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Thomas Dehaeze
2021-01-11 09:44:23 +01:00
parent c9fd923312
commit cb32883aa1
2 changed files with 213 additions and 205 deletions
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@@ -74,6 +74,9 @@ In this part, diagonal control using both the SVD and the Jacobian matrices are
- Section [[sec:gravimeter_decoupled_plant]]: the obtained decoupled plants are compared
- Section [[sec:gravimeter_diagonal_control]]: the diagonal controller is developed
- Section [[sec:gravimeter_closed_loop_results]]: the obtained closed-loop performances for the two methods are compared
- Section [[sec:robustness_actuator_position]]: the robustness to a change of actuator position is evaluated
- Section [[sec:choice_jacobian_reference]]: the choice of the reference frame for the evaluation of the Jacobian is discussed
- Section [[sec:decoupling_performances]]: the decoupling performances of SVD is evaluated for a low damped and an highly damped system
** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
@@ -1065,9 +1068,9 @@ G_cen_b = feedback(G, pinv(Jt')*K_cen*pinv(Ja));
G_svd_b = feedback(G, inv(V')*K_svd*U_inv(1:3, :));
#+end_src
The new plant is computed, and the centralized and SVD control architectures are applied using the previsouly computed Jacobian matrices and $U$ and $V$ matrices.
The new plant is computed, and the centralized and SVD control architectures are applied using the previously computed Jacobian matrices and $U$ and $V$ matrices.
The closed-loop system are still stable, and their
The closed-loop system are still stable in both cases, and the obtained transmissibility are equivalent as shown in Figure [[fig:gravimeter_transmissibility_offset_act]].
#+begin_src matlab :exports results
freqs = logspace(-2, 2, 1000);
@@ -1365,6 +1368,7 @@ If not the case, the system can either be decoupled as low frequency if the Jaco
Or it can be decoupled at high frequency if the Jacobians are evaluated at the CoM.
** SVD decoupling performances
<<sec:decoupling_performances>>
As the SVD is applied on a *real approximation* of the plant dynamics at a frequency $\omega_0$, it is foreseen that the effectiveness of the decoupling depends on the validity of the real approximation.
Let's do the SVD decoupling on a plant that is mostly real (low damping) and one with a large imaginary part (larger damping).