Update few notes

content/paper/bryson93_contr_spacec_aircr.md

@@ -0,0 +1,51 @@
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+title = "Control of spacecraft and aircraft"
+author = ["Thomas Dehaeze"]
+draft = false
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+
+Tags
+: [HAC-HAC]({{< relref "hac_hac" >}})
+
+Reference
+: <sup id="4970865a21830fff7b1daeec187bfa68"><a href="#bryson93_contr_spacec_aircr" title="Bryson, Control of Spacecraft and Aircraft, Princeton university press Princeton, New Jersey (1993).">(Bryson, 1993)</a></sup>
+
+Author(s)
+: Bryson, A. E.
+
+Year
+: 1993
+
+
+## 9.2.3 Roll-Off Filters {#9-dot-2-dot-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 "roll-off" 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 ("**spillover**").
+
+
+## 9.5 Robust Compensator Synthesis {#9-dot-5-robust-compensator-synthesis}
+
+> LQG synthesis using feedback of estimated states will produce almost the same good response as LQR [...] for systems with control system bandwidths that are well below the frequency of the first vibration mode.
+> However, it may not be true for systems with higher control system bandwidths, even when one or more vibration modes are included in the control design model.
+
+<!--quoteend-->
+
+> If a rate sensor is co-located with an actuator on a flexible body, and its signal is fed back to the actuator, all vibration modes are stabilized.
+> If a rate sensor is not co-located with an actuator on a flexible body, ans its signal is fed back to the actuator, some vibration modes are stabilized and others are destabilized, depending on the location of the sensor relative to the actuator.
+
+
+## 9.5.2 Low-Authority Control/High-Authority Control {#9-dot-5-dot-2-low-authority-control-high-authority-control}
+
+> Figure [fig:bryson93_hac_lac](#fig:bryson93_hac_lac) shows the concept of Low-Authority Control/High-Authority Control (LAC/HAC) is the s-plane.
+> LAC uses a co-located rate sensor to add damping to all the vibratory modes (but not the rigid-body mode).
+> HAC uses a separated displacement sensor to stabilize the rigid body mode, which slightly decreases the damping of the vibratory modes but not enough to produce instability (called "spillover")
+
+<a id="orgf5c85db"></a>
+
+{{< figure src="/ox-hugo/bryson93_hac_lac.png" caption="Figure 1: HAC-LAC control concept" >}}
+
+> LAC/HAC is usually insensitive to small deviation of the plant dynamics away from the design values, that is, it is **robust** to plant parameter changes.
+
+# Bibliography
+<a id="bryson93_contr_spacec_aircr"></a>Bryson, A. E., *Control of spacecraft and aircraft* (1993), : Princeton university press Princeton, New Jersey. [↩](#4970865a21830fff7b1daeec187bfa68)

content/paper/fleming13_review_nanom_resol_posit_sensor.md

@@ -33,7 +33,7 @@ Usually quoted as a percentage of the fill-scale range (FSR):
 
 With \\(e\_m(v)\\) is the mapping error.
 
-<a id="org64f54e9"></a>
+<a id="org18802f9"></a>
 
 {{< figure src="/ox-hugo/fleming13_mapping_error.png" caption="Figure 1: The actual position versus the output voltage of a position sensor. The calibration function \\(f\_{cal}(v)\\) is an approximation of the sensor mapping function \\(f\_a(v)\\) where \\(v\\) is the voltage resulting from a displacement \\(x\\). \\(e\_m(v)\\) is the residual error." >}}
 
@@ -42,7 +42,7 @@ With \\(e\_m(v)\\) is the mapping error.
 
 If the shape of the mapping function actually varies with time, the maximum error due to drift must be evaluated by finding the worst-case mapping error.
 
-<a id="org81ab6a9"></a>
+<a id="org65fb6f9"></a>
 
 {{< figure src="/ox-hugo/fleming13_drift_stability.png" caption="Figure 2: The worst case range of a linear mapping function \\(f\_a(v)\\) for a given error in sensitivity and offset." >}}
 
@@ -147,9 +147,9 @@ The empirical rule states that there is a \\(99.7\%\\) probability that a sample
 This if we define the resolution as \\(\delta = 6 \sigma\\), we will referred to as the \\(6\sigma\text{-resolution}\\).
 
 Another important parameter that must be specified when quoting resolution is the sensor bandwidth.
-There is usually a trade-off between bandwidth and resolution (figure [3](#orgd8c6776)).
+There is usually a trade-off between bandwidth and resolution (figure [3](#org954f29f)).
 
-<a id="orgd8c6776"></a>
+<a id="org954f29f"></a>
 
 {{< figure src="/ox-hugo/fleming13_tradeoff_res_bandwidth.png" caption="Figure 3: The resolution versus banwidth of a position sensor." >}}
 

content/paper/ito16_compar_class_high_precis_actuat.md

@@ -41,6 +41,8 @@ In this paper, the piezoelectric actuator/electronics adds a time delay which is
 -   **Low Stiffness** actuator is defined as the ones where the transmissibility stays below 0dB at all frequency
 -   **High Stiffness** actuator is defined as the ones where the transmissibility goes above 0dB at some frequency
 
+<a id="org6e18c94"></a>
+
 {{< figure src="/ox-hugo/ito16_low_high_stiffness_actuators.png" caption="Figure 1: Definition of low-stiffness and high-stiffness actuator" >}}
 
 
@@ -52,6 +54,8 @@ In this paper, the piezoelectric actuator/electronics adds a time delay which is
 
 ## Controller Design {#controller-design}
 
+<a id="orgc911fbe"></a>
+
 {{< figure src="/ox-hugo/ito16_transmissibility.png" caption="Figure 2: Obtained transmissibility" >}}
 
 

content/paper/oomen18_advan_motion_contr_precis_mechat.md

@@ -16,5 +16,9 @@ Author(s)
 Year
 : 2018
 
+<a id="org55ab131"></a>
+
+{{< figure src="/ox-hugo/oomen18_next_gen_loop_gain.png" caption="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
 <a id="oomen18_advan_motion_contr_precis_mechat"></a>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).  http://dx.doi.org/10.1541/ieejjia.7.127 [↩](#73fd325bd20a6ef8972145e535f38198)