Add study about reference tracking

This commit is contained in:
Thomas Dehaeze 2020-03-11 18:58:56 +01:00
parent 0aad830597
commit 7d67ff9ef2
46 changed files with 1310 additions and 34 deletions

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@ -38,6 +38,19 @@
#+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png") #+PROPERTY: header-args:latex+ :post pdf2svg(file=*this*, ext="png")
:END: :END:
* Introduction :ignore:
Control architectures can be divided in different ways.
It can depend on the sensor used:
- Sensors located in each strut: relative motion, force sensor, inertial sensor
- Sensors measuring the relative motion between the fixed base and the mobile platform
- Inertial sensors located on the mobile platform
It can also depends on the control objective:
- Reference Tracking
- Active Damping
- Vibration Isolation
* HAC-LAC (Cascade) Control - Integral Control * HAC-LAC (Cascade) Control - Integral Control
** Introduction ** Introduction
In this section, we wish to study the use of the High Authority Control - Low Authority Control (HAC-LAC) architecture on the Stewart platform. In this section, we wish to study the use of the High Authority Control - Low Authority Control (HAC-LAC) architecture on the Stewart platform.
@ -760,6 +773,8 @@ Let's define the system as shown in figure [[fig:general_control_names]].
#+name: tab:general_plant_signals #+name: tab:general_plant_signals
#+caption: Signals definition for the generalized plant #+caption: Signals definition for the generalized plant
| | *Symbol* | *Meaning* |
|---------------------+-----------------------------+----------------------------------------|
| *Exogenous Inputs* | $\bm{\mathcal{X}}_w$ | Ground motion | | *Exogenous Inputs* | $\bm{\mathcal{X}}_w$ | Ground motion |
| | $\bm{\mathcal{F}}_d$ | External Forces applied to the Payload | | | $\bm{\mathcal{F}}_d$ | External Forces applied to the Payload |
| | $\bm{r}$ | Reference signal for tracking | | | $\bm{r}$ | Reference signal for tracking |
@ -1177,9 +1192,150 @@ The results are shown in figure
#+caption: Frobenius norm of the Compliance and transmissibility matrices ([[./figs/static_decoupling_C_T_frobenius_norm.png][png]], [[./figs/static_decoupling_C_T_frobenius_norm.pdf][pdf]]) #+caption: Frobenius norm of the Compliance and transmissibility matrices ([[./figs/static_decoupling_C_T_frobenius_norm.png][png]], [[./figs/static_decoupling_C_T_frobenius_norm.pdf][pdf]])
[[file:figs/static_decoupling_C_T_frobenius_norm.png]] [[file:figs/static_decoupling_C_T_frobenius_norm.png]]
** Decoupling at Crossover ** TODO Decoupling at Crossover
- [ ] Find a method for real approximation of a complex matrix - [ ] Find a method for real approximation of a complex matrix
* Time Domain Simulation
** Matlab Init :noexport:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<<matlab-dir>>
#+end_src
#+begin_src matlab :exports none :results silent :noweb yes
<<matlab-init>>
#+end_src
#+begin_src matlab
simulinkproject('../');
#+end_src
#+begin_src matlab
open('stewart_platform_model.slx')
#+end_src
** Initialization
We first initialize the Stewart platform.
#+begin_src matlab
stewart = initializeStewartPlatform();
stewart = initializeFramesPositions(stewart, 'H', 90e-3, 'MO_B', 45e-3);
stewart = generateGeneralConfiguration(stewart);
stewart = computeJointsPose(stewart);
stewart = initializeStrutDynamics(stewart);
stewart = initializeJointDynamics(stewart, 'type_F', 'universal', 'type_M', 'spherical');
stewart = initializeCylindricalPlatforms(stewart);
stewart = initializeCylindricalStruts(stewart);
stewart = computeJacobian(stewart);
stewart = initializeStewartPose(stewart);
stewart = initializeInertialSensor(stewart, 'type', 'none');
#+end_src
The rotation point of the ground is located at the origin of frame $\{A\}$.
#+begin_src matlab
ground = initializeGround('type', 'rigid', 'rot_point', stewart.platform_F.FO_A);
payload = initializePayload('type', 'none');
#+end_src
#+begin_src matlab
load('./mat/motion_error_ol.mat', 'Eg')
#+end_src
** HAC IFF
#+begin_src matlab
controller = initializeController('type', 'iff');
K_iff = -(1e4/s)*eye(6);
%% Name of the Simulink File
mdl = 'stewart_platform_model';
%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Controller'], 1, 'input'); io_i = io_i + 1; % Actuator Force Inputs [N]
io(io_i) = linio([mdl, '/Absolute Motion Sensor'], 1, 'openoutput'); io_i = io_i + 1; % Absolute Sensor [m, rad]
%% Run the linearization
G_iff = linearize(mdl, io);
G_iff.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
G_iff.OutputName = {'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'};
Gc_iff = minreal(G_iff)/stewart.kinematics.J';
Gc_iff.InputName = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'};
#+end_src
#+begin_src matlab
wc = 2*pi*100; % Wanted Bandwidth [rad/s]
h = 1.2;
H_lead = 1/h*(1 + s/(wc/h))/(1 + s/(wc*h));
Kd_iff = diag(1./abs(diag(freqresp(1/s*Gc_iff, wc)))) .* H_lead .* 1/s;
K_hac_iff = inv(stewart.kinematics.J')*Kd_iff;
#+end_src
#+begin_src matlab
controller = initializeController('type', 'hac-iff');
#+end_src
** HAC-DVF
#+begin_src matlab
controller = initializeController('type', 'dvf');
K_dvf = -1e4*s/(1+s/2/pi/5000)*eye(6);
%% Name of the Simulink File
mdl = 'stewart_platform_model';
%% Input/Output definition
clear io; io_i = 1;
io(io_i) = linio([mdl, '/Controller'], 1, 'input'); io_i = io_i + 1; % Actuator Force Inputs [N]
io(io_i) = linio([mdl, '/Absolute Motion Sensor'], 1, 'openoutput'); io_i = io_i + 1; % Absolute Sensor [m, rad]
%% Run the linearization
G_dvf = linearize(mdl, io);
G_dvf.InputName = {'F1', 'F2', 'F3', 'F4', 'F5', 'F6'};
G_dvf.OutputName = {'Dx', 'Dy', 'Dz', 'Rx', 'Ry', 'Rz'};
Gc_dvf = minreal(G_dvf)/stewart.kinematics.J';
Gc_dvf.InputName = {'Fx', 'Fy', 'Fz', 'Mx', 'My', 'Mz'};
#+end_src
#+begin_src matlab
wc = 2*pi*100; % Wanted Bandwidth [rad/s]
h = 1.2;
H_lead = 1/h*(1 + s/(wc/h))/(1 + s/(wc*h));
Kd_dvf = diag(1./abs(diag(freqresp(1/s*Gc_dvf, wc)))) .* H_lead .* 1/s;
K_hac_dvf = inv(stewart.kinematics.J')*Kd_dvf;
#+end_src
#+begin_src matlab
controller = initializeController('type', 'hac-dvf');
#+end_src
** Results
#+begin_src matlab
figure;
subplot(1, 2, 1);
hold on;
plot(Eg.Time, Eg.Data(:, 1), 'DisplayName', 'X');
plot(Eg.Time, Eg.Data(:, 2), 'DisplayName', 'Y');
plot(Eg.Time, Eg.Data(:, 3), 'DisplayName', 'Z');
hold off;
xlabel('Time [s]');
ylabel('Position error [m]');
legend();
subplot(1, 2, 2);
hold on;
plot(simout.Xa.Time, simout.Xa.Data(:, 1));
plot(simout.Xa.Time, simout.Xa.Data(:, 2));
plot(simout.Xa.Time, simout.Xa.Data(:, 3));
hold off;
xlabel('Time [s]');
ylabel('Orientation error [rad]');
#+end_src
* Functions * Functions
** =initializeController=: Initialize the Controller ** =initializeController=: Initialize the Controller
:PROPERTIES: :PROPERTIES:
@ -1208,7 +1364,7 @@ The results are shown in figure
:END: :END:
#+begin_src matlab #+begin_src matlab
arguments arguments
args.type char {mustBeMember(args.type, {'open-loop', 'iff', 'dvf', 'hac-iff', 'hac-dvf'})} = 'open-loop' args.type char {mustBeMember(args.type, {'open-loop', 'iff', 'dvf', 'hac-iff', 'hac-dvf', 'ref-track-L', 'ref-track-X'})} = 'open-loop'
end end
#+end_src #+end_src
@ -1236,5 +1392,9 @@ The results are shown in figure
controller.type = 3; controller.type = 3;
case 'hac-dvf' case 'hac-dvf'
controller.type = 4; controller.type = 4;
case 'ref-track-L'
controller.type = 5;
case 'ref-track-X'
controller.type = 6;
end end
#+end_src #+end_src

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