tdehaeze/digital-brain
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

Update Content - 2022-03-15

Browse Source
This commit is contained in:
Thomas Dehaeze
2022-03-15 16:40:48 +01:00
parent e6390908c4
commit 22fb3361a5
148 changed files with 3981 additions and 3197 deletions
Download Patch File Download Diff File Expand all files Collapse all files

39
content/article/yang19_dynam_model_decoup_contr_flexib.md
View File

@@ -1,17 +1,17 @@
+++
title = "Dynamic modeling and decoupled control of a flexible stewart platform for vibration isolation"
author = ["Thomas Dehaeze"]
author = ["Dehaeze Thomas"]
draft = false
+++
Tags
: [Stewart Platforms]({{< relref "stewart_platforms" >}}), [Vibration Isolation]({{< relref "vibration_isolation" >}}), [Flexible Joints]({{< relref "flexible_joints" >}}), [Cubic Architecture]({{< relref "cubic_architecture" >}})
: [Stewart Platforms]({{< relref "stewart_platforms.md" >}}), [Vibration Isolation]({{< relref "vibration_isolation.md" >}}), [Flexible Joints]({{< relref "flexible_joints.md" >}}), [Cubic Architecture]({{< relref "cubic_architecture.md" >}})
Reference
: ([Yang et al. 2019](#orgb15122e))
: (<a href="#citeproc_bib_item_1">Yang et al. 2019</a>)
Author(s)
: Yang, X., Wu, H., Chen, B., Kang, S., & Cheng, S.
: Yang, X., Wu, H., Chen, B., Kang, S., &amp; Cheng, S.
Year
: 2019
@@ -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](#org479da8d)):
**Stewart platform** (Figure [1](#figure--fig:yang19-stewart-platform)):
- piezoelectric actuators
- flexible joints (Figure [2](#org83afe99))
- flexible joints (Figure [2](#figure--fig:yang19-flexible-joints))
- force sensors (used for vibration isolation)
- displacement sensors (used to decouple the dynamics)
- cubic (even though not said explicitly)
<a id="org479da8d"></a>
<a id="figure--fig:yang19-stewart-platform"></a>
{{< figure src="/ox-hugo/yang19_stewart_platform.png" caption="Figure 1: Stewart Platform" >}}
{{< figure src="/ox-hugo/yang19_stewart_platform.png" caption="<span class=\"figure-number\">Figure 1: </span>Stewart Platform" >}}
<a id="org83afe99"></a>
<a id="figure--fig:yang19-flexible-joints"></a>
{{< figure src="/ox-hugo/yang19_flexible_joints.png" caption="Figure 2: Flexible Joints" >}}
{{< figure src="/ox-hugo/yang19_flexible_joints.png" caption="<span class=\"figure-number\">Figure 2: </span>Flexible Joints" >}}
The stiffness of the flexible joints (Figure [2](#org83afe99)) 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](#figure--fig:yang19-flexible-joints)) 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">
@@ -105,11 +105,11 @@ 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](#orgd526d94).
The block diagram of the control strategy is represented in Figure [3](#figure--fig:yang19-control-arch).
<a id="orgd526d94"></a>
<a id="figure--fig:yang19-control-arch"></a>
{{< figure src="/ox-hugo/yang19_control_arch.png" caption="Figure 3: Control Architecture used" >}}
{{< figure src="/ox-hugo/yang19_control_arch.png" caption="<span class=\"figure-number\">Figure 3: </span>Control Architecture used" >}}
\\(H(s)\\) is designed as a proportional plus integral compensator:
\\[ H(s) = k\_p + k\_i/s \\]
@@ -121,12 +121,12 @@ 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](#orge73e046).
The results are shown in Figure [4](#figure--fig:yang19-results).
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.
<a id="orge73e046"></a>
<a id="figure--fig:yang19-results"></a>
{{< figure src="/ox-hugo/yang19_results.png" caption="Figure 4: Frequency response of the acceleration ratio between the paylaod and excitation (Transmissibility)" >}}
{{< figure src="/ox-hugo/yang19_results.png" caption="<span class=\"figure-number\">Figure 4: </span>Frequency response of the acceleration ratio between the paylaod and excitation (Transmissibility)" >}}
> A model-based controller is then designed based on the leg’s force and position feedback.
> The position feedback compensates the effect of parasitic bending and torsional stiffness of the flexible joints.
@@ -134,7 +134,8 @@ In theory, the vibration performance can be improved, however in practice, incre
> 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 {#bibliography}
<a id="orgb15122e"></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>.
<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
<div class="csl-entry"><a id="citeproc_bib_item_1"></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.” <i>Journal of Sound and Vibration</i> 439 (January). Elsevier BV: 398–412. doi:<a href="https://doi.org/10.1016/j.jsv.2018.10.007">10.1016/j.jsv.2018.10.007</a>.</div>
</div>