授業/制御工学特論2011
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開始行:
*Advanced Automation [#y48807b4]
** &color(green){[lecture #1]}; 2011.9.1 review of classi...
#ref(2011.09.01-1.jpg,left,noimg,whiteboard #1);
#ref(2011.09.01-2.jpg,left,noimg,whiteboard #2);
#ref(2011.09.01-3.jpg,left,noimg,whiteboard #3);
#ref(2011.09.01-4.jpg,left,noimg,whiteboard #4);
** &color(green){[lecture #2]}; 2011.9.8 CACSD introducti...
- introduction of Matlab and Simulink
--[[Basic usage of MATLAB and Simulink>/:~kobayasi/eastti...
used for 情報処理演習及び考究II/Consideration and Practic...
#ref(sample0908.m);
#ref(2011.09.08-1.jpg,left,noimg,whiteboard #1);
** %%&color(green){[lecture #3]}; 2011.9.15 given by Prof...
** %%&color(green){[lecture #4]}; 2011.9.22 given by Prof...
** %%&color(green){[lecture #5]}; 2011.9.29 given by Prof...
** &color(red){supplementary lectures will be given by Pr...
** &color(green){[lecture #3]}; 2011.10.6 CACSD introduct...
+relationship between &color(black,cyan){TF}; and &color(...
#ref(ex1006_1.m)
#ref(mod1006.mdl)
+open-loop stability
-- can be checked by &color(black,cyan){poles of TF}; and...
#ref(ex1006_2.m)
+closed-loop stability
-- can be checked graphically by &color(black,yellow){Nyq...
#ref(ex1006_3.m)
-- can be checked numerically by &color(black,cyan){poles...
#ref(ex1006_4.m)
%-- 10/6/2011 1:25 PM --%
ls
ex1006_1
ex1006_2
ex1006_3
grid on
-0.8*1.5
ex1006_4
#ref(2011.10.06-1.jpg,left,noimg,whiteboard #1);
#ref(2011.10.06-2.jpg,left,noimg,whiteboard #2);
#ref(2011.10.06-3.jpg,left,noimg,whiteboard #3);
** &color(green){[lecture #4]}; 2011.10.13 Intro. to robu...
- H infinity norm
++ robust stabilization
++ &color(black,yellow){performance optimization};
- Example of performance optimization problem : disturban...
-- controller design with trial and error
#ref(ex1013_1.m)
-- controller design with H infinity control theory
#ref(ex1013_2.m)
s = tf('s');
G = 1/(s+1);
norm(G, inf)
G = 1/(s^2+0.1*s+1);
norm(G, inf)
bode(G)
ex1013_1
ex1013_2
#ref(2011.10.13-1.jpg,left,noimg,whiteboard #1);
#ref(2011.10.13-2.jpg,left,noimg,whiteboard #2);
#ref(2011.10.13-3.jpg,left,noimg,whiteboard #3);
#ref(2011.10.13-4.jpg,left,noimg,whiteboard #4);
** &color(green){[lecture #5]}; 2011.10.7 Introduction to...
- H infinity norm
++ &color(black,yellow){robust stabilization};
++ performance optimization
+ a class used to represent plant uncertainty and/or pert...
+ small gain theorem
-- connects the closed-loop H infinity norm and robust st...
-- sketch proof ... Nyquist stability criterion
+ practical example of robust stabilization problem
-- unstable plant with perturbation
#ref(ex1020_1.m)
-- multiplicative uncertainty model
#ref(ex1020_2.m)
-- H infinity controller design
#ref(ex1020_3.m)
#ref(mod1020.mdl)
%-- 10/20/2011 1:41 PM --%
ex1020_1
ex1020_2
ex1020_3
mod1020
c
c = 0.8
#ref(2011.10.20-1.jpg,left,noimg,whiteboard #1);
#ref(2011.10.20-2.jpg,left,noimg,whiteboard #2);
#ref(2011.10.20-3.jpg,left,noimg,whiteboard #3);
#ref(2011.10.20-4.jpg,left,noimg,whiteboard #4);
** &color(green){[lecture #6]}; 2011.10.27 norm (vector s...
- H infinity &color(red){norm}; ... {robust stabilization...
- norm
#ref(norm.pdf);
-- size of {number, signal, system}
-- defined on &color(red){vector space (linear space)};
--- ---> normed linear space
--- ... optimization
- H infinity norm : scalar (SISO) ---> matrix (MIMO)
-- absolute value ---> maximum &color(red){singular value};
#ref(norm2.pdf);
-- &color(black,yellow){robust stabilization or performan...
- reference
-- Feedback control theory / John C. Doyle, Bruce A. Fran...
#ref(feedback_control_theory.jpg);
--- 2. Norms for signals and systems
--- 3. Basic concepts
--- 4. Uncertainty and robustness ... p.62 Eq.(4.10) H in...
-- Robust and optimal control / Kemin Zhou, John C. Doyle...
#ref(robust_and_optimal_control.jpg);
--- 2. Linear algebra (2.7 Vector norms and matrix norms,...
--- 4. Performance specifications (4.1 Normed spaces, 4.3...
--- 9. Model uncertainty and robustness
--- 16. H infinity control: simple case
--- 17. H infinity control: general case
#ref(2011.10.27-1.jpg,left,noimg,whiteboard #1);
#ref(2011.10.27-2.jpg,left,noimg,whiteboard #2);
#ref(2011.10.27-3.jpg,left,noimg,whiteboard #3);
#ref(2011.10.27-4.jpg,left,noimg,whiteboard #4);
#ref(2011.10.27-5.jpg,left,noimg,whiteboard #5);
** &color(green){[lecture #8]}; 2011.11.10 state space re...
see [[Prof. Kimura's page>http://sessyu.nagaokaut.ac.jp/~...
#ref(aa-111110-1.jpg,left,noimg,whiteboard #1);
#ref(aa-111110-2.jpg,left,noimg,whiteboard #2);
#ref(aa-111110-3.jpg,left,noimg,whiteboard #3);
#ref(aa-111110-4.jpg,left,noimg,whiteboard #4);
** &color(green){[lecture #9]}; 2011.12.1 robust control ...
** &color(green){[lecture #10]}; 2011.12.8 Speed control ...
- Experimental setup
#ref(apparatus.ppt);
#ref(setup.pdf)
-- Objective for control system design
++ speed tracking
++ robust against inertia-load variation
- Modelling
-- frequency response experiment results:
#ref(frdata_small_offset0.dat)
#ref(frdata_small_offset5.dat)
#ref(frdata_small_offset10.dat)
#ref(frdata_large_offset0.dat)
#ref(frdata_large_offset5.dat)
#ref(frdata_large_offset10.dat)
-- example of m-file
#ref(freqresp.m)
#ref(nominal.m)
#ref(weight.m);
>> freqresp
>> nominal
>> weight
- Controller design (mixed sensitivity problem)
-- example of m-file
#ref(cont.m)
>> cont
-- design example
#ref(cont.dat)
#ref(cont_order.dat)
#ref(cont.mat)
#ref(result_small.dat)
#ref(result_large.dat)
//-- example of m-file to compare designed controllers
//#ref(compare.m)
- report
+design your controller(s) so that the system performance...
+Draw the following figures and explain the difference be...
++bode diagram of controllers
++gain characteristic of closed-loop systems
++time response of control experiment
+Why is the performance of your system improved(or unfort...
--&size(30){&color(red){due date: 28th(Wed) Dec 17:00};};
--submit your report(pdf or doc) by e-mail to kobayasi@na...
--You can use Japanese
--maximum controller order is 20
--submit your cont.dat, cont_order.dat, and cont.mat to k...
- program sources for frequency response experiment
#ref(freqresp.h)
#ref(freqresp_module.c)
#ref(freqresp_app.c)
-- format of frdata.dat file
--- 1st column: frequency (Hz)
--- 2nd column: gain
--- 3rd column: phase (deg)
- program sources for control experiment
#ref(hinf.h)
#ref(hinf_module.c)
#ref(hinf_app.c)
-- format of result.dat file
--- 1st column: time (s)
--- 2nd column: motor speed (rad/s)
--- 3rd column: motor torque (Nm)
--- 4th column: reference speed (rad/s)
- configuration of control experiment
-- reference signal is generated as described in hinf_mod...
if((t > 3)&&(t < 7)){
r = 10.0;
}else{
r = 5;
}
-- two inertia-load discs (small and large) are used
- Difficulties of our plant:
As motor speed is approximately calculated by using diffe...
thetaM_rad = (double)read_theta(0) / (double)Pn212 * 2 *...
speedM_rad = (thetaM_rad - thetaM_rad_before) / msg->sam...
thetaM_rad_before = thetaM_rad
sampling period should not become too small.
On the other hand, sampling period should be chosen as sm...
Therefore, we have a dilemma to control our plant.
The sampling period 0.25 msec was chosen by traial and er...
The gain in high frequency range of continuous-time contr...
#ref(2011.12.08-1.jpg,left,noimg,whiteboard #1);
%-- 12/8/2011 1:22 PM --%
freqresp
nominal
weight
load result_small.dat
result_small
plot(result_small(:,1),result_small(:,2))
plot(result_small(:,1),result_small(:,2), 'b', result_sm...
** &color(green){[lecture #11]}; 2011.12.15 Speed control...
-explanation of design example (cont. from the previous l...
-preparation of your own controller(s)
#ref(2011.12.15-1.jpg,left,noimg,whiteboard #1);
#ref(2011.12.15-2.jpg,left,noimg,whiteboard #2);
%-- 12/15/2011 1:06 PM --%
cont
help hinfsyn
K
Ktf = tf(K)
bode(K, 'r', Ktf, 'b')
legend('ss', 'tf')
help fitsys
** &color(green){[lecture #12]}; 2011.12.22 Speed control...
-preparation of your own controller(s)
[[participant list2011]]
** &color(red){supplementary lectures will be given by Pr...
-example for changing ws = 2 pi 0.1 -> 2 pi 0.01
#ref(cont_ws.m, cont.m);
-example to compare time responces
#ref(compare_result.m);
%-- 12/22/2011 1:20 PM --%
nominal
ctrlpref
nominal
weight
cont
ks
cont
compare_result
//&color(black,red){!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!...
**related links [#m6b40e8e]
//-東ティモール工学部復興支援/support of rehabilitation f...
//--[[How to control objects>/:~kobayasi/easttimor/2009/i...
--[[Prof. Kimura's page>http://sessyu.nagaokaut.ac.jp/~ki...
終了行:
*Advanced Automation [#y48807b4]
** &color(green){[lecture #1]}; 2011.9.1 review of classi...
#ref(2011.09.01-1.jpg,left,noimg,whiteboard #1);
#ref(2011.09.01-2.jpg,left,noimg,whiteboard #2);
#ref(2011.09.01-3.jpg,left,noimg,whiteboard #3);
#ref(2011.09.01-4.jpg,left,noimg,whiteboard #4);
** &color(green){[lecture #2]}; 2011.9.8 CACSD introducti...
- introduction of Matlab and Simulink
--[[Basic usage of MATLAB and Simulink>/:~kobayasi/eastti...
used for 情報処理演習及び考究II/Consideration and Practic...
#ref(sample0908.m);
#ref(2011.09.08-1.jpg,left,noimg,whiteboard #1);
** %%&color(green){[lecture #3]}; 2011.9.15 given by Prof...
** %%&color(green){[lecture #4]}; 2011.9.22 given by Prof...
** %%&color(green){[lecture #5]}; 2011.9.29 given by Prof...
** &color(red){supplementary lectures will be given by Pr...
** &color(green){[lecture #3]}; 2011.10.6 CACSD introduct...
+relationship between &color(black,cyan){TF}; and &color(...
#ref(ex1006_1.m)
#ref(mod1006.mdl)
+open-loop stability
-- can be checked by &color(black,cyan){poles of TF}; and...
#ref(ex1006_2.m)
+closed-loop stability
-- can be checked graphically by &color(black,yellow){Nyq...
#ref(ex1006_3.m)
-- can be checked numerically by &color(black,cyan){poles...
#ref(ex1006_4.m)
%-- 10/6/2011 1:25 PM --%
ls
ex1006_1
ex1006_2
ex1006_3
grid on
-0.8*1.5
ex1006_4
#ref(2011.10.06-1.jpg,left,noimg,whiteboard #1);
#ref(2011.10.06-2.jpg,left,noimg,whiteboard #2);
#ref(2011.10.06-3.jpg,left,noimg,whiteboard #3);
** &color(green){[lecture #4]}; 2011.10.13 Intro. to robu...
- H infinity norm
++ robust stabilization
++ &color(black,yellow){performance optimization};
- Example of performance optimization problem : disturban...
-- controller design with trial and error
#ref(ex1013_1.m)
-- controller design with H infinity control theory
#ref(ex1013_2.m)
s = tf('s');
G = 1/(s+1);
norm(G, inf)
G = 1/(s^2+0.1*s+1);
norm(G, inf)
bode(G)
ex1013_1
ex1013_2
#ref(2011.10.13-1.jpg,left,noimg,whiteboard #1);
#ref(2011.10.13-2.jpg,left,noimg,whiteboard #2);
#ref(2011.10.13-3.jpg,left,noimg,whiteboard #3);
#ref(2011.10.13-4.jpg,left,noimg,whiteboard #4);
** &color(green){[lecture #5]}; 2011.10.7 Introduction to...
- H infinity norm
++ &color(black,yellow){robust stabilization};
++ performance optimization
+ a class used to represent plant uncertainty and/or pert...
+ small gain theorem
-- connects the closed-loop H infinity norm and robust st...
-- sketch proof ... Nyquist stability criterion
+ practical example of robust stabilization problem
-- unstable plant with perturbation
#ref(ex1020_1.m)
-- multiplicative uncertainty model
#ref(ex1020_2.m)
-- H infinity controller design
#ref(ex1020_3.m)
#ref(mod1020.mdl)
%-- 10/20/2011 1:41 PM --%
ex1020_1
ex1020_2
ex1020_3
mod1020
c
c = 0.8
#ref(2011.10.20-1.jpg,left,noimg,whiteboard #1);
#ref(2011.10.20-2.jpg,left,noimg,whiteboard #2);
#ref(2011.10.20-3.jpg,left,noimg,whiteboard #3);
#ref(2011.10.20-4.jpg,left,noimg,whiteboard #4);
** &color(green){[lecture #6]}; 2011.10.27 norm (vector s...
- H infinity &color(red){norm}; ... {robust stabilization...
- norm
#ref(norm.pdf);
-- size of {number, signal, system}
-- defined on &color(red){vector space (linear space)};
--- ---> normed linear space
--- ... optimization
- H infinity norm : scalar (SISO) ---> matrix (MIMO)
-- absolute value ---> maximum &color(red){singular value};
#ref(norm2.pdf);
-- &color(black,yellow){robust stabilization or performan...
- reference
-- Feedback control theory / John C. Doyle, Bruce A. Fran...
#ref(feedback_control_theory.jpg);
--- 2. Norms for signals and systems
--- 3. Basic concepts
--- 4. Uncertainty and robustness ... p.62 Eq.(4.10) H in...
-- Robust and optimal control / Kemin Zhou, John C. Doyle...
#ref(robust_and_optimal_control.jpg);
--- 2. Linear algebra (2.7 Vector norms and matrix norms,...
--- 4. Performance specifications (4.1 Normed spaces, 4.3...
--- 9. Model uncertainty and robustness
--- 16. H infinity control: simple case
--- 17. H infinity control: general case
#ref(2011.10.27-1.jpg,left,noimg,whiteboard #1);
#ref(2011.10.27-2.jpg,left,noimg,whiteboard #2);
#ref(2011.10.27-3.jpg,left,noimg,whiteboard #3);
#ref(2011.10.27-4.jpg,left,noimg,whiteboard #4);
#ref(2011.10.27-5.jpg,left,noimg,whiteboard #5);
** &color(green){[lecture #8]}; 2011.11.10 state space re...
see [[Prof. Kimura's page>http://sessyu.nagaokaut.ac.jp/~...
#ref(aa-111110-1.jpg,left,noimg,whiteboard #1);
#ref(aa-111110-2.jpg,left,noimg,whiteboard #2);
#ref(aa-111110-3.jpg,left,noimg,whiteboard #3);
#ref(aa-111110-4.jpg,left,noimg,whiteboard #4);
** &color(green){[lecture #9]}; 2011.12.1 robust control ...
** &color(green){[lecture #10]}; 2011.12.8 Speed control ...
- Experimental setup
#ref(apparatus.ppt);
#ref(setup.pdf)
-- Objective for control system design
++ speed tracking
++ robust against inertia-load variation
- Modelling
-- frequency response experiment results:
#ref(frdata_small_offset0.dat)
#ref(frdata_small_offset5.dat)
#ref(frdata_small_offset10.dat)
#ref(frdata_large_offset0.dat)
#ref(frdata_large_offset5.dat)
#ref(frdata_large_offset10.dat)
-- example of m-file
#ref(freqresp.m)
#ref(nominal.m)
#ref(weight.m);
>> freqresp
>> nominal
>> weight
- Controller design (mixed sensitivity problem)
-- example of m-file
#ref(cont.m)
>> cont
-- design example
#ref(cont.dat)
#ref(cont_order.dat)
#ref(cont.mat)
#ref(result_small.dat)
#ref(result_large.dat)
//-- example of m-file to compare designed controllers
//#ref(compare.m)
- report
+design your controller(s) so that the system performance...
+Draw the following figures and explain the difference be...
++bode diagram of controllers
++gain characteristic of closed-loop systems
++time response of control experiment
+Why is the performance of your system improved(or unfort...
--&size(30){&color(red){due date: 28th(Wed) Dec 17:00};};
--submit your report(pdf or doc) by e-mail to kobayasi@na...
--You can use Japanese
--maximum controller order is 20
--submit your cont.dat, cont_order.dat, and cont.mat to k...
- program sources for frequency response experiment
#ref(freqresp.h)
#ref(freqresp_module.c)
#ref(freqresp_app.c)
-- format of frdata.dat file
--- 1st column: frequency (Hz)
--- 2nd column: gain
--- 3rd column: phase (deg)
- program sources for control experiment
#ref(hinf.h)
#ref(hinf_module.c)
#ref(hinf_app.c)
-- format of result.dat file
--- 1st column: time (s)
--- 2nd column: motor speed (rad/s)
--- 3rd column: motor torque (Nm)
--- 4th column: reference speed (rad/s)
- configuration of control experiment
-- reference signal is generated as described in hinf_mod...
if((t > 3)&&(t < 7)){
r = 10.0;
}else{
r = 5;
}
-- two inertia-load discs (small and large) are used
- Difficulties of our plant:
As motor speed is approximately calculated by using diffe...
thetaM_rad = (double)read_theta(0) / (double)Pn212 * 2 *...
speedM_rad = (thetaM_rad - thetaM_rad_before) / msg->sam...
thetaM_rad_before = thetaM_rad
sampling period should not become too small.
On the other hand, sampling period should be chosen as sm...
Therefore, we have a dilemma to control our plant.
The sampling period 0.25 msec was chosen by traial and er...
The gain in high frequency range of continuous-time contr...
#ref(2011.12.08-1.jpg,left,noimg,whiteboard #1);
%-- 12/8/2011 1:22 PM --%
freqresp
nominal
weight
load result_small.dat
result_small
plot(result_small(:,1),result_small(:,2))
plot(result_small(:,1),result_small(:,2), 'b', result_sm...
** &color(green){[lecture #11]}; 2011.12.15 Speed control...
-explanation of design example (cont. from the previous l...
-preparation of your own controller(s)
#ref(2011.12.15-1.jpg,left,noimg,whiteboard #1);
#ref(2011.12.15-2.jpg,left,noimg,whiteboard #2);
%-- 12/15/2011 1:06 PM --%
cont
help hinfsyn
K
Ktf = tf(K)
bode(K, 'r', Ktf, 'b')
legend('ss', 'tf')
help fitsys
** &color(green){[lecture #12]}; 2011.12.22 Speed control...
-preparation of your own controller(s)
[[participant list2011]]
** &color(red){supplementary lectures will be given by Pr...
-example for changing ws = 2 pi 0.1 -> 2 pi 0.01
#ref(cont_ws.m, cont.m);
-example to compare time responces
#ref(compare_result.m);
%-- 12/22/2011 1:20 PM --%
nominal
ctrlpref
nominal
weight
cont
ks
cont
compare_result
//&color(black,red){!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!...
**related links [#m6b40e8e]
//-東ティモール工学部復興支援/support of rehabilitation f...
//--[[How to control objects>/:~kobayasi/easttimor/2009/i...
--[[Prof. Kimura's page>http://sessyu.nagaokaut.ac.jp/~ki...
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