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Remove the "lead" in the HAC

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Thomas Dehaeze 2025-07-03 10:22:56 +02:00
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1 changed files with 3 additions and 3 deletions
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@ -13252,11 +13252,11 @@ This design choice, while beneficial for system simplicity, introduces inherent
A diagonal controller was designed to be robust against changes in payload mass, which means that every damped plant shown in Figure\nbsp{}ref:fig:test_id31_comp_all_undamped_damped_plants must be considered during the controller design. A diagonal controller was designed to be robust against changes in payload mass, which means that every damped plant shown in Figure\nbsp{}ref:fig:test_id31_comp_all_undamped_damped_plants must be considered during the controller design.
For this controller design, a crossover frequency of $5\,\text{Hz}$ was chosen to limit the multivariable effects, as explain in Section\nbsp{}ref:sec:test_id31_hac_interaction_analysis. For this controller design, a crossover frequency of $5\,\text{Hz}$ was chosen to limit the multivariable effects, as explain in Section\nbsp{}ref:sec:test_id31_hac_interaction_analysis.
One integrator is added to increase the low-frequency gain, a lead is added around $5\,\text{Hz}$ to increase the stability margins and a first-order low-pass filter with a cut-off frequency of $30\,\text{Hz}$ is added to improve the robustness to dynamical uncertainty at high-frequency. One integrator is added to increase the low-frequency gain and a first-order low-pass filter with a cut-off frequency of $30\,\text{Hz}$ is added to improve the robustness to dynamical uncertainty at high-frequency.
The controller transfer function is shown in\nbsp{}eqref:eq:test_id31_robust_hac. The controller transfer function is shown in\nbsp{}eqref:eq:test_id31_robust_hac.
\begin{equation}\label{eq:test_id31_robust_hac} \begin{equation}\label{eq:test_id31_robust_hac}
K_{\text{HAC}}(s) = g_0 \cdot \underbrace{\frac{\omega_c}{s}}_{\text{int}} \cdot \underbrace{\frac{1}{\sqrt{\alpha}}\frac{1 + \frac{s}{\omega_c/\sqrt{\alpha}}}{1 + \frac{s}{\omega_c\sqrt{\alpha}}}}_{\text{lead}} \cdot \underbrace{\frac{1}{1 + \frac{s}{\omega_0}}}_{\text{LPF}}, \quad \left( \omega_c = 2\pi5\,\text{rad/s},\ \alpha = 2,\ \omega_0 = 2\pi30\,\text{rad/s} \right) K_{\text{HAC}}(s) = g_0 \cdot \underbrace{\frac{\omega_c}{s}}_{\text{int}} \cdot \underbrace{\frac{1}{1 + \frac{s}{\omega_0}}}_{\text{LPF}}, \quad \left( \omega_c = 2\pi5\,\text{rad/s},\ \omega_0 = 2\pi30\,\text{rad/s} \right)
\end{equation} \end{equation}
The obtained "decentralized" loop-gains (i.e. the diagonal element of the controller times the diagonal terms of the plant) are shown in Figure\nbsp{}ref:fig:test_id31_hac_loop_gain. The obtained "decentralized" loop-gains (i.e. the diagonal element of the controller times the diagonal terms of the plant) are shown in Figure\nbsp{}ref:fig:test_id31_hac_loop_gain.
@ -13332,7 +13332,7 @@ The multi-body model was first validated by comparing it with the measured frequ
This validation confirmed that the model can be reliably used to tune the feedback controller and evaluate its performance. This validation confirmed that the model can be reliably used to tune the feedback controller and evaluate its performance.
An interaction analysis using the RGA-number was then performed, which revealed that higher payload masses lead to increased coupling when implementing control in the strut reference frame. An interaction analysis using the RGA-number was then performed, which revealed that higher payload masses lead to increased coupling when implementing control in the strut reference frame.
Based on this analysis, a diagonal controller with a crossover frequency of $5\,\text{Hz}$ was designed, incorporating an integrator, a lead compensator, and a first-order low-pass filter. Based on this analysis, a diagonal controller with a crossover frequency of $5\,\text{Hz}$ was designed, incorporating an integrator and a first-order low-pass filter.
Finally, tomography experiments were simulated to validate the acrshort:haclac architecture. Finally, tomography experiments were simulated to validate the acrshort:haclac architecture.
The closed-loop system remained stable under all tested payload conditions (0 to $39\,\text{kg}$). The closed-loop system remained stable under all tested payload conditions (0 to $39\,\text{kg}$).