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content/article/yang19_dynam_model_decoup_contr_flexib.md
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@@ -8,7 +8,7 @@ Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Vibration Isolation]({{< relref "vibration_isolation" >}}), [Flexible Joints]({{< relref "flexible_joints" >}}), [Cubic Architecture]({{< relref "cubic_architecture" >}})
Reference
: <sup id="d39b6222c8dd2baf188d677733c2826c"><a class="reference-link" href="#yang19_dynam_model_decoup_contr_flexib" title="Yang, Wu, Chen, Kang, ShengZheng \&amp; Cheng, Dynamic Modeling and Decoupled Control of a Flexible Stewart Platform for Vibration Isolation, {Journal of Sound and Vibration}, v(), 398-412 (2019).">(Yang {\it et al.}, 2019)</a></sup>
: ([Yang et al. 2019](#org1678fd1))
Author(s)
: Yang, X., Wu, H., Chen, B., Kang, S., & Cheng, S.
@@ -25,23 +25,23 @@ Year
The joint stiffness impose a limitation on the control performance using force sensors as it adds a zero at low frequency in the dynamics.
Thus, this stiffness is taken into account in the dynamics and compensated for.
**Stewart platform** (Figure [1](#org96fb07f)):
**Stewart platform** (Figure [1](#org082a4f7)):
- piezoelectric actuators
- flexible joints (Figure [2](#org62b30be))
- flexible joints (Figure [2](#org66efbec))
- force sensors (used for vibration isolation)
- displacement sensors (used to decouple the dynamics)
- cubic (even though not said explicitly)
<a id="org96fb07f"></a>
<a id="org082a4f7"></a>
{{< figure src="/ox-hugo/yang19_stewart_platform.png" caption="Figure 1: Stewart Platform" >}}
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<a id="org66efbec"></a>
{{< figure src="/ox-hugo/yang19_flexible_joints.png" caption="Figure 2: Flexible Joints" >}}
The stiffness of the flexible joints (Figure [2](#org62b30be)) are computed with an FEM model and shown in Table [1](#table--tab:yang19-stiffness-flexible-joints).
The stiffness of the flexible joints (Figure [2](#org66efbec)) are computed with an FEM model and shown in Table [1](#table--tab:yang19-stiffness-flexible-joints).
<a id="table--tab:yang19-stiffness-flexible-joints"></a>
<div class="table-caption">
@@ -105,9 +105,9 @@ In order to apply this control strategy:
- The jacobian has to be computed
- No information about modal matrix is needed
The block diagram of the control strategy is represented in Figure [3](#org6a06ad2).
The block diagram of the control strategy is represented in Figure [3](#orgc6324f9).
<a id="org6a06ad2"></a>
<a id="orgc6324f9"></a>
{{< figure src="/ox-hugo/yang19_control_arch.png" caption="Figure 3: Control Architecture used" >}}
@@ -121,10 +121,10 @@ Substituting \\(H(s)\\) in the equation of motion gives that:
**Experimental Validation**:
An external Shaker is used to excite the base and accelerometers are located on the base and mobile platforms to measure their motion.
The results are shown in Figure [4](#orgb8bd696).
The results are shown in Figure [4](#org45c63bf).
In theory, the vibration performance can be improved, however in practice, increasing the gain causes saturation of the piezoelectric actuators and then the instability occurs.
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{{< figure src="/ox-hugo/yang19_results.png" caption="Figure 4: Frequency response of the acceleration ratio between the paylaod and excitation (Transmissibility)" >}}
@@ -133,5 +133,7 @@ In theory, the vibration performance can be improved, however in practice, incre
> The force feedback makes the six-DOF MIMO system decoupled into six SISO subsystems in modal space, where the control gains can be designed and analyzed more effectively and conveniently.
> The proportional and integral gains in the sub-controller are used to separately regulate the vibration isolation bandwidth and active damping simultaneously for the six vibration modes.
# Bibliography
<a class="bibtex-entry" id="yang19_dynam_model_decoup_contr_flexib">Yang, X., Wu, H., Chen, B., Kang, S., & Cheng, S., *Dynamic modeling and decoupled control of a flexible stewart platform for vibration isolation*, Journal of Sound and Vibration, *439()*, 398–412 (2019). http://dx.doi.org/10.1016/j.jsv.2018.10.007</a> [↩](#d39b6222c8dd2baf188d677733c2826c)
## Bibliography {#bibliography}
<a id="org1678fd1"></a>Yang, XiaoLong, HongTao Wu, Bai Chen, ShengZheng Kang, and ShiLi Cheng. 2019. “Dynamic Modeling and Decoupled Control of a Flexible Stewart Platform for Vibration Isolation.” _Journal of Sound and Vibration_ 439 (January). Elsevier BV:398–412. <https://doi.org/10.1016/j.jsv.2018.10.007>.