授業/制御工学特論2010
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開始行:
*Advanced Automation [#n6ab2895]
** &color(green){[lecture #1]}; 2010.9.2 review of classi...
** &color(green){[lecture #2]}; 2010.9.9 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(2010.9.9-1.jpg,left,noimg,whiteboard #1);
#ref(2010.9.9-2.jpg,left,noimg,whiteboard #2);
** &color(green){[lecture #3]}; 2010.9.16 CACSD introduct...
-review of clasical control theory
++ transfer function
++ Bode diagram
++ characteristics of 2nd-order system
++ Nyquist stability criterion
++ gain margin and phase margin
-review of modern control theory
++ state-space representation
#ref(ex1.m)
#ref(mod1.mdl)
#ref(ex2.m)
#ref(ex3.m)
#ref(ex4.m)
#ref(2010.9.16-1.jpg,left,noimg,whiteboard #1);
#ref(2010.9.16-2.jpg,left,noimg,whiteboard #2);
** &color(green){[lecture #4]}; 2010.9.30 Intro. to Robus...
- H infinity norm
++ robust stabilization
++ performance improvement
#ref(ex21.m)
#ref(ex22.m)
s = tf('s')
G = 1/(s+1)
norm(G, 'inf')
P = 1/(s^2 + 0.2*s + 1)
K = 1
nyquist(P*K)
help impulse
impulse(P)
T = 1/(1 + P*K)
impulse(T)
sqrt(2)/(2*pi)
1/ans
step(T)
ex21
ex22
#ref(2010.9.30-1.jpg,left,noimg,whiteboard #1);
#ref(2010.9.30-2.jpg,left,noimg,whiteboard #2);
#ref(2010.9.30-3.jpg,left,noimg,whiteboard #3);
** &color(green){[lecture #5]}; 2010.10.7 Introduction to...
- H infinity norm
++ robust stabilization <--
++ performance improvement
#ref(ex23.m)
#ref(ex24.m)
#ref(ex25.m)
#ref(mod2.mdl)
#ref(2010.10.7-1.jpg,left,noimg,whiteboard #1);
#ref(2010.10.7-2.jpg,left,noimg,whiteboard #2);
#ref(2010.10.7-3.jpg,left,noimg,whiteboard #3);
#ref(2010.10.7-4.jpg,left,noimg,whiteboard #4);
** &color(green){[lecture #6]}; 2010.10.14 norm, vector s...
- H infinity &color(red){norm}; ... {robust stabilization...
- norm
-- size of {number, signal, system}
-- defined on &color(red){vector space (linear space)};
--- ---> normed linear space
--- ... optimization
#ref(norm.pdf)
#ref(2010.10.14-1.jpg,left,noimg,whiteboard #1);
#ref(2010.10.14-2.jpg,left,noimg,whiteboard #2);
#ref(2010.10.14-3.jpg,left,noimg,whiteboard #3);
#ref(2010.10.14-4.jpg,left,noimg,whiteboard #4);
** &color(green){[lecture #7]}; 2010.10.21 eigenvalue, ei...
- H infinity norm : scalar (SISO) ---> matrix (MIMO)
-- absolute value ---> maximum &color(red){singular value...
-- background: mixed sensitivity problem {robust stabiliz...
#ref(norm2.pdf)
A = [2, 1; 0, 1]
[X, L] = eig(A)
X*L/X - A
[U, S, V] = svd(A)
U*U'
V*V'
U*S*V'
U*S*V' - A
sqrt(eig(A'*A))
S
#ref(2010.10.21-1.jpg,left,noimg,whiteboard #1);
#ref(2010.10.21-2.jpg,left,noimg,whiteboard #2);
#ref(2010.10.21-3.jpg,left,noimg,whiteboard #3);
#ref(2010.10.21-4.jpg,left,noimg,whiteboard #4);
#ref(2010.10.21-5.jpg,left,noimg,whiteboard #5);
** &color(green){[lecture #8]}; 2010.10.28 state space re...
#ref(2010.10.28-1.jpg,left,noimg,whiteboard #1);
#ref(2010.10.28-2.jpg,left,noimg,whiteboard #2);
#ref(ex26.m)
** &color(green){[lecture #9]}; 2010.11.4 robust control ...
see [[RubustControlOfPneumatic-e.pdf>http://sessyu.nagaok...
#ref(2010.11.4-1.jpg,left,noimg,whiteboard #1);
#ref(2010.11.4-2.jpg,left,noimg,whiteboard #2);
** &color(green){[lecture #10]}; 2010.11.11 robust contro...
+ Design H infinity controller with Eqs.(41)-(47) and gen...
++ Confirm the following m-file for design:
#ref(pneum.m);
#ref(pneum_ans.m);
++ Derive the generalized plant by hand and correct the m...
++ Run the m-file to find controller.
+ Simulation
#ref(simu_pneum.mdl);
#ref(simu_pneum_noise.mdl);
simu_pneum
plot(t, y, 'r', t, r, 'b');
simu_pneum_noise
plot(t, y, 'r', t, n, 'b')
#ref(2010.11.11-1.jpg,left,noimg,whiteboard #1);
#ref(2010.11.11-2.jpg,left,noimg,whiteboard #2);
** &color(green){[lecture #11]}; 2010.11.18 robust contro...
Exercise
+step response
+noise response (noise type: step, sinusoidal wave 1Hz, 5...
+initial response (x(0) = [1;0;0])
#ref(2010.11.18-1.jpg,left,noimg,whiteboard #1);
** &color(green){[lecture #12]}; 2010.11.25 Speed control...
- simulation (cont. from Nov.18)
- Problem setup
#ref(apparatus.pptx);
- Modelling (frequency response experiment)
#ref(2010.11.25-1.jpg,left,noimg,whiteboard #1);
** &color(green){[lecture #13]}; 2010.12.2 Speed control ...
- %%reduced-order controller design%% (will be given by P...
#ref(2010.12.2-1.jpg,left,noimg,whiteboard #1);
#ref(2010.12.2-2.jpg,left,noimg,whiteboard #2);
- Problem setup
-- Objective for control system design
++ speed tracking
++ robust against inertia-load variation
#ref(setup.pdf)
- Modelling
-- frequency response experiment results:
#ref(frdata_offset0_small.dat)
#ref(frdata_offset0_large.dat)
#ref(frdata_offset5_small.dat)
#ref(frdata_offset5_large.dat)
#ref(frdata_offset10_small.dat)
#ref(frdata_offset10_large.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 1 (wt1 = 2*pi*50 is set in weight.m)
#ref(cont1.dat)
#ref(cont_order1.dat)
#ref(cont1.mat)
#ref(result_small1.dat)
#ref(result_large1.dat)
-- design example 2 (wt1 = 2*pi*20 is set in weight.m)
#ref(cont2.dat)
#ref(cont_order2.dat)
#ref(cont2.mat)
#ref(result_small2.dat)
#ref(result_large2.dat)
-- example of m-file to compare designed controllers
#ref(compare.m)
- report
+design your controller so that the system performance is...
+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(Tue) 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 and cont_order.dat to kobayasi@nag...
- 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(1) / (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...
** &color(green){[lecture #14]}; 2010.12.9 Speed control ...
Due to a dimension change of the driven shaft, frequency ...
-- frequency response experiment results:
#ref(frdata_offset5_small_fixed.dat)
#ref(frdata_offset5_large_fixed.dat)
#ref(frdata_offset10_small_fixed.dat)
#ref(frdata_offset10_large_fixed.dat)
-- example of m-file
#ref(freqresp_fixed.m)
#ref(nominal_fixed.m)
#ref(weight_fixed.m);
#ref(cont_fixed.m)
-- design example 1 (wt1 = 2*pi*20 is set in weight.m)
#ref(cont1_fixed.dat)
#ref(cont_order1_fixed.dat)
#ref(cont1_fixed.mat)
#ref(result_small1_fixed.dat)
#ref(result_large1_fixed.dat)
-- design example 2 (wt1 = 2*pi*5 is set in weight.m)
#ref(cont2_fixed.dat)
#ref(cont_order2_fixed.dat)
#ref(cont2_fixed.mat)
#ref(result_small2_fixed.dat)
#ref(result_large2_fixed.dat)
#ref(2010.12.9-1.jpg,left,noimg,whiteboard #1);
** &color(green){[lecture #15]}; 2010.12.16 Speed control...
-preparation of your own controller(s)
[[participant list2010]]
**related links [#c31aa7a5]
//-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 [#n6ab2895]
** &color(green){[lecture #1]}; 2010.9.2 review of classi...
** &color(green){[lecture #2]}; 2010.9.9 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(2010.9.9-1.jpg,left,noimg,whiteboard #1);
#ref(2010.9.9-2.jpg,left,noimg,whiteboard #2);
** &color(green){[lecture #3]}; 2010.9.16 CACSD introduct...
-review of clasical control theory
++ transfer function
++ Bode diagram
++ characteristics of 2nd-order system
++ Nyquist stability criterion
++ gain margin and phase margin
-review of modern control theory
++ state-space representation
#ref(ex1.m)
#ref(mod1.mdl)
#ref(ex2.m)
#ref(ex3.m)
#ref(ex4.m)
#ref(2010.9.16-1.jpg,left,noimg,whiteboard #1);
#ref(2010.9.16-2.jpg,left,noimg,whiteboard #2);
** &color(green){[lecture #4]}; 2010.9.30 Intro. to Robus...
- H infinity norm
++ robust stabilization
++ performance improvement
#ref(ex21.m)
#ref(ex22.m)
s = tf('s')
G = 1/(s+1)
norm(G, 'inf')
P = 1/(s^2 + 0.2*s + 1)
K = 1
nyquist(P*K)
help impulse
impulse(P)
T = 1/(1 + P*K)
impulse(T)
sqrt(2)/(2*pi)
1/ans
step(T)
ex21
ex22
#ref(2010.9.30-1.jpg,left,noimg,whiteboard #1);
#ref(2010.9.30-2.jpg,left,noimg,whiteboard #2);
#ref(2010.9.30-3.jpg,left,noimg,whiteboard #3);
** &color(green){[lecture #5]}; 2010.10.7 Introduction to...
- H infinity norm
++ robust stabilization <--
++ performance improvement
#ref(ex23.m)
#ref(ex24.m)
#ref(ex25.m)
#ref(mod2.mdl)
#ref(2010.10.7-1.jpg,left,noimg,whiteboard #1);
#ref(2010.10.7-2.jpg,left,noimg,whiteboard #2);
#ref(2010.10.7-3.jpg,left,noimg,whiteboard #3);
#ref(2010.10.7-4.jpg,left,noimg,whiteboard #4);
** &color(green){[lecture #6]}; 2010.10.14 norm, vector s...
- H infinity &color(red){norm}; ... {robust stabilization...
- norm
-- size of {number, signal, system}
-- defined on &color(red){vector space (linear space)};
--- ---> normed linear space
--- ... optimization
#ref(norm.pdf)
#ref(2010.10.14-1.jpg,left,noimg,whiteboard #1);
#ref(2010.10.14-2.jpg,left,noimg,whiteboard #2);
#ref(2010.10.14-3.jpg,left,noimg,whiteboard #3);
#ref(2010.10.14-4.jpg,left,noimg,whiteboard #4);
** &color(green){[lecture #7]}; 2010.10.21 eigenvalue, ei...
- H infinity norm : scalar (SISO) ---> matrix (MIMO)
-- absolute value ---> maximum &color(red){singular value...
-- background: mixed sensitivity problem {robust stabiliz...
#ref(norm2.pdf)
A = [2, 1; 0, 1]
[X, L] = eig(A)
X*L/X - A
[U, S, V] = svd(A)
U*U'
V*V'
U*S*V'
U*S*V' - A
sqrt(eig(A'*A))
S
#ref(2010.10.21-1.jpg,left,noimg,whiteboard #1);
#ref(2010.10.21-2.jpg,left,noimg,whiteboard #2);
#ref(2010.10.21-3.jpg,left,noimg,whiteboard #3);
#ref(2010.10.21-4.jpg,left,noimg,whiteboard #4);
#ref(2010.10.21-5.jpg,left,noimg,whiteboard #5);
** &color(green){[lecture #8]}; 2010.10.28 state space re...
#ref(2010.10.28-1.jpg,left,noimg,whiteboard #1);
#ref(2010.10.28-2.jpg,left,noimg,whiteboard #2);
#ref(ex26.m)
** &color(green){[lecture #9]}; 2010.11.4 robust control ...
see [[RubustControlOfPneumatic-e.pdf>http://sessyu.nagaok...
#ref(2010.11.4-1.jpg,left,noimg,whiteboard #1);
#ref(2010.11.4-2.jpg,left,noimg,whiteboard #2);
** &color(green){[lecture #10]}; 2010.11.11 robust contro...
+ Design H infinity controller with Eqs.(41)-(47) and gen...
++ Confirm the following m-file for design:
#ref(pneum.m);
#ref(pneum_ans.m);
++ Derive the generalized plant by hand and correct the m...
++ Run the m-file to find controller.
+ Simulation
#ref(simu_pneum.mdl);
#ref(simu_pneum_noise.mdl);
simu_pneum
plot(t, y, 'r', t, r, 'b');
simu_pneum_noise
plot(t, y, 'r', t, n, 'b')
#ref(2010.11.11-1.jpg,left,noimg,whiteboard #1);
#ref(2010.11.11-2.jpg,left,noimg,whiteboard #2);
** &color(green){[lecture #11]}; 2010.11.18 robust contro...
Exercise
+step response
+noise response (noise type: step, sinusoidal wave 1Hz, 5...
+initial response (x(0) = [1;0;0])
#ref(2010.11.18-1.jpg,left,noimg,whiteboard #1);
** &color(green){[lecture #12]}; 2010.11.25 Speed control...
- simulation (cont. from Nov.18)
- Problem setup
#ref(apparatus.pptx);
- Modelling (frequency response experiment)
#ref(2010.11.25-1.jpg,left,noimg,whiteboard #1);
** &color(green){[lecture #13]}; 2010.12.2 Speed control ...
- %%reduced-order controller design%% (will be given by P...
#ref(2010.12.2-1.jpg,left,noimg,whiteboard #1);
#ref(2010.12.2-2.jpg,left,noimg,whiteboard #2);
- Problem setup
-- Objective for control system design
++ speed tracking
++ robust against inertia-load variation
#ref(setup.pdf)
- Modelling
-- frequency response experiment results:
#ref(frdata_offset0_small.dat)
#ref(frdata_offset0_large.dat)
#ref(frdata_offset5_small.dat)
#ref(frdata_offset5_large.dat)
#ref(frdata_offset10_small.dat)
#ref(frdata_offset10_large.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 1 (wt1 = 2*pi*50 is set in weight.m)
#ref(cont1.dat)
#ref(cont_order1.dat)
#ref(cont1.mat)
#ref(result_small1.dat)
#ref(result_large1.dat)
-- design example 2 (wt1 = 2*pi*20 is set in weight.m)
#ref(cont2.dat)
#ref(cont_order2.dat)
#ref(cont2.mat)
#ref(result_small2.dat)
#ref(result_large2.dat)
-- example of m-file to compare designed controllers
#ref(compare.m)
- report
+design your controller so that the system performance is...
+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(Tue) 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 and cont_order.dat to kobayasi@nag...
- 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(1) / (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...
** &color(green){[lecture #14]}; 2010.12.9 Speed control ...
Due to a dimension change of the driven shaft, frequency ...
-- frequency response experiment results:
#ref(frdata_offset5_small_fixed.dat)
#ref(frdata_offset5_large_fixed.dat)
#ref(frdata_offset10_small_fixed.dat)
#ref(frdata_offset10_large_fixed.dat)
-- example of m-file
#ref(freqresp_fixed.m)
#ref(nominal_fixed.m)
#ref(weight_fixed.m);
#ref(cont_fixed.m)
-- design example 1 (wt1 = 2*pi*20 is set in weight.m)
#ref(cont1_fixed.dat)
#ref(cont_order1_fixed.dat)
#ref(cont1_fixed.mat)
#ref(result_small1_fixed.dat)
#ref(result_large1_fixed.dat)
-- design example 2 (wt1 = 2*pi*5 is set in weight.m)
#ref(cont2_fixed.dat)
#ref(cont_order2_fixed.dat)
#ref(cont2_fixed.mat)
#ref(result_small2_fixed.dat)
#ref(result_large2_fixed.dat)
#ref(2010.12.9-1.jpg,left,noimg,whiteboard #1);
** &color(green){[lecture #15]}; 2010.12.16 Speed control...
-preparation of your own controller(s)
[[participant list2010]]
**related links [#c31aa7a5]
//-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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