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Update Content - 2024-12-17

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Thomas Dehaeze
2024-12-17 15:37:17 +01:00
parent 4d585dd592
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content/article/yang19_dynam_model_decoup_contr_flexib.md
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@@ -25,10 +25,10 @@ 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](#figure--fig:yang19-stewart-platform)):
**Stewart platform** ([Figure 1](#figure--fig:yang19-stewart-platform)):
- piezoelectric actuators
- flexible joints (Figure [2](#figure--fig:yang19-flexible-joints))
- 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)
@@ -41,11 +41,11 @@ Thus, this stiffness is taken into account in the dynamics and compensated for.
{{< 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](#figure--fig:yang19-flexible-joints)) 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">
<span class="table-number"><a href="#table--tab:yang19-stiffness-flexible-joints">Table 1</a></span>:
<span class="table-number"><a href="#table--tab:yang19-stiffness-flexible-joints">Table 1</a>:</span>
Stiffness of flexible joints obtained by FEM
</div>
@@ -105,7 +105,7 @@ 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](#figure--fig:yang19-control-arch).
The block diagram of the control strategy is represented in [Figure 3](#figure--fig:yang19-control-arch).
<a id="figure--fig:yang19-control-arch"></a>
@@ -121,7 +121,7 @@ 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](#figure--fig:yang19-results).
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="figure--fig:yang19-results"></a>