_control.png"
alt="Figure 2: Block diagram of a single-stage actuation system"/> <figcaption>
<p>Figure 2: Block diagram of a single-stage actuation system</p>
</figcaption>
</figure>
<h3 id="dual-stage-actuation-systems">Dual-Stage Actuation Systems</h3>
<p>Dual-stage actuation mechanism for the hard disk drives consists of a VCM actuator and a secondary actuator placed between the VCM and the sensor head.
The VCM is used as the primary stage to provide long track seeking but with poor accuracy and slow response time, while the secondary stage actuator is used to provide higher positioning accuracy and faster response but with a stroke limit.</p>
<p><a id="org8f04825"></a></p>
<figure>
<img src="/ox-hugo/du19_dual_stage_control.png"
alt="Figure 3: Block diagram of dual-stage actuation system"/> <figcaption>
<p>Figure 3: Block diagram of dual-stage actuation system</p>
</figcaption>
</figure>
<h3 id="three-stage-actuation-systems">Three-Stage Actuation Systems</h3>
<p>Due to the limited allowed stroke of the microactuator, the control bandwidth has to be restricted and that limits the dual-stage disturbance rejection capability.</p>
<p>A three-stage actuation system is therefore introduced to further increase the bandwidth.</p>
<p>Typically, a VCM actuator is used as the primary actuator, PZT milliactuator as the second stage actuator and a third actuator more collocated is used.</p>
<h2 id="high-precision-positioning-control-of-dual-stage-actuation-systems">High-Precision Positioning Control of Dual-Stage Actuation Systems</h2>
<h3 id="introduction">Introduction</h3>
<p>The sensitivity function of the closed-loop system has provided a straightforward view of its disturbance rejection capability.
It is demanded that the sensitivity function magnitude in the low-frequency range be sufficiently low, while its hump in high-frequency range stays low enough.
In view of this, the controller design for dual-stage actuation systems adopts a weighting function to shape the sensitivity function.</p>
<h3 id="control-schemes">Control Schemes</h3>
<p>A popular control scheme for dual-stage actuation system is the <strong>decoupled structure</strong> as shown in figure <a href="#org03d53e8">4</a>.</p>
<ul>
<li>\(C_v(z)\) and \(C_p(z)\) are the controllers respectively, for the primary VCM actuator \(P_v(s)\) and the secondary actuator \(P_p(s)\).</li>
<li>\(\hat{P}_p(z)\) is an approximation of \(P_p\) to estimate \(y_p\).</li>
<li>\(d_1\) and \(d_2\) denote internal disturbances</li>
<li>\(n\) is the measurement noise</li>
<li>\(d_u\) stands for external vibration</li>
</ul>
<p><a id="org03d53e8"></a></p>
<figure>
<img src="/ox-hugo/du19_decoupled_control.png"
alt="Figure 4: Decoupled control structure for the dual-stage actuation system"/> <figcaption>
<p>Figure 4: Decoupled control structure for the dual-stage actuation system</p>
</figcaption>
</figure>
<p>The open-loop transfer function from \(pes\) to \(y\) is
\[ G(z) = P_p(z) C_p(z) + P_v(z) C_v(z) + P_v(z) C_v(z) \hat{P}_p(z) C_p(z) \]
And the overall sensitivity function of the closed loop system from \(r\) to \(pes\) is
\[ S(z) = \frac{1}{1 + G(z)} \]
which is approximately
\[ S(z) = \frac{1}{[1 + P_p(z) C_p(z)] [1 + P_v(z)C_v(z)]} \]
since within a certain bandwidth
\[ \hat{P}_p(z) \approx P_p(z) \]</p>
<p>The sensitivity functions of the VCM loop and the secondary actuator loop are</p>
<p>\begin{equation}
S_v(z) = \frac{1}{1 + P_v(z) C_v(z)}, \quad S_p(z) = \frac{1}{1 + P_p(z) C_p(z)}
\end{equation}</p>
<p>And we obtain that the dual-stage sensitivity function \(S(z)\) is the product of \(S_v(z)\) and \(S_p(z)\).
Thus, the dual-stage system control design can be decoupled into two independent controller designs.</p>
<p>Another type of control scheme is the <strong>parallel structure</strong> as shown in figure <a href="#org37116a9">5</a>.
The open-loop transfer function from \(pes\) to \(y\) is
\[ G(z) = P_p(z) C_p(z) + P_v(z) C_v(z) \]</p>
<p>The overall sensitivity function of the closed-loop system from \(r\) to \(pes\) is
\[ S(z) = \frac{1}{1 + G(z)} = \frac{1}{1 + P_p(z) C_p(z) + P_v(z) C_v(z)} \]</p>
<p><a id="org37116a9"></a></p>
<figure>
<img src="/ox-hugo/du19_parallel_control_structure.png"
alt="Figure 5: Parallel control structure for the dual-stage actuator system"/> <figcaption>
<p>Figure 5: Parallel control structure for the dual-stage actuator system</p>
</figcaption>
</figure>
<p>Because of the limited displacement range of the secondary actuator, the control efforts for the two actuators should be distributed properly when designing respective controllers to meet the required performance, make the actuators not conflict with each other, as well as prevent the saturation of the secondary actuator.</p>
<h3 id="controller-design-method-in-the-continuous-time-domain">Controller Design Method in the Continuous-Time Domain</h3>
<p>\(\mathcal{H}_\infty\) loop shaping method is used to design the controllers for the primary and secondary actuators.
The structure of the \(\mathcal{H}_\infty\) loop shaping method is plotted in figure <a href="#org299b914">6</a> where \(W(s)\) is a weighting function relevant to the designed control system performance such as the sensitivity function.</p>
<p>For a plant model \(P(s)\), a controller \(C(s)\) is to be designed such that the closed-loop system is stable and</p>
<p>\begin{equation}
\|T_{zw}\|_\infty &lt; 1
\end{equation}</p>
<p>is satisfied, where \(T_{zw}\) is the transfer function from \(w\) to \(z\): \(T_{zw} = S(s) W(s)\).</p>
<p><a id="org299b914"></a></p>
<figure>
<img src="/ox-hugo/du19_h_inf_diagram.png"
alt="Figure 6: Block diagram for \(\mathcal{H}_\infty\) loop shaping method to design the controller \(C(s)\) with the weighting function \(W(s)\)"/> <figcaption>
<p>Figure 6: Block diagram for \(\mathcal{H}_\infty\) loop shaping method to design the controller \(C(s)\) with the weighting function \(W(s)\)</p>
</figcaption>
</figure>
<p>Equation <a href="#org361ec91">1</a> means that \(S(s)\) can be shaped similarly to the inverse of the chosen weighting function \(W(s)\).
One form of \(W(s)\) is taken as</p>
<p>\begin{equation}
W(s) = \frac{\frac{1}{M}s^2 + 2\xi\omega\frac{1}{\sqrt{M}}s + \omega^2}{s^2 + 2\omega\sqrt{\epsilon}s + \omega^2\epsilon}
\end{equation}</p>
<p>where \(\omega\) is the desired bandwidth, \(\epsilon\) is used to determine the desired low frequency level of sensitivity magnitude and \(\xi\) is the damping ratio.</p>
<p>The controller can then be synthesis using the linear matrix inequality (LMI) approach.</p>
<p>The primary and secondary actuator control loops are designed separately for the dual-stage control systems.
But when designing their respective controllers, certain performances are required for the two actuators, so that control efforts for the two actuators are distributed properly and the actuators don&rsquo;t conflict with each other&rsquo;s control authority.
As seen in figure <a href="#org60ad057">7</a>, the VCM primary actuator open loop has a higher gain at low frequencies, and the secondary actuator open loop has a higher gain in the high-frequency range.</p>
<p><a id="org60ad057"></a></p>
<figure>
<img src="/ox-hugo/du19_dual_stage_loop_gain.png"
alt="Figure 7: Frequency responses of \(G_v(s) = C_v(s)P_v(s)\) (solid line) and \(G_p(s) = C_p(s) P_p(s)\) (dotted line)"/> <figcaption>
<p>Figure 7: Frequency responses of \(G_v(s) = C_v(s)P_v(s)\) (solid line) and \(G_p(s) = C_p(s) P_p(s)\) (dotted line)</p>
</figcaption>
</figure>
<p>The sensitivity functions are shown in figure <a href="#org1d6afb9">8</a>, where the hump of \(S_v\) is arranged within the bandwidth of \(S_p\) and the hump of \(S_p\) is lowered as much as possible.
This needs to decrease the bandwidth of the primary actuator loop and increase the bandwidth of the secondary actuator loop.</p>
<p><a id="org1d6afb9"></a></p>
<figure>
<img src="/ox-hugo/du19_dual_stage_sensitivity.png"
alt="Figure 8: Frequency response of \(S_v(s)\) and \(S_p(s)\)"/> <figcaption>
<p>Figure 8: Frequency response of \(S_v(s)\) and \(S_p(s)\)</p>
</figcaption>
</figure>
<p>A basic requirement of the dual-stage actuation control system is to make the individual primary and secondary loops stable.
It also required that the primary actuator path has a higher gain than the secondary actuator path at low frequency range and the secondary actuator path has a higher gain than the primary actuator path in high-frequency range.
These can be achieve by choosing appropriate weighting function for the controllers design.</p>
<h3 id="conclusion">Conclusion</h3>
<p>The controller design has been discussed for high-precision positioning control of the dual-stage actuation systems.
The \(\mathcal{H}_\infty\) loop shaping method has been applied and the design method has been presented.
With the weighting functions, the desired sensitivity function can achieved.
Such a design method can produce robust controllers with more disturbance rejection in the low frequency range and less disturbance amplification in the high-frequency range.</p>
<h2 id="modeling-and-control-of-a-three-stage-actuation-system">Modeling and Control of a Three-Stage Actuation System</h2>
<h3 id="introduction">Introduction</h3>
<p>In view of the additional bandwidth requirement which is limited by stroke constraint and saturation of secondary actuators, three-stage actuation systems are thereby proposed to meet the demand of a higher bandwidth.
In this section, a specific three-stage actuation system is presented and a controller strategy is proposed, which is based on a decoupled master-slave dual-stage control structure combined with a third stage actuation in parallel format.</p>
<h3 id="actuator-and-vibration-modeling">Actuator and Vibration Modeling</h3>
<p>A VCM actuator is used as the first-stage actuator denoted by \(P_v(s)\), a PZT milliactuator as the second-stage actuator denoted by \(P_p(s)\), and a thermal microactuator denoted by \(P_m(s)\).</p>
<h3 id="control-strategy-and-controller-design">Control Strategy and Controller Design</h3>
<p>Figure <a href="#org0e50764">9</a> shows the control structure for the three-stage actuation system.</p>
<p>The control scheme is based on the decoupled master-slave dual-stage control and the third stage microactuator is added in parallel with the dual-stage control system.
The parallel format is advantageous to the overall control bandwidth enhancement, especially for the microactuator having limited stroke which restricts the bandwidth of its own loop.
The reason why the decoupled control structure is adopted here is that its overall sensitivity function is the product of those of the two individual loops, and the VCM and the PTZ controllers can be designed separately.</p>
<p><a id="org0e50764"></a></p>
<figure>
<img src="/ox-hugo/du19_three_stage_control.png"
alt="Figure 9: Control system for the three-stage actuation system"/> <figcaption>
<p>Figure 9: Control system for the three-stage actuation system</p>
</figcaption>
</figure>
<p>The open-loop transfer function of the three-stage actuation system is derived as</p>
<p>\begin{equation}
G(z) = G_v(z) + G_p(z) + G_v(z) G_p(z) + G_m(z)
\end{equation}</p>
<p>with</p>
<p>\begin{align*}
G_v(z) &amp;= P_v(z) C_v(z) \\\<br>
G_p(z) &amp;= P_p(z) C_p(z) \\\<br>
G_m(z) &amp;= P_m(z) C_m(z)
\end{align*}</p>
<p>The overall sensitivity function is given by</p>
<p>\begin{equation}
S(z) = \frac{1}{1 + G(z)}
\end{equation}</p>
<p>The VCM actuator \(P_v(s)\) works in a low bandwidth below \(\SI{1}{kHz}\).
The PZT actuated milliactuator \(P_p(s)\) works under a reasonably high bandwidth up to \(\SI{3}{kHz}\).
The third-stage actuator \(P_m(s)\) is used to further push the bandwidth as high as possible.</p>
<p>The control performances of both the VCM and the PZT actuators are limited by their dominant resonance modes.
The open-loop frequency responses of the three stages are shown on figure <a href="#orgefe88f9">10</a>.</p>
<p><a id="orgefe88f9"></a></p>
<figure>
<img src="/ox-hugo/du19_open_loop_three_stage.png"
alt="Figure 10: Frequency response of the open-loop transfer function"/> <figcaption>
<p>Figure 10: Frequency response of the open-loop transfer function</p>
</figcaption>
</figure>
<p>The obtained sensitivity function is shown on figure <a href="#orgd0c25f8">11</a>.</p>
<p><a id="orgd0c25f8"></a></p>
<figure>
<img src="/ox-hugo/du19_sensitivity_three_stage.png"
alt="Figure 11: Sensitivity function of the VCM single stage, the dual-stage and the three-stage loops"/> <figcaption>
<p>Figure 11: Sensitivity function of the VCM single stage, the dual-stage and the three-stage loops</p>
</figcaption>
</figure>
<h3 id="performance-evaluation">Performance Evaluation</h3>
<p>External vibration from the system working environment is much higher than the internal disturbance, especially for ultra-high precision positioning systems.
In the presence of external vibration, the actuators control effort is dominantly determined by the external vibration.
But because the actuator input is constrained, the external vibration level has to be limited.
Otherwise, saturation will occur in the control loop and the control system performance will be degraded.</p>
<p>Therefore, the stroke specification of the actuators, especially milliactuator and microactuators, is very important for achievable control performance.
Higher stroke actuators have stronger abilities to make sure that the control performances are not degraded in the presence of external vibrations.</p>
<p>For the three-stage control architecture as shown on figure <a href="#org0e50764">9</a>, the position error is
\[ e = -S(P_v d_1 + d_2 + d_e) + S n \]
The control signals and positions of the actuators are given by</p>
<p>\begin{align*}
u_p &amp;= C_p e,\ y_p = P_p C_p e \\\<br>
u_m &amp;= C_m e,\ y_m = P_m C_m e \\\<br>
u_v &amp;= C_v ( 1 + \hat{P}_pC_p ) e,\ y_v = P_v ( u_v + d_1 )
\end{align*}</p>
<p>The controller design for the microactuators with input constraints must take into account both external vibration requirements and actuators&rsquo; stroke, based on which an appropriate bandwidth should be decided when designing the control system.
Higher bandwidth/higher level of disturbance generally means high stroke needed.</p>
<h3 id="different-configurations-of-the-control-system">Different Configurations of the Control System</h3>
<p>A decoupled control structure can be used for the three-stage actuation system (see figure <a href="#org5bb499d">12</a>).</p>
<p>The overall sensitivity function is
\[ S(z) = \approx S_v(z) S_p(z) S_m(z) \]
with \(S_v(z)\) and \(S_p(z)\) are defined in equation <a href="#orga34ddfe">1</a> and
\[ S_m(z) = \frac{1}{1 + P_m(z) C_m(z)} \]</p>
<p>Denote the dual-stage open-loop transfer function as \(G_d\)
\[ G_d(z) = G_v(z) + G_p(z) + G_v(z) G_p(z) \]</p>
<p>The open-loop transfer function of the overall system is
\[ G(z) = G_d(z) + G_m(z) + G_d(z) G_m(z) \]</p>
<p><a id="org5bb499d"></a></p>
<figure>
<img src="/ox-hugo/du19_three_stage_decoupled.png"
alt="Figure 12: Decoupled control structure for the three-stage actuation system"/> <figcaption>
<p>Figure 12: Decoupled control structure for the three-stage actuation system</p>
</figcaption>
</figure>
<p>The control signals and the positions of the three actuators are</p>
<p>\begin{align*}
u_p &amp;= C_p(1 + \hat{P}_m C_m) e, \ y_p = P_p u_p \\\<br>
u_m &amp;= C_m e, \ y_m = P_m M_m e \\\<br>
u_v &amp;= C_v(1 + \hat{P}_p C_p) (1 + \hat{P}_m C_m) e, \ y_v = P_v u_v
\end{align*}</p>
<p>The decoupled configuration makes the low frequency gain much higher, and consequently there is much better rejection capability at low frequency compared to the parallel architecture (see figure <a href="#org0a46272">13</a>).</p>
<p><a id="org0a46272"></a></p>
<figure>
<img src="/ox-hugo/du19_three_stage_decoupled_loop_gain.png"
alt="Figure 13: Frequency responses of the open-loop transfer functions for the three-stages parallel and decoupled structure"/> <figcaption>
<p>Figure 13: Frequency responses of the open-loop transfer functions for the three-stages parallel and decoupled structure</p>
</figcaption>
</figure>
<h3 id="conclusion">Conclusion</h3>
<p>The relationship among the external vibration, the microactuator stroke, and the achievable control bandwidth has been discussed for being considered in the controller design.
The discussion suggests that in addition to the traditional wisdom of just increasing the resonant frequency, adding more stroke to the microactuator will give more freedom to the loop shaping for the control system design.</p>
<h2 id="dual-stage-system-control-considering-secondary-actuator-stroke-limitation">Dual-Stage System Control Considering Secondary Actuator Stroke Limitation</h2>
<h3 id="introduction">Introduction</h3>
<h3 id="more-freedom-loop-shaping-for-microactuator-controller-design">More Freedom Loop Shaping for Microactuator Controller Design</h3>
<h3 id="dual-stage-system-control-design-for-5-khz-bandwidth">Dual-Stage System Control Design for 5 kHz Bandwidth</h3>
<h3 id="evaluation-with-the-consideration-of-external-vibration-and-microactuator-stroke">Evaluation with the Consideration of External Vibration and Microactuator Stroke</h3>
<h3 id="conclusion">Conclusion</h3>
<h2 id="saturation-control-for-microactuators-in-dual-stage-actuation-systems">Saturation Control for Microactuators in Dual-Stage Actuation Systems</h2>
<h3 id="introduction">Introduction</h3>
<h3 id="modeling-and-feedback-control">Modeling and Feedback Control</h3>
<h3 id="anti-windup-compensation-design">Anti-Windup Compensation Design</h3>
<h3 id="simulation-and-experimental-results">Simulation and Experimental Results</h3>
<h3 id="conclusion">Conclusion</h3>
<h2 id="time-delay-and-sampling-rate-effect-on-control-performance-of-dual-stage-actuation-systems">Time Delay and Sampling Rate Effect on Control Performance of Dual-Stage Actuation Systems</h2>
<h3 id="introduction">Introduction</h3>
<h3 id="modeling-of-time-delay">Modeling of Time Delay</h3>
<h3 id="dual-stage-actuation-system-modeling-with-time-delay-for-controller-design">Dual-Stage Actuation System Modeling with Time Delay for Controller Design</h3>
<h3 id="controller-design-with-time-delay-for-the-dual-stage-actuation-systems">Controller Design with Time Delay for the Dual-Stage Actuation Systems</h3>
<h3 id="time-delay-effect-on-dual-stage-system-control-performance">Time Delay Effect on Dual-Stage System Control Performance</h3>
<h3 id="sampling-rate-effect-on-dual-stage-system-control-performance">Sampling Rate Effect on Dual-Stage System Control Performance</h3>
<h3 id="conclusion">Conclusion</h3>
<h2 id="pzt-hysteresis-modeling-and-compensation">PZT Hysteresis Modeling and Compensation</h2>
<h3 id="introduction">Introduction</h3>
<h3 id="modeling-of-hysteresis">Modeling of Hysteresis</h3>
<h4 id="pi-model">PI Model</h4>
<h4 id="gpi-model">GPI Model</h4>
<h4 id="inverse-gpi-model">Inverse GPI Model</h4>
<h3 id="application-of-gpi-model-to-a-pzt-actuated-structure">Application of GPI Model to a PZT-Actuated Structure</h3>
<h4 id="modeling-of-the-hysteresis-in-the-pzt-actuated-structure">Modeling of the Hysteresis in the PZT-Actuated Structure</h4>
<h4 id="hysteresis-compensator-design">Hysteresis Compensator Design</h4>
<h4 id="experimental-verification">Experimental Verification</h4>
<h3 id="conclusion">Conclusion</h3>
<h2 id="seeking-control-of-dual-stage-actuation-systems-with-trajectory-optimization">Seeking Control of Dual-Stage Actuation Systems with Trajectory Optimization</h2>
<h3 id="introduction">Introduction</h3>
<h3 id="current-profile-of-vcm-primary-actuator">Current Profile of VCM Primary Actuator</h3>
<h4 id="ptos-method">PTOS Method</h4>
<h4 id="a-general-form-of-vcm-current-profiles">A General Form of VCM Current Profiles</h4>
<h3 id="control-system-structure-for-the-dual-stage-actuation-system">Control System Structure for the Dual-Stage Actuation System</h3>
<h3 id="design-of-vcm-current-profile-a-sub--v--and-dual-stage-reference-trajectory-r-sub--d">Design of VCM Current Profile a[sub(v)] and Dual-Stage Reference Trajectory r[sub(d)]</h3>
<h3 id="seeking-within-pzt-milliactuator-stroke">Seeking within PZT Milliactuator Stroke</h3>
<h3 id="seeking-over-pzt-milliactuator-stroke">Seeking over PZT Milliactuator Stroke</h3>
<h3 id="conclusion">Conclusion</h3>
<h2 id="high-frequency-vibration-control-using-pzt-active-damping">High-Frequency Vibration Control Using PZT Active Damping</h2>
<h3 id="introduction">Introduction</h3>
<h3 id="singular-perturbation-method-based-controller-design">Singular Perturbation Method-Based Controller Design</h3>
<h4 id="singular-perturbation-control-topology">Singular Perturbation Control Topology</h4>
<h4 id="identification-of-fast-dynamics-using-pzt-as-a-sensor">Identification of Fast Dynamics Using PZT as a Sensor</h4>
<h4 id="design-of-controllers">Design of Controllers</h4>
<h5 id="fast-subsystem-estimator-g-sub--v--sup">Fast Subsystem Estimator G[sub(v)][sup(*)]</h5>
<h5 id="fast-controller-c-sub--v">Fast Controller C[sub(v)]</h5>
<h5 id="slow-controller-c-sub--v">Slow Controller C[sub(v)]</h5>
<h4 id="simulation-and-experimental-results">Simulation and Experimental Results</h4>
<h5 id="frequency-responses">Frequency Responses</h5>
<h5 id="time-responses">Time Responses</h5>
<h3 id="h-sub--2--controller-design">H[sub(2)] Controller Design</h3>
<h3 id="design-of-c-sub--d----z--with-h-sub--2--method-and-notch-filters">Design of C<a href="z">sub(d)</a> with H[sub(2)] Method and Notch Filters</h3>
<h3 id="design-of-mixed-h-sub--2--h-sub-----controller-c-sub--d----z">Design of Mixed H[sub(2)]/H[sub(∞)] Controller C<a href="z">sub(d)</a></h3>
<h3 id="application-results">Application Results</h3>
<h4 id="system-modeling">System Modeling</h4>
<h4 id="h-sub--2--active-damping-control">H[sub(2)] Active Damping Control</h4>
<h4 id="mixed-h-sub--2--h-sub-----active-damping-control">Mixed H[sub(2)]/H[sub(∞)] Active Damping Control</h4>
<h4 id="experimental-results">Experimental Results</h4>
<h3 id="conclusion">Conclusion</h3>
<h2 id="self-sensing-actuation-of-dual-stage-systems">Self-Sensing Actuation of Dual-Stage Systems</h2>
<h3 id="introduction">Introduction</h3>
<h3 id="estimation-of-pzt-secondary-actuator-s-displacement-y-sub--p--sup">Estimation of PZT Secondary Actuator’s Displacement y[sub(p)][sup(*)]</h3>
<h4 id="self-sensing-actuation-and-bridge-circuit">Self-Sensing Actuation and Bridge Circuit</h4>
<h4 id="pzt-displacement-estimation-circuit-h-sub--b">PZT Displacement Estimation Circuit H[sub(B)]</h4>
<h3 id="design-of-controllers">Design of Controllers</h3>
<h4 id="vcm-controller-and-controller-c-sub--d">VCM Controller and Controller C[sub(D)]</h4>
<h4 id="pzt-controller">PZT Controller</h4>
<h3 id="performance-evaluation">Performance Evaluation</h3>
<h4 id="effectiveness-of-c-sub--d">Effectiveness of C[sub(D)]</h4>
<h4 id="position-errors">Position Errors</h4>
<h3 id="conclusion">Conclusion</h3>
<h2 id="modeling-and-control-of-a-mems-micro-x-y-stage-media-platform">Modeling and Control of a MEMS Micro X–Y Stage Media Platform</h2>
<h3 id="introduction">Introduction</h3>
<h3 id="mems-micro-x-y-stage">MEMS Micro X–Y Stage</h3>
<h4 id="design-and-simulation-of-micro-x-y-stage">Design and Simulation of Micro X–Y Stage</h4>
<h5 id="static">Static</h5>
<h5 id="dynamic">Dynamic</h5>
<h4 id="modeling-of-micro-x-y-stage">Modeling of Micro X–Y Stage</h4>
<h4 id="fabrication-of-the-mems-micro-x-y-stage">Fabrication of the MEMS Micro X–Y Stage</h4>
<h3 id="capacitive-self-sensing-actuation">Capacitive Self-Sensing Actuation</h3>
<h4 id="design-of-cssa-bridge-circuit">Design of CSSA Bridge Circuit</h4>
<h4 id="experimental-verification">Experimental Verification</h4>
<h3 id="robust-decoupling-controller-design">Robust Decoupling Controller Design</h3>
<h4 id="choice-of-pre-shaping-filters">Choice of Pre-Shaping Filters</h4>
<h4 id="controller-synthesis">Controller Synthesis</h4>
<h4 id="frequency-responses">Frequency Responses</h4>
<h4 id="time-responses">Time Responses</h4>
<h4 id="robustness-analysis">Robustness Analysis</h4>
<h3 id="conclusion">Conclusion</h3>
<h2 id="conclusions">Conclusions</h2>
<p>Many secondary actuators have been developed in addition to primary actuators in the field of mechanical actuation systems.
The aim is to provide high performance such as high precision and fast response.
Several types of secondary actuators have been introduced such as PZT milliactuator, electrostatic microactuator, PZT microactuator, and thermal microactuator.
Comparison of these secondary actuators has been made, and these secondary actuators have made dual and multi-stage actuation mechanisms possible.</p>
<p>Three-stage actuation systems have been proposed for the demand of wider bandwidth, to overcome the limitation by stroke constraint and saturation of secondary actuators.
After the characteristics of the three-stage systems have been developed and the models have been identified, the control strategy and algorithm have been developed to deal with vibrations and meet different requirements.
Particularly, for the three-stage actuation systems, the presented control strategies make it easy to further push the bandwidth and meet the performance requirement.
The control of the thermal microactuator based dual-stage system has been discussed in detail, including linearization and controller design method.</p>
<p>The developed advanced algorithms applied in the multi-stage systems include \(\mathcal{H}_\infty\) loop shaping, anti-windup compensation, \(\mathcal{H}_2\) control method,
and mixed \(\mathcal{H}_2/\mathcal{H}_\infty\) control method.
Typical problems of the milli and micro-actuators as the secondary actuators have been considered and appropriate solutions have been presented such as saturation compensation, hysteresis modeling and compensation, stroke limitation, and PZT self-sensing scheme.
Time delay and sampling rate effect on the control performance have been analyzed to help select appropriate sampling rate and design suitable controllers.</p>
<p>Specific usage of PZT elements has been produced for system performance improvement.
Using PZT elements as a sensor to deal with high-frequency vibration beyond the bandwidth has been proposed and systematic controller design methods have been developed.
As a more advanced concept, PZT elements being used as actuator and sensor simultaneously has also been addressed in this book with detailed scheme and controller design methodology for effective utilization.</p>
<h1 id="bibliography">Bibliography</h1>
<p><a id="du19_multi_actuat_system_contr"></a>Du, C., &amp; Pang, C. K., <em>Multi-stage actuation systems and control</em> (2019), Boca Raton, FL: CRC Press. <a href="#28e6aa60b8446943c921ff0d6578ac85">↩</a></p>
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<dd><sup id="1851788e0c4aa5b06afe3362c73ea5eb"><a href="#fleming14_desig_model_contr_nanop_system" title="Andrew Fleming \&amp; Kam Leang, Design, Modeling and Control of Nanopositioning Systems, Springer International Publishing (2014).">(Andrew Fleming &amp; Kam Leang, 2014)</a></sup></dd>
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<dt>Year</dt>
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<h1 id="bibliography">Bibliography</h1>
<p><a id="fleming14_desig_model_contr_nanop_system"></a>Fleming, A. J., &amp; Leang, K. K., <em>Design, modeling and control of nanopositioning systems</em> (2014), : Springer International Publishing. <a href="#1851788e0c4aa5b06afe3362c73ea5eb">↩</a></p>
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Reference (Chunling Du &amp;amp; Chee Khiang Pang, 2019) Author(s) Du, C., &amp;amp; Pang, C. K. Year 2019 Mechanical Actuation Systems Introduction When high bandwidth, high position accuracy and long stroke are required simultaneously: dual-stage systems composed of a coarse (or primary) actuator and a fine actuator working together are used.
Popular choices for coarse actuator are:
DC motor Voice coil motor (VCM) Permanent magnet stepper motor Permanent magnet linear synchronous motor As fine actuators, most of the time piezoelectric actuator are used.</description>
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Instrument principles:
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error sources that are proportional to the displacement being measured \(L\): cumulative errors error sources that are independent of the displacement being measured: non-cumulative errors Thermal expansion of the metrology frame Deadpath length Deadpath length, \(d\), is defined as the difference in distance in air between the reference and measurement reflectors and the beam splitter when the interferometer measurement is initiated." />
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<dd><a href="/zettels/metrology/">Metrology</a></dd>
<dt>Reference</dt>
<dd><sup id="58bd6e601168ed1397ab2ec3cc3bab2d"><a href="#leach14_fundam_princ_engin_nanom" title="Richard Leach, Fundamental Principles of Engineering Nanometrology, Elsevier (2014).">(Richard Leach, 2014)</a></sup></dd>
<dt>Author(s)</dt>
<dd>Leach, R.</dd>
<dt>Year</dt>
<dd>2014</dd>
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<h2 id="measurement-of-angles">Measurement of angles</h2>
<p>Unit:</p>
<ul>
<li>radian for plane angle</li>
<li>steradian for solid angle</li>
</ul>
<p>\(1 rad \approx 55.3deg\)</p>
<p>Instrument principles:</p>
<ul>
<li>subdivision: index tacle, angular gratings, polygons, &hellip;</li>
<li>ratio of two lengths: angular interferometers, sin cars, small angle generators, &hellip;</li>
<li>autocollimators with a flat mirror</li>
</ul>
<h2 id="sources-of-error-in-displacement-interferometry">Sources of error in displacement interferometry</h2>
<p>Two error sources:</p>
<ul>
<li>error sources that are proportional to the displacement being measured \(L\): cumulative errors</li>
<li>error sources that are independent of the displacement being measured: non-cumulative errors</li>
</ul>
<h3 id="thermal-expansion-of-the-metrology-frame">Thermal expansion of the metrology frame</h3>
<h3 id="deadpath-length">Deadpath length</h3>
<p>Deadpath length, \(d\), is defined as the difference in distance in air between the reference and measurement reflectors and the beam splitter when the interferometer measurement is initiated.
Deadpath error occurs when there is a non-zero deadpath and environmental conditions change during a measurement.</p>
<h3 id="cosine-error">Cosine error</h3>
<p>\(\Delta l = l(1-\cos(\theta))\)</p>
<p>For small angles: \(\Delta l = \frac{l \theta^2}{2}\)</p>
<p>The cosine error is then a second-order effect, contrary to the Abbe error which is a first order effect.
The second order nature means that cosine error quickly diminish as the alignment is improved.</p>
<h2 id="latest-advances-in-displacement-interferometry">Latest advances in displacement interferometry</h2>
<p>Commercial interferometers
=&gt; fused silica optics housed in Invar mounts
=&gt; all the optical components are mounted to one central optic to reduce the susceptibility to thermal variations</p>
<p>One advantage that homodyme systems have over heterodyne systems is their ability to readily have the source fibre delivered to the interferometer.</p>
<h3 id="spatially-separated-interferometers">Spatially separated interferometers</h3>
<p>It uses heterodyne interferometer and one quadrant photodiode.
By knowing the beam size and detector geometry, the measurement target&rsquo;s angle change can be determined by differencing matched pairs of measured phase from the quadrant photodiode while the displacement is determined from the average phase over the four quadrants.</p>
<h2 id="angular-interferometers">Angular interferometers</h2>
<p>Determination of an angle by the ratio of two lengths.
The angular optics is used to create two parallel beam paths between the angular interferometer and the angular reflector.</p>
<p>The beam that illuminates the angular optics contains two frequencies, \(f1\) and \(f2\). A polarising beam splitter in the angular interferometer splits the frequencies that travel along separate paths.</p>
<p>The measurement of angles is then relative.</p>
<p>This type of angular interferometer is used to measure small angles (less than \(10deg\)).</p>
<h1 id="bibliography">Bibliography</h1>
<p><a id="leach14_fundam_princ_engin_nanom"></a>Leach, R., <em>Fundamental principles of engineering nanometrology</em> (2014), : Elsevier. <a href="#58bd6e601168ed1397ab2ec3cc3bab2d">↩</a></p>
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<dt>Reference</dt>
<dd><sup id="cc6e42420309d21c1aa596152d84cf8b"><a href="#leach18_basic_precis_engin_edition" title="Richard Leach \&amp; Stuart Smith, Basics of Precision Engineering - 1st Edition, CRC Press (2018).">(Richard Leach &amp; Stuart Smith, 2018)</a></sup></dd>
<dt>Author(s)</dt>
<dd>Leach, R., &amp; Smith, S. T.</dd>
<dt>Year</dt>
<dd>2018</dd>
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<h1 id="bibliography">Bibliography</h1>
<p><a id="leach18_basic_precis_engin_edition"></a>Leach, R., &amp; Smith, S. T., <em>Basics of precision engineering - 1st edition</em> (2018), : CRC Press. <a href="#cc6e42420309d21c1aa596152d84cf8b">↩</a></p>
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The core of a mechatronic system is its mechanical construction and in spite of many decade of excellent designs, optimizing the mechanical structure in strength, mass and endurance, the mechanical behavior will always remain the limiting factor of the performance of any mechatronic system." />
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<dd><sup id="37468bbe5988cc7f4878fcd664d9cb7f"><a href="#schmidt14_desig_high_perfor_mechat_revis_edition" title="Schmidt, Schitter \&amp; Rankers, The Design of High Performance Mechatronics - 2nd Revised Edition, Ios Press (2014).">(Schmidt {\it et al.}, 2014)</a></sup></dd>
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<p>Section 2.2 Mechanics</p>
<blockquote>
<p>The core of a mechatronic system is its mechanical construction and in spite of many decade of excellent designs, optimizing the mechanical structure in strength, mass and endurance, the mechanical behavior will always remain the limiting factor of the performance of any mechatronic system.</p>
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<p>Section 2.2.2 Force and Motion</p>
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<p><em>Statics</em> deals with the stress levels that are present in the mechanical system when (quasi-)static forces are exerted on it.
It analyses the linear and non-linear strain effects that are caused by elastic and plastic deformation under these stress levels.</p>
<p><em>Dynamics</em> deals with the behaviour of the mechanical system under changing forces, while often the effects are linearised and limited to strain levels well below any irreversible plastic deformation.
One should however be aware that another non-destructive source of non-linearity is found in a tried important field of mechanics, called <em>kinematics</em>.
The relation between angles and positions is often non-linear in such a mechanism, because of the changing angles, and controlling these often requires special precautions to overcome the inherent non-linearities by linearisation around actual position and adapting the optimal settings of the controller to each position.</p>
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<p>Figure 1: Stabiliby condition and robustness of a feedback controlled system. The desired shape of these curves guide the control design by optimising the lvels and sloppes of the amplitude Bode-plot at low and high frequencies for suppression of the disturbances and of the base Bode-plot in the cross-over frequency region. This is called <strong>loop shaping design</strong></p>
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<p>On might say that a high value of the unity-gain crossover frequency and corresponding high-frequency bandwidth limit is rather an unwanted side-effect of the required high loop-gain at lower frequencies, than a target for the design of a control system as such.</p>
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<p><a id="schmidt14_desig_high_perfor_mechat_revis_edition"></a>Schmidt, R. M., Schitter, G., &amp; Rankers, A., <em>The design of high performance mechatronics - 2nd revised edition</em> (2014), : Ios Press. <a href="#37468bbe5988cc7f4878fcd664d9cb7f">↩</a></p>
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Reference (Rabih Alkhatib &amp;amp; Golnaraghi, 2003) Author(s) Alkhatib, R., &amp;amp; Golnaraghi, M. F. Year 2003 Process of designing an active vibration control system Analyze the structure to be controled Obtain an idealized mathematical model with FEM or experimental modal analysis Reduce the model order is necessary Analyze the resulting model: dynamics properties, types of disturbances, &amp;hellip; Quantify sensors and actuators requirements. Decide on their types and location Analyze the impact of the sensors and actuators on the overall dynamic characteristics Specify performance criteria and stability tradeoffs Device of the type of control algorythm to be employed and design a controller to meet the specifications Simulate the resulting controlled system on a computer If the controller does not meet the requirements, adjust the specifications or modify the type of controller Choose hardware and software and integrate the components on a pilot plant Formulate experiments and perform system identification and model updating Implement controller and carry out system test to evaluate the performance Feedback control Active damping The objective is to reduce the resonance peaks of the closed loop transfer function.</description>
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Reference (Rabih Alkhatib &amp;amp; Golnaraghi, 2003) Author(s) Alkhatib, R., &amp;amp; Golnaraghi, M. F. Year 2003 Process of designing an active vibration control system Analyze the structure to be controled Obtain an idealized mathematical model with FEM or experimental modal analysis Reduce the model order is necessary Analyze the resulting model: dynamics properties, types of disturbances, &amp;hellip; Quantify sensors and actuators requirements. Decide on their types and location Analyze the impact of the sensors and actuators on the overall dynamic characteristics Specify performance criteria and stability tradeoffs Device of the type of control algorythm to be employed and design a controller to meet the specifications Simulate the resulting controlled system on a computer If the controller does not meet the requirements, adjust the specifications or modify the type of controller Choose hardware and software and integrate the components on a pilot plant Formulate experiments and perform system identification and model updating Implement controller and carry out system test to evaluate the performance Feedback control Active damping The objective is to reduce the resonance peaks of the closed loop transfer function.</description>
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<rss version="2.0" xmlns:atom="http://www.w3.org/2005/Atom">
<channel>
<title>My digital brain</title>
<link>/</link>
<description>Recent content on My digital brain</description>
<generator>Hugo -- gohugo.io</generator>
<language>en</language>
<atom:link href="/index.xml" rel="self" type="application/rss+xml" />
<item>
<title>A new isotropic and decoupled 6-dof parallel manipulator</title>
<link>/paper/legnani12_new_isotr_decoup_paral_manip/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/legnani12_new_isotr_decoup_paral_manip/</guid>
<description>Tags Stewart Platforms Reference (Legnani {\it et al.}, 2012) Author(s) Legnani, G., Fassi, I., Giberti, H., Cinquemani, S., &amp;amp; Tosi, D. Year 2012 Concepts of isotropy and decoupling for parallel manipulators isotropy: the kinetostatic properties (same applicable force, same possible velocity, same stiffness) are identical in all directions (e.g. cubic configuration for Stewart platform) decoupling: each DoF of the end effector can be controlled by a single actuator (not the case for the Stewart platform) Example of generated isotropic manipulator (not decoupled).</description>
</item>
<item>
<title>A review of nanometer resolution position sensors: operation and performance</title>
<link>/paper/fleming13_review_nanom_resol_posit_sensor/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/fleming13_review_nanom_resol_posit_sensor/</guid>
<description>Tags Position Sensors Reference (Andrew Fleming, 2013) Author(s) Fleming, A. J. Year 2013 Define concise performance metric and provide expressions for errors sources (non-linearity, drift, noise) Review current position sensor technologies and compare their performance Sensor Characteristics Calibration and nonlinearity Usually quoted as a percentage of the fill-scale range (FSR):
\begin{equation} \text{mapping error (%)} = \pm 100 \frac{\max{}|e_m(v)|}{\text{FSR}} \end{equation}
With \(e_m(v)\) is the mapping error.</description>
</item>
<item>
<title>A six-axis single-stage active vibration isolator based on stewart platform</title>
<link>/paper/preumont07_six_axis_singl_stage_activ/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/preumont07_six_axis_singl_stage_activ/</guid>
<description>Tags Vibration Isolation, Stewart Platforms, Flexible Joints Reference (Preumont {\it et al.}, 2007) Author(s) Preumont, A., Horodinca, M., Romanescu, I., Marneffe, B. d., Avraam, M., Deraemaeker, A., Bossens, F., … Year 2007 Summary:
Cubic Stewart platform (Figure 3) Provides uniform control capability Uniform stiffness in all directions minimizes the cross-coupling among actuators and sensors of different legs Flexible joints (Figure 2) Piezoelectric force sensors Voice coil actuators Decentralized feedback control approach for vibration isolation Effect of parasitic stiffness of the flexible joints on the IFF performance (Figure 1) The Stewart platform has 6 suspension modes at different frequencies.</description>
</item>
<item>
<title>A soft 6-axis active vibration isolator</title>
<link>/paper/spanos95_soft_activ_vibrat_isolat/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/spanos95_soft_activ_vibrat_isolat/</guid>
<description>Tags Stewart Platforms, Vibration Isolation Reference (Spanos {\it et al.}, 1995) Author(s) Spanos, J., Rahman, Z., &amp;amp; Blackwood, G. Year 1995 Stewart Platform (Figure 1):
Voice Coil Flexible joints (cross-blades) Force Sensors Cubic Configuration
Figure 1: Stewart Platform
Total mass of the paylaod: 30kg Center of gravity is 9cm above the geometry center of the mount (cube&amp;rsquo;s center?).
Limitation of the Decentralized Force Feedback:</description>
</item>
<item>
<title>A survey of control issues in nanopositioning</title>
<link>/paper/devasia07_survey_contr_issues_nanop/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/devasia07_survey_contr_issues_nanop/</guid>
<description>Tags :
Reference (Devasia {\it et al.}, 2007) Author(s) Devasia, S., Eleftheriou, E., &amp;amp; Moheimani, S. R. Year 2007 Talks about Scanning Tunneling Microscope (STM) and Scanning Probe Microscope (SPM) Piezoelectric actuators: Creep, Hysteresis, Vibrations, Modeling errors Interesting analysis about Bandwidth-Precision-Range tradeoffs Control approaches for piezoelectric actuators: feedforward, Feedback, Iterative, Sensorless controls
Figure 1: Tradeoffs between bandwidth, precision and range
Bibliography Devasia, S.</description>
</item>
<item>
<title>Active Damping</title>
<link>/zettels/active_damping/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/zettels/active_damping/</guid>
<description>Tags :
&amp;lt;./biblio/references.bib&amp;gt;
Backlinks Active isolation and damping of vibrations via stewart platform Active damping based on decoupled collocated control </description>
</item>
<item>
<title>Active damping based on decoupled collocated control</title>
<link>/paper/holterman05_activ_dampin_based_decoup_colloc_contr/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/holterman05_activ_dampin_based_decoup_colloc_contr/</guid>
<description>Tags Active Damping Reference (Holterman &amp;amp; deVries, 2005) Author(s) Holterman, J., &amp;amp; deVries, T. Year 2005 Bibliography Holterman, J., &amp;amp; deVries, T., Active damping based on decoupled collocated control, IEEE/ASME Transactions on Mechatronics, 10(2), 135–145 (2005). http://dx.doi.org/10.1109/tmech.2005.844702 ↩</description>
</item>
<item>
<title>Active isolation and damping of vibrations via stewart platform</title>
<link>/paper/hanieh03_activ_stewar/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/hanieh03_activ_stewar/</guid>
<description>Tags Stewart Platforms, Vibration Isolation, Active Damping Reference @phdthesis{hanieh03_activ_stewar, author = {Hanieh, Ahmed Abu}, school = {Universit{&#39;e} Libre de Bruxelles, Brussels, Belgium}, title = {Active isolation and damping of vibrations via Stewart platform}, year = 2003, tags = {parallel robot}, } Author(s) Hanieh, A. A. Year 2003 Bibliography Hanieh, A. A., Active isolation and damping of vibrations via stewart platform (Doctoral dissertation) (2003). Universit{&#39;e} Libre de Bruxelles, Brussels, Belgium, .</description>
</item>
<item>
<title>Active structural vibration control: a review</title>
<link>/paper/alkhatib03_activ_struc_vibrat_contr/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/alkhatib03_activ_struc_vibrat_contr/</guid>
<description>Tags :
Reference (Rabih Alkhatib &amp;amp; Golnaraghi, 2003) Author(s) Alkhatib, R., &amp;amp; Golnaraghi, M. F. Year 2003 Process of designing an active vibration control system Analyze the structure to be controled Obtain an idealized mathematical model with FEM or experimental modal analysis Reduce the model order is necessary Analyze the resulting model: dynamics properties, types of disturbances, &amp;hellip; Quantify sensors and actuators requirements. Decide on their types and location Analyze the impact of the sensors and actuators on the overall dynamic characteristics Specify performance criteria and stability tradeoffs Device of the type of control algorythm to be employed and design a controller to meet the specifications Simulate the resulting controlled system on a computer If the controller does not meet the requirements, adjust the specifications or modify the type of controller Choose hardware and software and integrate the components on a pilot plant Formulate experiments and perform system identification and model updating Implement controller and carry out system test to evaluate the performance Feedback control Active damping The objective is to reduce the resonance peaks of the closed loop transfer function.</description>
</item>
<item>
<title>Actuators</title>
<link>/zettels/actuators/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/zettels/actuators/</guid>
<description>Tags :
How to choose the correct actuator for my application? For vibration isolation:
In (Shingo Ito &amp;amp; Georg Schitter, 2016), the effect of the actuator stiffness on the attainable vibration isolation is studied (Notes) Piezoelectric Suppliers Links Cedrat link PI link Piezo System link Noliac link A model of a multi-layer monolithic piezoelectric stack actuator is described in (Fleming, 2010) (Notes).</description>
</item>
<item>
<title>Advanced motion control for precision mechatronics: control, identification, and learning of complex systems</title>
<link>/paper/oomen18_advan_motion_contr_precis_mechat/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/oomen18_advan_motion_contr_precis_mechat/</guid>
<description>Tags Motion Control Reference (Tom Oomen, 2018) Author(s) Oomen, T. Year 2018
Figure 1: Envisaged developments in motion systems. In traditional motion systems, the control bandwidth takes place in the rigid-body region. In the next generation systemes, flexible dynamics are foreseen to occur within the control bandwidth.
Bibliography Oomen, T., Advanced motion control for precision mechatronics: control, identification, and learning of complex systems, IEEJ Journal of Industry Applications, 7(2), 127–140 (2018).</description>
</item>
<item>
<title>Advances in internal model control technique: a review and future prospects</title>
<link>/paper/saxena12_advan_inter_model_contr_techn/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/saxena12_advan_inter_model_contr_techn/</guid>
<description>Tags Complementary Filters Reference (Sahaj Saxena &amp;amp; YogeshV Hote, 2012) Author(s) Saxena, S., &amp;amp; Hote, Y. Year 2012 Proposed Filter \(F(s)\) \begin{align*} F(s) &amp;amp;= \frac{1}{(\lambda s + 1)^n} \\\
F(s) &amp;amp;= \frac{n \lambda + 1}{(\lambda s + 1)^n} \end{align*}
Internal Model Control Central concept in IMC: control can be acheive only if the control system involves, either implicitly or explicitly, some representation of the process to be controlled.</description>
</item>
<item>
<title>An exploration of active hard mount vibration isolation for precision equipment</title>
<link>/paper/poel10_explor_activ_hard_mount_vibrat/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/poel10_explor_activ_hard_mount_vibrat/</guid>
<description>Tags Vibration Isolation Reference @phdthesis{poel10_explor_activ_hard_mount_vibrat, author = {van der Poel, Gerrit Wijnand}, doi = {10.3990/1.9789036530163}, isbn = {978-90-365-3016-3}, school = {University of Twente}, title = {An Exploration of Active Hard Mount Vibration Isolation for Precision Equipment}, url = {https://doi.org/10.3990/1.9789036530163}, year = 2010, year = 2010, tags = {parallel robot}, } Author(s) van der Poel, G. W. Year 2010 Bibliography van der Poel, G. W., An exploration of active hard mount vibration isolation for precision equipment (Doctoral dissertation) (2010).</description>
</item>
<item>
<title>An instrument for 3d x-ray nano-imaging</title>
<link>/paper/holler12_instr_x_ray_nano_imagin/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/holler12_instr_x_ray_nano_imagin/</guid>
<description>Tags Nano Active Stabilization System, Positioning Stations Reference (Holler {\it et al.}, 2012) Author(s) Holler, M., Raabe, J., Diaz, A., Guizar-Sicairos, M., Quitmann, C., Menzel, A., &amp;amp; Bunk, O. Year 2012 Instrument similar to the NASS. Obtain position stability of 10nm (standard deviation).
Figure 1: Schematic of the tomography setup
Limited resolution due to instrumentation: The resolution of ptychographic tomography remains above 100nm due to instabilities and drifts of the scanning systems.</description>
</item>
<item>
<title>An intelligent control system for multiple degree-of-freedom vibration isolation</title>
<link>/paper/geng95_intel_contr_system_multip_degree/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/geng95_intel_contr_system_multip_degree/</guid>
<description>Tags Stewart Platforms, Vibration Isolation Reference (Jason Geng {\it et al.}, 1995) Author(s) Geng, Z. J., Pan, G. G., Haynes, L. S., Wada, B. K., &amp;amp; Garba, J. A. Year 1995
Figure 1: Local force feedback and adaptive acceleration feedback for active isolation
Bibliography Geng, Z. J., Pan, G. G., Haynes, L. S., Wada, B. K., &amp;amp; Garba, J. A., An intelligent control system for multiple degree-of-freedom vibration isolation, Journal of Intelligent Material Systems and Structures, 6(6), 787–800 (1995).</description>
</item>
<item>
<title>Automated markerless full field hard x-ray microscopic tomography at sub-50 nm 3-dimension spatial resolution</title>
<link>/paper/wang12_autom_marker_full_field_hard/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/wang12_autom_marker_full_field_hard/</guid>
<description>Tags Nano Active Stabilization System Reference (Jun Wang {\it et al.}, 2012) Author(s) Wang, J., Chen, Y. K., Yuan, Q., Tkachuk, A., Erdonmez, C., Hornberger, B., &amp;amp; Feser, M. Year 2012 Introduction of Markers: That limits the type of samples that is studied
There is a need for markerless nano-tomography =&amp;gt; the key requirement is the precision and stability of the positioning stages.
Passive rotational run-out error system: It uses calibrated metrology disc and capacitive sensors</description>
</item>
<item>
<title>Basics of precision engineering - 1st edition</title>
<link>/book/leach18_basic_precis_engin_edition/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/book/leach18_basic_precis_engin_edition/</guid>
<description>Tags Precision Engineering Reference (Richard Leach &amp;amp; Stuart Smith, 2018) Author(s) Leach, R., &amp;amp; Smith, S. T. Year 2018 Bibliography Leach, R., &amp;amp; Smith, S. T., Basics of precision engineering - 1st edition (2018), : CRC Press. ↩</description>
</item>
<item>
<title>Comparison and classification of high-precision actuators based on stiffness influencing vibration isolation</title>
<link>/paper/ito16_compar_class_high_precis_actuat/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/ito16_compar_class_high_precis_actuat/</guid>
<description>Tags Vibration Isolation, Actuators Reference (Shingo Ito &amp;amp; Georg Schitter, 2016) Author(s) Ito, S., &amp;amp; Schitter, G. Year 2016 Classification of high-precision actuators Table 1: Zero/Low and High stiffness actuators Categories Pros Cons Zero stiffness No vibration transmission Large and Heavy Low stiffness High vibration isolation Typically for low load High Stiffness High control bandwidth High vibration transmission Time Delay of Piezoelectric Electronics In this paper, the piezoelectric actuator/electronics adds a time delay which is much higher than the time delay added by the voice coil/electronics.</description>
</item>
<item>
<title>Complementary Filters</title>
<link>/zettels/complementary_filters/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/zettels/complementary_filters/</guid>
<description>Tags :
&amp;lt;./biblio/references.bib&amp;gt;
Backlinks Advances in internal model control technique: a review and future prospects </description>
</item>
<item>
<title>Control Bootcamp</title>
<link>/websites/control_bootcamp/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/websites/control_bootcamp/</guid>
<description>Tags :
https://www.youtube.com/playlist?list=PLMrJAkhIeNNR20Mz-VpzgfQs5zrYi085m
Overview Linear Systems Stability and Eigenvalues Linearizing Around a Fixed Point Controllability Controllability, Reachability, and Eigenvalue Placement Controllability and the Discrete-Time Impulse Response Degrees of Controllability and Gramians Controllability and the PBH Test Cayley-Hamilton Theorem Reachability and Controllability with Cayley-Hamilton Inverted Pendulum on a Cart Eigenvalue Placement for the Inverted Pendulum on a Cart Linear Quadratic Regulator (LQR) Control for the Inverted Pendulum on a Cart Motivation for Full-State Estimation Observability Full-State Estimation Kalman Filter Observability Example in Matlab Observability Example in Matlab (Part 2) Kalman Filter Example in Matlab Linear Quadratic Gaussian (LQG) LQG Example in Matlab Introduction to Robust Control Three Equivalent Representations of Linear Systems Example Frequency Response (Bode Plot) for Spring-Mass-Damper Laplace Transforms and the Transfer Function Benefits of Feedback on Cruise Control Example Benefits of Feedback on Cruise Control Example (Part 2) Cruise Control Example with Proportional-Integral (PI) control Sensitivity and Complementary Sensitivity Sensitivity and Complementary Sensitivity (Part 2) Loop shaping Loop Shaping Example for Cruise Control Sensitivity and Robustness Limitations on Robustness Cautionary Tale About Inverting the Plant Dynamics Control systems with non-minimum phase dynamics &amp;lt;.</description>
</item>
<item>
<title>Control of spacecraft and aircraft</title>
<link>/paper/bryson93_contr_spacec_aircr/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/bryson93_contr_spacec_aircr/</guid>
<description>Tags HAC-HAC Reference (Bryson, 1993) Author(s) Bryson, A. E. Year 1993 9.2.3 Roll-Off Filters Synthesizing control logic using only one vibration mode means we are consciously neglecting the higher-order vibration modes. When doing this, it is a good idea to insert &amp;ldquo;roll-off&amp;rdquo; into the control logic, so that the loop-transfer gain decreases rapidly with frequency beyond the control bandwidth. This reduces the possibility of destabilizing the unmodelled higher frequency dynamics (&amp;quot;spillover&amp;quot;).</description>
</item>
<item>
<title>Cubic Architecture</title>
<link>/zettels/cubic_architecture/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/zettels/cubic_architecture/</guid>
<description>Tags :
&amp;lt;./biblio/references.bib&amp;gt;
Backlinks Sensors and control of a space-based six-axis vibration isolation system Dynamic modeling and decoupled control of a flexible stewart platform for vibration isolation Simultaneous, fault-tolerant vibration isolation and pointing control of flexure jointed hexapods </description>
</item>
<item>
<title>Data-Driven Dynamical Systems with Machine Learning</title>
<link>/websites/data_driven_dynamical_systems_with_machine_learning/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/websites/data_driven_dynamical_systems_with_machine_learning/</guid>
<description>Tags :
Data-Driven Control Overview Challenges With modern control (LQR, LQG, H-Infinity), we work with linear system (or linearized systems) and we develop a control law that minimize some cost function.
Challenging systems where modern control is not efficient:
Non-linear systems System with unknown dynamics High dimensional systems Limited measurements or control inputs For these kinds of systems, data-driven control seems to be a good alternative.
What is control?</description>
</item>
<item>
<title>Decentralized vibration control of a voice coil motor-based stewart parallel mechanism: simulation and experiments</title>
<link>/paper/tang18_decen_vibrat_contr_voice_coil/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/tang18_decen_vibrat_contr_voice_coil/</guid>
<description>Tags Stewart Platforms Reference (Jie Tang {\it et al.}, 2018) Author(s) Tang, J., Cao, D., &amp;amp; Yu, T. Year 2018 Bibliography Tang, J., Cao, D., &amp;amp; Yu, T., Decentralized vibration control of a voice coil motor-based stewart parallel mechanism: simulation and experiments, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 233(1), 132–145 (2018). http://dx.doi.org/10.1177/0954406218756941 ↩</description>
</item>
<item>
<title>Design for precision: current status and trends</title>
<link>/paper/schellekens98_desig_precis/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/schellekens98_desig_precis/</guid>
<description>Tags Precision Engineering Reference (Schellekens {\it et al.}, 1998) Author(s) Schellekens, P., Rosielle, N., Vermeulen, H., Vermeulen, M., Wetzels, S., &amp;amp; Pril, W. Year 1998 Bibliography Schellekens, P., Rosielle, N., Vermeulen, H., Vermeulen, M., Wetzels, S., &amp;amp; Pril, W., Design for precision: current status and trends, Cirp Annals, (2), 557–586 (1998). http://dx.doi.org/10.1016/s0007-8506(07)63243-0 ↩</description>
</item>
<item>
<title>Design, modeling and control of nanopositioning systems</title>
<link>/book/fleming14_desig_model_contr_nanop_system/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/book/fleming14_desig_model_contr_nanop_system/</guid>
<description>Tags :
Reference (Andrew Fleming &amp;amp; Kam Leang, 2014) Author(s) Fleming, A. J., &amp;amp; Leang, K. K. Year 2014 Bibliography Fleming, A. J., &amp;amp; Leang, K. K., Design, modeling and control of nanopositioning systems (2014), : Springer International Publishing. ↩</description>
</item>
<item>
<title>Dynamic modeling and decoupled control of a flexible stewart platform for vibration isolation</title>
<link>/paper/yang19_dynam_model_decoup_contr_flexib/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/yang19_dynam_model_decoup_contr_flexib/</guid>
<description>Tags Stewart Platforms, Vibration Isolation, Flexible Joints, Cubic Architecture Reference (Yang {\it et al.}, 2019) Author(s) Yang, X., Wu, H., Chen, B., Kang, S., &amp;amp; Cheng, S. Year 2019 Discusses:
flexible-rigid model of Stewart platform the impact of joint stiffness is compensated using a displacement sensor and a force sensor then the MIMO system is decoupled in modal space and 6 SISO controllers are applied for vibration isolation using force sensors The joint stiffness impose a limitation on the control performance using force sensors as it adds a zero at low frequency in the dynamics.</description>
</item>
<item>
<title>Dynamic modeling and experimental analyses of stewart platform with flexible hinges</title>
<link>/paper/jiao18_dynam_model_exper_analy_stewar/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/jiao18_dynam_model_exper_analy_stewar/</guid>
<description>Tags Stewart Platforms, Flexible Joints Reference (Jian Jiao {\it et al.}, 2018) Author(s) Jiao, J., Wu, Y., Yu, K., &amp;amp; Zhao, R. Year 2018 Bibliography Jiao, J., Wu, Y., Yu, K., &amp;amp; Zhao, R., Dynamic modeling and experimental analyses of stewart platform with flexible hinges, Journal of Vibration and Control, 25(1), 151–171 (2018). http://dx.doi.org/10.1177/1077546318772474 ↩</description>
</item>
<item>
<title>Electronics</title>
<link>/zettels/electronics/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/zettels/electronics/</guid>
<description>Tags :
&amp;lt;./biblio/references.bib&amp;gt;
Backlinks The art of electronics - third edition </description>
</item>
<item>
<title>Estimating the resolution of nanopositioning systems from frequency domain data</title>
<link>/paper/fleming12_estim/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/fleming12_estim/</guid>
<description>Tags :
Reference (Andrew Fleming, 2012) Author(s) Fleming, A. J. Year 2012 Bibliography Fleming, A. J., Estimating the resolution of nanopositioning systems from frequency domain data, In , 2012 IEEE International Conference on Robotics and Automation (pp. ) (2012). : . ↩</description>
</item>
<item>
<title>Flexible Joints</title>
<link>/zettels/flexible_joints/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/zettels/flexible_joints/</guid>
<description>Tags :
&amp;lt;./biblio/references.bib&amp;gt;
Backlinks A six-axis single-stage active vibration isolator based on stewart platform Nanometre-cutting machine using a stewart-platform parallel mechanism Dynamic modeling and experimental analyses of stewart platform with flexible hinges Dynamic modeling and decoupled control of a flexible stewart platform for vibration isolation Simultaneous, fault-tolerant vibration isolation and pointing control of flexure jointed hexapods Investigation on active vibration isolation of a stewart platform with piezoelectric actuators Identification and decoupling control of flexure jointed hexapods </description>
</item>
<item>
<title>Force feedback versus acceleration feedback in active vibration isolation</title>
<link>/paper/preumont02_force_feedb_versus_accel_feedb/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/preumont02_force_feedb_versus_accel_feedb/</guid>
<description>Tags Vibration Isolation Reference (Preumont {\it et al.}, 2002) Author(s) Preumont, A., A. Francois, Bossens, F., &amp;amp; Abu-Hanieh, A. Year 2002 Summary:
Compares the force feedback and acceleration feedback for active damping The use of a force sensor always give alternating poles and zeros in the open-loop transfer function between for force actuator and the force sensor which guarantees the stability of the closed loop Acceleration feedback produces alternating poles and zeros only when the flexible structure is stiff compared to the isolation system The force applied to a rigid body is proportional to its acceleration, thus sensing the total interface force gives a measured of the absolute acceleration of the solid body.</description>
</item>
<item>
<title>Force Sensors</title>
<link>/zettels/force_sensors/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/zettels/force_sensors/</guid>
<description>Tags :
Suppliers PCB link Dynamics and Noise of a piezoelectric force sensor An analysis the dynamics and noise of a piezoelectric force sensor is done in (Fleming, 2010) (Notes).
Bibliography Fleming, A., Nanopositioning system with force feedback for high-performance tracking and vibration control, IEEE/ASME Transactions on Mechatronics, 15(3), 433–447 (2010). http://dx.doi.org/10.1109/tmech.2009.2028422 ↩</description>
</item>
<item>
<title>Fundamental principles of engineering nanometrology</title>
<link>/book/leach14_fundam_princ_engin_nanom/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/book/leach14_fundam_princ_engin_nanom/</guid>
<description>Tags Metrology Reference (Richard Leach, 2014) Author(s) Leach, R. Year 2014 Measurement of angles Unit:
radian for plane angle steradian for solid angle \(1 rad \approx 55.3deg\)
Instrument principles:
subdivision: index tacle, angular gratings, polygons, &amp;hellip; ratio of two lengths: angular interferometers, sin cars, small angle generators, &amp;hellip; autocollimators with a flat mirror Sources of error in displacement interferometry Two error sources:
error sources that are proportional to the displacement being measured \(L\): cumulative errors error sources that are independent of the displacement being measured: non-cumulative errors Thermal expansion of the metrology frame Deadpath length Deadpath length, \(d\), is defined as the difference in distance in air between the reference and measurement reflectors and the beam splitter when the interferometer measurement is initiated.</description>
</item>
<item>
<title>Guidelines for the selection of weighting functions for h-infinity control</title>
<link>/paper/bibel92_guidel_h/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/bibel92_guidel_h/</guid>
<description>Tags H Infinity Control Reference (Bibel &amp;amp; Malyevac, 1992) Author(s) Bibel, J. E., &amp;amp; Malyevac, D. S. Year 1992 Properties of feedback control
Figure 1: Control System Diagram
From the figure 1, we have:
\begin{align*} y(s) &amp;amp;= T(s) r(s) + S(s) d(s) - T(s) n(s)\\\
e(s) &amp;amp;= S(s) r(s) - S(s) d(s) - S(s) n(s)\\\
u(s) &amp;amp;= S(s)K(s) r(s) - S(s)K(s) d(s) - S(s)K(s) n(s) \end{align*}</description>
</item>
<item>
<title>H Infinity Control</title>
<link>/zettels/h_infinity_control/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/zettels/h_infinity_control/</guid>
<description>Tags :
Nice Citations From Rosenbrock, H. H. (1974). Computer-Aided Control System Design, Academic Press, New York:
Solutions are constrained by so many requirements that it is virtually impossible to list them all. The designer finds himself threading a maze of such requirements, attempting to reconcile conflicting demands of cost, performance, easy maintenance, and so on. A good design usually has strong aesthetic appeal to those who are competent in the subject.</description>
</item>
<item>
<title>HAC-HAC</title>
<link>/zettels/hac_hac/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/zettels/hac_hac/</guid>
<description>Tags :
High-Authority Control/Low-Authority Control
From (Andre Preumont, 2018):
The HAC/LAC approach consist of combining the two approached in a dual-loop control as shown in Figure 1. The inner loop uses a set of collocated actuator/sensor pairs for decentralized active damping with guaranteed stability ; the outer loop consists of a non-collocated HAC based on a model of the actively damped structure. This approach has the following advantages:
The active damping extends outside the bandwidth of the HAC and reduces the settling time of the modes which are outsite the bandwidth The active damping makes it easier to gain-stabilize the modes outside the bandwidth of the output loop (improved gain margin) The larger damping of the modes within the controller bandwidth makes them more robust to the parmetric uncertainty (improved phase margin)</description>
</item>
<item>
<title>Identification and decoupling control of flexure jointed hexapods</title>
<link>/paper/chen00_ident_decoup_contr_flexur_joint_hexap/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/chen00_ident_decoup_contr_flexur_joint_hexap/</guid>
<description>Tags Stewart Platforms, Flexible Joints Reference (Yixin Chen &amp;amp; McInroy, 2000) Author(s) Chen, Y., &amp;amp; McInroy, J. Year 2000 Bibliography Chen, Y., &amp;amp; McInroy, J., Identification and decoupling control of flexure jointed hexapods, In , Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065) (pp. ) (2000). : . ↩</description>
</item>
<item>
<title>Implementation challenges for multivariable control: what you did not learn in school!</title>
<link>/paper/garg07_implem_chall_multiv_contr/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/garg07_implem_chall_multiv_contr/</guid>
<description>Tags Multivariable Control Reference (Sanjay Garg, 2007) Author(s) Garg, S. Year 2007 Discusses:
When to use multivariable control and when not to? Two major issues with implementing multivariable control: gain scheduling and integrator wind up protection Inline simple gain and phase margin measured for SISO, &amp;ldquo;robustness&amp;rdquo; determination of multivariable control requires complex analyses using singular value techniques and Monte Carlo simulations.
When to use multivariable control:</description>
</item>
<item>
<title>Inertial Sensors</title>
<link>/zettels/inertial_sensors/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/zettels/inertial_sensors/</guid>
<description>Tags Position Sensors Reviews (Collette {\it et al.}, 2012) Accelerometers Micromega Dynamics link MMF link PCB link Wireless Accelerometers
https://micromega-dynamics.com/products/recovib/miniature-vibration-recorder/
Figure 1: Characteristics of commercially available accelerometers (Collette {it et al.}, 2011)
Geophones Sercel link Wilcoxon link</description>
</item>
<item>
<title>Interferometric characterization of rotation stages for x-ray nanotomography</title>
<link>/paper/stankevic17_inter_charac_rotat_stages_x_ray_nanot/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/stankevic17_inter_charac_rotat_stages_x_ray_nanot/</guid>
<description>Tags Nano Active Stabilization System, Positioning Stations Reference (Tomas Stankevic {\it et al.}, 2017) Author(s) Stankevic, T., Engblom, C., Langlois, F., Alves, F., Lestrade, A., Jobert, N., Cauchon, G., … Year 2017 Similar Station than the NASS Similar Metrology with fiber based interferometers and cylindrical reference mirror
Figure 1: Positioning Station
Thermal expansion: Stabilized down to \(5mK/h\) using passive water flow through the baseplate below the sample stage and in the interferometry reference frame.</description>
</item>
<item>
<title>Investigation on active vibration isolation of a stewart platform with piezoelectric actuators</title>
<link>/paper/wang16_inves_activ_vibrat_isolat_stewar/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/wang16_inves_activ_vibrat_isolat_stewar/</guid>
<description>Tags Stewart Platforms, Vibration Isolation, Flexible Joints Reference (Wang {\it et al.}, 2016) Author(s) Wang, C., Xie, X., Chen, Y., &amp;amp; Zhang, Z. Year 2016 Model of the Stewart platform:
Struts are treated as flexible beams Payload and the base are treated as flexible plates The FRF synthesis method permits to derive FRFs of the Stewart platform The model is compared with a Finite Element model and is shown to give the same results.</description>
</item>
<item>
<title>Measurement technologies for precision positioning</title>
<link>/paper/gao15_measur_techn_precis_posit/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/gao15_measur_techn_precis_posit/</guid>
<description>Tags Position Sensors Reference (Gao {\it et al.}, 2015) Author(s) Gao, W., Kim, S., Bosse, H., Haitjema, H., Chen, Y., Lu, X., Knapp, W., … Year 2015 Bibliography Gao, W., Kim, S., Bosse, H., Haitjema, H., Chen, Y., Lu, X., Knapp, W., …, Measurement technologies for precision positioning, CIRP Annals, 64(2), 773–796 (2015). http://dx.doi.org/10.1016/j.cirp.2015.05.009 ↩</description>
</item>
<item>
<title>Metrology</title>
<link>/zettels/metrology/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/zettels/metrology/</guid>
<description>Tags :
&amp;lt;./biblio/references.bib&amp;gt;
Backlinks Fundamental principles of engineering nanometrology </description>
</item>
<item>
<title>Modal testing: theory, practice and application</title>
<link>/book/ewins00_modal/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/book/ewins00_modal/</guid>
<description>Tags System Identification, Reference Books Reference (Ewins, 2000) Author(s) Ewins, D. Year 2000 Overview Introduction to Modal Testing The major objectives of modal testing are:
Determining the nature and extent of vibration response levels in operation Verifying theoretical models and predictions of the vibrations Measurement of the essential materials properties under dynamic loading, such as damping capacity, friction and fatigue endurance For many applications, vibrations is directly related to performance and it is important that the vibration levels are anticipated and brought under satisfactory control.</description>
</item>
<item>
<title>Modeling and control of vibration in mechanical systems</title>
<link>/book/du10_model_contr_vibrat_mechan_system/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/book/du10_model_contr_vibrat_mechan_system/</guid>
<description>Tags Stewart Platforms, Vibration Isolation Reference (Chunling Du &amp;amp; Lihua Xie, 2010) Author(s) Du, C., &amp;amp; Xie, L. Year 2010 Read Chapter 1 and 3.
Bibliography Du, C., &amp;amp; Xie, L., Modeling and control of vibration in mechanical systems (2010), : CRC Press. ↩</description>
</item>
<item>
<title>Motion Control</title>
<link>/zettels/motion_control/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/zettels/motion_control/</guid>
<description>Tags :
&amp;lt;./biblio/references.bib&amp;gt;
Backlinks Advanced motion control for precision mechatronics: control, identification, and learning of complex systems </description>
</item>
<item>
<title>Multi-stage actuation systems and control</title>
<link>/book/du19_multi_actuat_system_contr/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/book/du19_multi_actuat_system_contr/</guid>
<description>Tags :
Reference (Chunling Du &amp;amp; Chee Khiang Pang, 2019) Author(s) Du, C., &amp;amp; Pang, C. K. Year 2019 Mechanical Actuation Systems Introduction When high bandwidth, high position accuracy and long stroke are required simultaneously: dual-stage systems composed of a coarse (or primary) actuator and a fine actuator working together are used.
Popular choices for coarse actuator are:
DC motor Voice coil motor (VCM) Permanent magnet stepper motor Permanent magnet linear synchronous motor As fine actuators, most of the time piezoelectric actuator are used.</description>
</item>
<item>
<title>Multivariable Control</title>
<link>/zettels/multivariable_control/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/zettels/multivariable_control/</guid>
<description>Tags :
&amp;lt;./biblio/references.bib&amp;gt;
Backlinks Position control in lithographic equipment Implementation challenges for multivariable control: what you did not learn in school! Simultaneous, fault-tolerant vibration isolation and pointing control of flexure jointed hexapods Multivariable control systems: an engineering approach Multivariable feedback control: analysis and design </description>
</item>
<item>
<title>Multivariable control systems: an engineering approach</title>
<link>/book/albertos04_multiv_contr_system/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/book/albertos04_multiv_contr_system/</guid>
<description>Tags Multivariable Control Reference (Albertos &amp;amp; Antonio, 2004) Author(s) Albertos, P., &amp;amp; Antonio, S. Year 2004 Bibliography Albertos, P., &amp;amp; Antonio, S., Multivariable control systems: an engineering approach (2004), : Springer-Verlag. ↩</description>
</item>
<item>
<title>Multivariable feedback control: analysis and design</title>
<link>/book/skogestad07_multiv_feedb_contr/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/book/skogestad07_multiv_feedb_contr/</guid>
<description>Tags Reference Books, Multivariable Control Reference (Skogestad &amp;amp; Postlethwaite, 2007) Author(s) Skogestad, S., &amp;amp; Postlethwaite, I. Year 2007 \( % H Infini \newcommand{\hinf}{\mathcal{H}_\infty} % H 2 \newcommand{\htwo}{\mathcal{H}_2} % Omega \newcommand{\w}{\omega} % H-Infinity Norm \newcommand{\hnorm}[1]{\left\|#1\right\|_{\infty}} % H-2 Norm \newcommand{\normtwo}[1]{\left\|#1\right\|_{2}} % Norm \newcommand{\norm}[1]{\left\|#1\right\|} % Absolute value \newcommand{\abs}[1]{\left\lvert#1\right\lvert} % Maximum for all omega \newcommand{\maxw}{\text{max}_{\omega}} % Maximum singular value \newcommand{\maxsv}{\overline{\sigma}} % Minimum singular value \newcommand{\minsv}{\underline{\sigma}} % Under bar \newcommand{\ubar}[1]{\text{\b{$#1$}}} % Diag keyword \newcommand{\diag}[1]{\text{diag}\{{#1}\}} % Vector \newcommand{\colvec}[1]{\begin{bmatrix}#1\end{bmatrix}} \) \( \newcommand{\tcmbox}[1]{\boxed{#1}} % Simulate SIunitx \newcommand{\SI}[2]{#1\,#2} \newcommand{\ang}[1]{#1^{\circ}} \newcommand{\degree}{^{\circ}} \newcommand{\radian}{\text{rad}} \newcommand{\percent}{\%} \newcommand{\decibel}{\text{dB}} \newcommand{\per}{/} % Bug with subequations \newcommand{\eatLabel}[2]{} \newenvironment{subequations}{\eatLabel}{} \) Introduction</description>
</item>
<item>
<title>Nano Active Stabilization System</title>
<link>/zettels/nano_active_stabilization_system/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/zettels/nano_active_stabilization_system/</guid>
<description>Tags :
&amp;lt;./biblio/references.bib&amp;gt;
Backlinks Interferometric characterization of rotation stages for x-ray nanotomography Automated markerless full field hard x-ray microscopic tomography at sub-50 nm 3-dimension spatial resolution An instrument for 3d x-ray nano-imaging </description>
</item>
<item>
<title>Nanometre-cutting machine using a stewart-platform parallel mechanism</title>
<link>/paper/furutani04_nanom_cuttin_machin_using_stewar/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/furutani04_nanom_cuttin_machin_using_stewar/</guid>
<description>Tags Stewart Platforms, Flexible Joints Reference (Katsushi Furutani {\it et al.}, 2004) Author(s) Furutani, K., Suzuki, M., &amp;amp; Kudoh, R. Year 2004 Lever mechanism to amplify the motion of piezoelectric stack actuators Use of flexure joints Eddy current displacement sensors for control (decentralized) Isotropic performance (cubic configuration even if not said so) Possible sources of error:
position error of the link ends in assembly =&amp;gt; simulation of position error and it is not significant Inaccurate modelling of the links insufficient generative force unwanted deformation of the links To minimize the errors, a calibration is done between the required leg length and the wanted platform pose.</description>
</item>
<item>
<title>Nanopositioning system with force feedback for high-performance tracking and vibration control</title>
<link>/paper/fleming10_nanop_system_with_force_feedb/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/fleming10_nanop_system_with_force_feedb/</guid>
<description>Tags Sensor Fusion, Force Sensors Reference (Fleming, 2010) Author(s) Fleming, A. Year 2010 Summary:
The noise generated by a piezoelectric force sensor is much less than a capacitive sensor Dynamical model of a piezoelectric stack actuator and piezoelectric force sensor Noise of a piezoelectric force sensor IFF with a piezoelectric stack actuator and piezoelectric force sensor A force sensor is used as a displacement sensor below the frequency of the first zero Sensor fusion architecture with a capacitive sensor and a force sensor and using complementary filters Virtual sensor fusion architecture (called low-frequency bypass) Analog implementation of the control strategies to avoid quantization noise, finite resolution and sampling delay Model of a multi-layer monolithic piezoelectric stack actuator</description>
</item>
<item>
<title>Nanopositioning with multiple sensors: a case study in data storage</title>
<link>/paper/sebastian12_nanop_with_multip_sensor/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/sebastian12_nanop_with_multip_sensor/</guid>
<description>Tags Sensor Fusion Reference (Abu Sebastian &amp;amp; Angeliki Pantazi, 2012) Author(s) Sebastian, A., &amp;amp; Pantazi, A. Year 2012 Bibliography Sebastian, A., &amp;amp; Pantazi, A., Nanopositioning with multiple sensors: a case study in data storage, IEEE Transactions on Control Systems Technology, 20(2), 382–394 (2012). http://dx.doi.org/10.1109/tcst.2011.2177982 ↩</description>
</item>
<item>
<title>Parallel robots : mechanics and control</title>
<link>/book/taghirad13_paral/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/book/taghirad13_paral/</guid>
<description>Tags Stewart Platforms, Reference Books Reference (Taghirad, 2013) Author(s) Taghirad, H. Year 2013 Introduction
This book is intended to give some analysis and design tools for the increase number of engineers and researchers who are interested in the design and implementation of parallel robots. A systematic approach is presented to analyze the kinematics, dynamics and control of parallel robots. To define the motion characteristics of such robots, it is necessary to represent 3D motion of the robot moving platform with respect to a fixed coordinate.</description>
</item>
<item>
<title>Position control in lithographic equipment</title>
<link>/paper/butler11_posit_contr_lithog_equip/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/butler11_posit_contr_lithog_equip/</guid>
<description>Tags Multivariable Control, Positioning Stations Reference (Hans Butler, 2011) Author(s) Butler, H. Year 2011 Bibliography Butler, H., Position control in lithographic equipment, IEEE Control Systems, 31(5), 28–47 (2011). http://dx.doi.org/10.1109/mcs.2011.941882 ↩</description>
</item>
<item>
<title>Position Sensors</title>
<link>/zettels/position_sensors/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/zettels/position_sensors/</guid>
<description>Tags Inertial Sensors Reviews of position sensors (Collette {\it et al.}, 2012) Fleming, A. J., A review of nanometer resolution position sensors: operation and performance (Andrew Fleming, 2013) (Notes) Relative Position Sensors
Table 1: Characteristics of relative measurement sensors collette11_review Technology Frequency Resolution Range T Range LVDT DC-200 Hz 10 nm rms 1-10 mm -50,100 °C Eddy current 5 kHz 0.</description>
</item>
<item>
<title>Positioning Stations</title>
<link>/zettels/positioning_stations/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/zettels/positioning_stations/</guid>
<description>Tags :
&amp;lt;./biblio/references.bib&amp;gt;
Backlinks Interferometric characterization of rotation stages for x-ray nanotomography Position control in lithographic equipment An instrument for 3d x-ray nano-imaging </description>
</item>
<item>
<title>Precision Engineering</title>
<link>/zettels/precision_engineering/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/zettels/precision_engineering/</guid>
<description>Tags :
&amp;lt;./biblio/references.bib&amp;gt;
Backlinks Design for precision: current status and trends Basics of precision engineering - 1st edition </description>
</item>
<item>
<title>Reference Books</title>
<link>/zettels/reference_books/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/zettels/reference_books/</guid>
<description>Tags :
&amp;lt;./biblio/references.bib&amp;gt;
Backlinks Modal testing: theory, practice and application The art of electronics - third edition Vibration Control of Active Structures - Fourth Edition Parallel robots : mechanics and control The design of high performance mechatronics - 2nd revised edition Multivariable feedback control: analysis and design </description>
</item>
<item>
<title>Review of active vibration isolation strategies</title>
<link>/paper/collette11_review_activ_vibrat_isolat_strat/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/collette11_review_activ_vibrat_isolat_strat/</guid>
<description>Tags Vibration Isolation Reference (Christophe Collette {\it et al.}, 2011) Author(s) Collette, C., Janssens, S., &amp;amp; Artoos, K. Year 2011 Background and Motivations Passive Isolation Tradeoffs \[ X(s) = \underbrace{\frac{cs + k}{ms^2 + cs + k}}_{T_{wx}(s)} W(s) + \underbrace{\frac{1}{ms^2 + cs + k}}_{T_{Fx}(s)} F(s) \]
\(T_{wx}(s)\) is called the transmissibility of the isolator. It characterize the way seismic vibrations \(w\) are transmitted to the equipment. \(T_{Fx}(s)\) is called the compliance.</description>
</item>
<item>
<title>Search Results</title>
<link>/search/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/search/</guid>
<description>This file exists solely to respond to /search URL with the related search layout template.
No content shown here is rendered, all content is based in the template layouts/page/search.html
Setting a very low sitemap priority will tell search engines this is not important content.
This implementation uses Fusejs, jquery and mark.js
Initial setup Search depends on additional output content type of JSON in config.toml ``` [outputs] home = [&amp;ldquo;HTML&amp;rdquo;, &amp;ldquo;JSON&amp;rdquo;] ```</description>
</item>
<item>
<title>Sensor Fusion</title>
<link>/zettels/sensor_fusion/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/zettels/sensor_fusion/</guid>
<description>Tags :
&amp;lt;./biblio/references.bib&amp;gt;
Backlinks Sensor fusion for active vibration isolation in precision equipment Vibration control of flexible structures using fusion of inertial sensors and hyper-stable actuator-sensor pairs Sensor fusion methods for high performance active vibration isolation systems Nanopositioning system with force feedback for high-performance tracking and vibration control Nanopositioning with multiple sensors: a case study in data storage </description>
</item>
<item>
<title>Sensor fusion for active vibration isolation in precision equipment</title>
<link>/paper/tjepkema12_sensor_fusion_activ_vibrat_isolat_precis_equip/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/tjepkema12_sensor_fusion_activ_vibrat_isolat_precis_equip/</guid>
<description>Tags Sensor Fusion, Vibration Isolation Reference (Tjepkema {\it et al.}, 2012) Author(s) Tjepkema, D., Dijk, J. v., &amp;amp; Soemers, H. Year 2012 Relative motion Control Control law: \(f = -G(x-w)\)
\[ \frac{x}{w} = \frac{k+G}{ms^2 + k+G} \] \[ \frac{x}{F} = \frac{1}{ms^2 + k+G} \]
Force Control Control law: \(f = -G F_a = -G \left(f-k(x-w)\right)\)
\[ \frac{x}{w} = \frac{k}{(1+G)ms^2 + k} \] \[ \frac{x}{F} = \frac{1+G}{(1+G)ms^2 + k} \]</description>
</item>
<item>
<title>Sensor fusion methods for high performance active vibration isolation systems</title>
<link>/paper/collette15_sensor_fusion_method_high_perfor/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/collette15_sensor_fusion_method_high_perfor/</guid>
<description>Tags Sensor Fusion, Vibration Isolation Reference (Collette &amp;amp; Matichard, 2015) Author(s) Collette, C., &amp;amp; Matichard, F. Year 2015 In order to have good stability margins, it is common practice to collocate sensors and actuators. This ensures alternating poles and zeros along the imaginary axis. Then, each phase lag introduced by the poles is compensed by phase leag introduced by the zeroes. This guarantees stability and such system is referred to as hyperstable.</description>
</item>
<item>
<title>Sensors and control of a space-based six-axis vibration isolation system</title>
<link>/paper/hauge04_sensor_contr_space_based_six/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/hauge04_sensor_contr_space_based_six/</guid>
<description>Tags Stewart Platforms, Vibration Isolation, Cubic Architecture Reference (Hauge &amp;amp; Campbell, 2004) Author(s) Hauge, G., &amp;amp; Campbell, M. Year 2004 Discusses:
Choice of sensors and control architecture Predictability and limitations of the system dynamics Two-Sensor control architecture Vibration isolation using a Stewart platform Experimental comparison of Force sensor and Inertial Sensor and associated control architecture for vibration isolation
Figure 1: Hexapod for active vibration isolation</description>
</item>
<item>
<title>Simultaneous vibration isolation and pointing control of flexure jointed hexapods</title>
<link>/paper/li01_simul_vibrat_isolat_point_contr/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/li01_simul_vibrat_isolat_point_contr/</guid>
<description>Tags Stewart Platforms, Vibration Isolation Reference (Xiaochun Li {\it et al.}, 2001) Author(s) Li, X., Hamann, J. C., &amp;amp; McInroy, J. E. Year 2001 if the hexapod is designed such that the payload mass/inertia matrix (\(M_x\)) and \(J^T J\) are diagonal, the dynamics from \(u\) to \(y\) are decoupled. Bibliography Li, X., Hamann, J. C., &amp;amp; McInroy, J. E., Simultaneous vibration isolation and pointing control of flexure jointed hexapods, In , Smart Structures and Materials 2001: Smart Structures and Integrated Systems (pp.</description>
</item>
<item>
<title>Simultaneous, fault-tolerant vibration isolation and pointing control of flexure jointed hexapods</title>
<link>/paper/li01_simul_fault_vibrat_isolat_point/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/li01_simul_fault_vibrat_isolat_point/</guid>
<description>Tags Stewart Platforms, Vibration Isolation, Cubic Architecture, Flexible Joints, Multivariable Control Reference @phdthesis{li01_simul_fault_vibrat_isolat_point, author = {Li, Xiaochun}, school = {University of Wyoming}, title = {Simultaneous, Fault-tolerant Vibration Isolation and Pointing Control of Flexure Jointed Hexapods}, year = 2001, tags = {parallel robot}, } Author(s) Li, X. Year 2001 Introduction Stewart Platform:
Cubic (mutually orthogonal) Flexure Joints =&amp;gt; eliminate friction and backlash but add complexity to the dynamics</description>
</item>
<item>
<title>Six dof active vibration control using stewart platform with non-cubic configuration</title>
<link>/paper/zhang11_six_dof/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/zhang11_six_dof/</guid>
<description>Tags Stewart Platforms, Vibration Isolation Reference (Zhen Zhang {\it et al.}, 2011) Author(s) Zhang, Z., Liu, J., Mao, J., Guo, Y., &amp;amp; Ma, Y. Year 2011 Non-cubic stewart platform Flexible joints Magnetostrictive actuators Strong coupled motions along different axes Non-cubic architecture =&amp;gt; permits to have larger workspace which was required Structure parameters (radius of plates, length of struts) are determined by optimization of the condition number of the Jacobian matrix Accelerometers for active isolation Adaptive FIR filters for active isolation control</description>
</item>
<item>
<title>Stewart Platforms</title>
<link>/zettels/stewart_platforms/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/zettels/stewart_platforms/</guid>
<description>Tags :
&amp;lt;./biblio/references.bib&amp;gt;
Backlinks Six dof active vibration control using stewart platform with non-cubic configuration Decentralized vibration control of a voice coil motor-based stewart parallel mechanism: simulation and experiments Dynamic modeling and decoupled control of a flexible stewart platform for vibration isolation Parallel robots : mechanics and control Investigation on active vibration isolation of a stewart platform with piezoelectric actuators Identification and decoupling control of flexure jointed hexapods The stewart platform manipulator: a review Modeling and control of vibration in mechanical systems Studies on stewart platform manipulator: a review Nanometre-cutting machine using a stewart-platform parallel mechanism An intelligent control system for multiple degree-of-freedom vibration isolation Active isolation and damping of vibrations via stewart platform Sensors and control of a space-based six-axis vibration isolation system Dynamic modeling and experimental analyses of stewart platform with flexible hinges Simultaneous, fault-tolerant vibration isolation and pointing control of flexure jointed hexapods A new isotropic and decoupled 6-dof parallel manipulator Simultaneous vibration isolation and pointing control of flexure jointed hexapods A six-axis single-stage active vibration isolator based on stewart platform Vibration Control of Active Structures - Fourth Edition A soft 6-axis active vibration isolator </description>
</item>
<item>
<title>Studies on stewart platform manipulator: a review</title>
<link>/paper/furqan17_studies_stewar_platf_manip/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/furqan17_studies_stewar_platf_manip/</guid>
<description>Tags Stewart Platforms Reference (Mohd Furqan {\it et al.}, 2017) Author(s) Furqan, M., Suhaib, M., &amp;amp; Ahmad, N. Year 2017 Lots of references.
Bibliography Furqan, M., Suhaib, M., &amp;amp; Ahmad, N., Studies on stewart platform manipulator: a review, Journal of Mechanical Science and Technology, 31(9), 4459–4470 (2017). http://dx.doi.org/10.1007/s12206-017-0846-1 ↩</description>
</item>
<item>
<title>System Identification</title>
<link>/zettels/system_identification/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/zettels/system_identification/</guid>
<description>Tags :
&amp;lt;./biblio/references.bib&amp;gt;
Backlinks Modal testing: theory, practice and application </description>
</item>
<item>
<title>Test File</title>
<link>/zettels/test/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/zettels/test/</guid>
<description>This is a quote!
1 2 a = 2; figure; This is an important part of the text.
See Eq. eq:test1 and eq:test2.
\begin{equation} a = 1 \end{equation}
\begin{equation} a = 2 \label{eq:test2} \end{equation}
Also look at 1 \eqref{eq:test2}.
Some text.
Some text.
Some text.
Some text.
Some text.
Some text.
Some text.
Some text.
Some text.
Some text.
Some text.
Some text.</description>
</item>
<item>
<title>The art of electronics - third edition</title>
<link>/book/horowitz15_art_of_elect_third_edition/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/book/horowitz15_art_of_elect_third_edition/</guid>
<description>Tags Reference Books, Electronics Reference (Horowitz, 2015) Author(s) Horowitz, P. Year 2015 Bibliography Horowitz, P., The art of electronics - third edition (2015), New York, NY, USA: Cambridge University Press. ↩</description>
</item>
<item>
<title>The design of high performance mechatronics - 2nd revised edition</title>
<link>/book/schmidt14_desig_high_perfor_mechat_revis_edition/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/book/schmidt14_desig_high_perfor_mechat_revis_edition/</guid>
<description>Tags Reference Books Reference (Schmidt {\it et al.}, 2014) Author(s) Schmidt, R. M., Schitter, G., &amp;amp; Rankers, A. Year 2014 Section 2.2 Mechanics
The core of a mechatronic system is its mechanical construction and in spite of many decade of excellent designs, optimizing the mechanical structure in strength, mass and endurance, the mechanical behavior will always remain the limiting factor of the performance of any mechatronic system.</description>
</item>
<item>
<title>The stewart platform manipulator: a review</title>
<link>/paper/dasgupta00_stewar_platf_manip/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/dasgupta00_stewar_platf_manip/</guid>
<description>Tags Stewart Platforms Reference (Bhaskar Dasgupta &amp;amp; Mruthyunjaya, 2000) Author(s) Dasgupta, B., &amp;amp; Mruthyunjaya, T. Year 2000
Table 1: Parallel VS serial manipulators Advantages Disadvantages Serial Manoeuverability Poor precision Large workspace Bends under high load Vibrate at high speed Parallel High stiffness Small workspace Good dynamic performances Precise positioning The generalized Stewart platforms consists of two rigid bodies (referred to as the base and the platoform) connected through six extensible legs, each with sherical joints at both ends.</description>
</item>
<item>
<title>Vibration Control of Active Structures - Fourth Edition</title>
<link>/book/preumont18_vibrat_contr_activ_struc_fourt_edition/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/book/preumont18_vibrat_contr_activ_struc_fourt_edition/</guid>
<description>Tags Vibration Isolation, Reference Books, Stewart Platforms, HAC-HAC Reference (Andre Preumont, 2018) Author(s) Preumont, A. Year 2018 Introduction Active Versus Passive Active structure may be cheaper or lighter than passive structures of comparable performances; or they may offer performances that no passive structure could offer.
Active is not always better, and a control systems cannot compensate for a bad design. Active solution should be considered only after all other passive means have been exhausted.</description>
</item>
<item>
<title>Vibration control of flexible structures using fusion of inertial sensors and hyper-stable actuator-sensor pairs</title>
<link>/paper/collette14_vibrat/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/paper/collette14_vibrat/</guid>
<description>Tags Vibration Isolation, Sensor Fusion Reference (Collette &amp;amp; Matichard, 2014) Author(s) Collette, C., &amp;amp; Matichard, F. Year 2014 Introduction Sensor fusion is used to combine the benefits of different types of sensors:
Relative sensor for DC positioning capability at low frequency Inertial sensors for isolation at high frequency Force sensor / collocated sensor to improve the robustness Different types of sensors In this paper, three types of sensors are used.</description>
</item>
<item>
<title>Vibration Isolation</title>
<link>/zettels/vibration_isolation/</link>
<pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
<guid>/zettels/vibration_isolation/</guid>
<description>Tags :
&amp;lt;./biblio/references.bib&amp;gt;
Backlinks Six dof active vibration control using stewart platform with non-cubic configuration Dynamic modeling and decoupled control of a flexible stewart platform for vibration isolation Investigation on active vibration isolation of a stewart platform with piezoelectric actuators Review of active vibration isolation strategies Vibration control of flexible structures using fusion of inertial sensors and hyper-stable actuator-sensor pairs Sensor fusion methods for high performance active vibration isolation systems Modeling and control of vibration in mechanical systems An intelligent control system for multiple degree-of-freedom vibration isolation Active isolation and damping of vibrations via stewart platform Sensors and control of a space-based six-axis vibration isolation system Comparison and classification of high-precision actuators based on stiffness influencing vibration isolation Simultaneous, fault-tolerant vibration isolation and pointing control of flexure jointed hexapods Simultaneous vibration isolation and pointing control of flexure jointed hexapods An exploration of active hard mount vibration isolation for precision equipment Force feedback versus acceleration feedback in active vibration isolation A six-axis single-stage active vibration isolator based on stewart platform Vibration Control of Active Structures - Fourth Edition A soft 6-axis active vibration isolator Sensor fusion for active vibration isolation in precision equipment </description>
</item>
</channel>
</rss>

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function param(name) {
return decodeURIComponent((location.search.split(name + '=')[1] || '').split('&')[0]).replace(/\+/g, ' ');
}
function render(templateString, data) {
var conditionalMatches,conditionalPattern,copy;
conditionalPattern = /\$\{\s*isset ([a-zA-Z]*) \s*\}(.*)\$\{\s*end\s*}/g;
//since loop below depends on re.lastInxdex, we use a copy to capture any manipulations whilst inside the loop
copy = templateString;
while ((conditionalMatches = conditionalPattern.exec(templateString)) !== null) {
if(data[conditionalMatches[1]]){
//valid key, remove conditionals, leave contents.
copy = copy.replace(conditionalMatches[0],conditionalMatches[2]);
}else{
//not valid, remove entire section
copy = copy.replace(conditionalMatches[0],'');
}
}
templateString = copy;
//now any conditionals removed we can do simple substitution
var key, find, re;
for (key in data) {
find = '\\$\\{\\s*' + key + '\\s*\\}';
re = new RegExp(find, 'g');
templateString = templateString.replace(re, data[key]);
}
return templateString;
}

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{
"name": "",
"icons": [
{
"src": "/android-chrome-192x192.png",
"sizes": "192x192",
"type": "image/png"
},
{
"src": "/android-chrome-512x512.png",
"sizes": "512x512",
"type": "image/png"
}
],
"theme_color": "#ffffff",
"background_color": "#ffffff",
"display": "standalone"
}

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