授業/制御工学特論2009
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開始行:
*Advanced Automation [#y8aaf13b]
**2009.9.10 CACSD introduction [#y138ae77]
- 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...
-review of clasical control theory
++ transfer function
++ state-space representation
++ Bode diagram
++ characteristics of 2nd-order system
++ Nyquist stability criterion
++ gain margin and phase margin
++ characteristic polynomial
++ poles and impulse response
#ref(ex.m)
#ref(mod1.mdl)
**2009.9.17 Intro. to Robust Control [#pce7e512]
-robust stability
- performance improvement
- H infinity norm
#ref(ex21.m)
#ref(ex22.m)
#ref(ex23.m)
#ref(ex24.m)
#ref(mod2.mdl)
** 2009.10.15 norm, vector space, normed linear space [#l...
** 2009.10.22 eigenvalue, eigenvector, singular value dec...
** 2009.11.5 state space representation of connected syst...
#ref(ex61.m)
** 2009.11.19 [#q528f91a]
#ref(rub2.m)
... generalized plant is described by hand
#ref(rub.m)
... function sysic() is used to obtain generalized plant
simulink model
#ref(simurub.mdl)
simulink model for noise problem
#ref(simurub_noise.mdl)
execution example for Matlab
rub2
size(Ap)
size(Ap,1)
size(Ap,2)
M = zeros(3,2)
size(M,1)
size(M,2)
gopt
simulink
simout
plot(t, y)
plot(t, y, 'r', t, r, 'b')
figure(3);
bodemag(S, 'r', gopt/WS, 'r--', T, 'b', gopt/WT, 'b--');
ctrlpref
bodemag(S, 'r', gopt/WS, 'r--', T, 'b', gopt/WT, 'b--');
grid on
ctrlpref
figure(6);
plot(t, y, 'r', t, r, 'b')
grid on
figure(7);
bodemag(P0, 'r', K, 'b')
grid on
rub2
grid on
gopt
plot(t, y, 'r', t, r, 'b')
grid on
simulink
plot(t, y, 'r', t, r, 'b')
plot(t, y, 'r', t, n, 'b')
plot(t, y*10, 'r', t, n, 'b')
plot(t, y, 'r', t, n, 'b')
bodemag(P0, 'r', K, 'b')
grid on
bode(P0, 'r', K, 'b')
grid on
bode(P0, 'r', K, 'b', P0*K, 'm')
grid on
bode(P0, 'r', K, 'b', -P0*K, 'm')
grid on
size(K.a)
size(WS.a)
size(WT.a)
size(P0.a)
** 2009.12.3 [#bc440c69]
#ref(rub3.m)
#ref(rub4.m)
** 2009.12.10 Speed control of two inertia system with se...
- Problem setup
- Modelling (frequency response experiment)
#ref(setup.pdf)
#ref(freqresp.m)
#ref(frdata_amp2_offset10.dat)
#ref(frdata_amp3_offset10.dat)
#ref(frdata_amp4_offset10.dat)
#ref(frdata_amp3_offset5.dat)
#ref(frdata_amp3_offset0.dat)
#ref(nominal.m)
** 2009.12.17 Speed control of two inertia system with se...
- Controller design
- frequency response experiments are re-executed so that ...
#ref(freqresp_fixed.m)
#ref(frdata_amp2_offset10_fixed.dat)
#ref(frdata_amp3_offset10_fixed.dat)
#ref(frdata_amp4_offset10_fixed.dat)
#ref(frdata_amp3_offset5_fixed.dat)
#ref(frdata_amp3_offset0_fixed.dat)
#ref(frdata_amp10_offset20_fixed.dat)
-You can design controllers based on mixed sensitivity pr...
#ref(nominal_fixed.m)
#ref(weight.m)
#ref(cont.m)
-example of results
#ref(cont.dat)
#ref(cont_order.dat)
#ref(result.dat)
-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...
--due date: %%28th(Mon) Dec 17:00%% --> &color(red){&size...
--submit your report by e-mail to kobayasi@nagaokaut.ac.j...
--You can use Japanese
--maximum controller order is 20
--submit your cont.dat and cont_order.dat to kobayasi@nag...
&size(30){&color(black,red){2009.12.22 announcement to de...
&size(20){&color(black,red){Please use LMI based H infini...
[K, clp, gopt] = hinfsyn(G, 1, 1, 'DISPLAY', 'on', 'METH...
&color(red){There were some numerical problems in the exe...
#ref(cont.png);
&color(red){You can also check if the design result is OK...
>> cont
Test bounds: 0.0000 < gamma <= 0.9051
gamma hamx_eig xinf_eig hamy_eig yinf_eig nrh...
0.905 4.1e-03 -2.2e-08 1.5e-03 -1.9e-20 0.0...
0.453 4.1e-03# ******** 1.5e-03 -3.8e-05# ****...
0.679 4.1e-03# ******** 1.5e-03 -1.5e-04# ****...
0.792 4.1e-03 -2.2e-08 1.5e-03 -3.9e-04# 0.00...
0.849 4.1e-03 -2.2e-08 1.5e-03 -9.0e-04# 0.00...
0.877 4.1e-03 -2.2e-08 1.5e-03 -2.1e-03# 0.01...
0.891 4.1e-03 -2.2e-08 1.5e-03 -5.3e-03# 0.03...
0.898 4.1e-03 -2.2e-08 1.5e-03 -2.2e-02# 0.13...
Gamma value achieved: 0.9051
>> norm(clp, 'inf')
ans =
1.2593
&color(red){In the above result, the closed-loop H infini...
** 2009.12.24 Speed control of two inertia system with se...
- Control experiment
[[participant list]]
#ref(cont_fixed.m)
#ref(cont_lmi.m)
#ref(compare.m)
#ref(load_cont_data.m)
** 2009.12.25 [#t6f1b7a7]
- program sources for frequency response experiment
#ref(freqresp.h)
#ref(freqresp_module.c)
#ref(freqresp_app.c)
- program sources for control experiment
#ref(hinf.h)
#ref(hinf_module.c)
#ref(hinf_app.c)
- format of result.dat file
-- 1st column: time [sec]
-- 2nd column: motor speed [rad/sec] (measured output)
-- 3rd column: load speed [rad/sec]
-- 4th column: motor torque [Nm] (control input)
-- 5th column: reference speed [rad/sec]
- configuration of control experiment
-- reference signal is generated as described in hinf_mod...
if((t > 5)&&(t < 15)){
r = 15.0;
}else{
r = 5;
}
-- 30% of rated torque is loaded from 10 to 12 sec as spe...
if((t > 10.)&&(t < 12.)){
daconv(0, bit16_conv(torq_volt_conv(RATED_TORQ*-0.3)));
}else{
daconv(0, bit16_conv(torq_volt_conv(0)));
}
** 2009.12.28 [#bfcaad4f]
- 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...
There are some ways to tackle the problem:
-- Use loose weight WT(s) (over estimate of modeling erro...
-- Loop shaping design procedure
-- sampled-data H infinity control design
-- Evaluate of control input u with a high pass filter
-- ...
The final option will be explained below:
- [[Design example with evaluation of control input u]]
**related links [#od998635]
//-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 [#y8aaf13b]
**2009.9.10 CACSD introduction [#y138ae77]
- 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...
-review of clasical control theory
++ transfer function
++ state-space representation
++ Bode diagram
++ characteristics of 2nd-order system
++ Nyquist stability criterion
++ gain margin and phase margin
++ characteristic polynomial
++ poles and impulse response
#ref(ex.m)
#ref(mod1.mdl)
**2009.9.17 Intro. to Robust Control [#pce7e512]
-robust stability
- performance improvement
- H infinity norm
#ref(ex21.m)
#ref(ex22.m)
#ref(ex23.m)
#ref(ex24.m)
#ref(mod2.mdl)
** 2009.10.15 norm, vector space, normed linear space [#l...
** 2009.10.22 eigenvalue, eigenvector, singular value dec...
** 2009.11.5 state space representation of connected syst...
#ref(ex61.m)
** 2009.11.19 [#q528f91a]
#ref(rub2.m)
... generalized plant is described by hand
#ref(rub.m)
... function sysic() is used to obtain generalized plant
simulink model
#ref(simurub.mdl)
simulink model for noise problem
#ref(simurub_noise.mdl)
execution example for Matlab
rub2
size(Ap)
size(Ap,1)
size(Ap,2)
M = zeros(3,2)
size(M,1)
size(M,2)
gopt
simulink
simout
plot(t, y)
plot(t, y, 'r', t, r, 'b')
figure(3);
bodemag(S, 'r', gopt/WS, 'r--', T, 'b', gopt/WT, 'b--');
ctrlpref
bodemag(S, 'r', gopt/WS, 'r--', T, 'b', gopt/WT, 'b--');
grid on
ctrlpref
figure(6);
plot(t, y, 'r', t, r, 'b')
grid on
figure(7);
bodemag(P0, 'r', K, 'b')
grid on
rub2
grid on
gopt
plot(t, y, 'r', t, r, 'b')
grid on
simulink
plot(t, y, 'r', t, r, 'b')
plot(t, y, 'r', t, n, 'b')
plot(t, y*10, 'r', t, n, 'b')
plot(t, y, 'r', t, n, 'b')
bodemag(P0, 'r', K, 'b')
grid on
bode(P0, 'r', K, 'b')
grid on
bode(P0, 'r', K, 'b', P0*K, 'm')
grid on
bode(P0, 'r', K, 'b', -P0*K, 'm')
grid on
size(K.a)
size(WS.a)
size(WT.a)
size(P0.a)
** 2009.12.3 [#bc440c69]
#ref(rub3.m)
#ref(rub4.m)
** 2009.12.10 Speed control of two inertia system with se...
- Problem setup
- Modelling (frequency response experiment)
#ref(setup.pdf)
#ref(freqresp.m)
#ref(frdata_amp2_offset10.dat)
#ref(frdata_amp3_offset10.dat)
#ref(frdata_amp4_offset10.dat)
#ref(frdata_amp3_offset5.dat)
#ref(frdata_amp3_offset0.dat)
#ref(nominal.m)
** 2009.12.17 Speed control of two inertia system with se...
- Controller design
- frequency response experiments are re-executed so that ...
#ref(freqresp_fixed.m)
#ref(frdata_amp2_offset10_fixed.dat)
#ref(frdata_amp3_offset10_fixed.dat)
#ref(frdata_amp4_offset10_fixed.dat)
#ref(frdata_amp3_offset5_fixed.dat)
#ref(frdata_amp3_offset0_fixed.dat)
#ref(frdata_amp10_offset20_fixed.dat)
-You can design controllers based on mixed sensitivity pr...
#ref(nominal_fixed.m)
#ref(weight.m)
#ref(cont.m)
-example of results
#ref(cont.dat)
#ref(cont_order.dat)
#ref(result.dat)
-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...
--due date: %%28th(Mon) Dec 17:00%% --> &color(red){&size...
--submit your report by e-mail to kobayasi@nagaokaut.ac.j...
--You can use Japanese
--maximum controller order is 20
--submit your cont.dat and cont_order.dat to kobayasi@nag...
&size(30){&color(black,red){2009.12.22 announcement to de...
&size(20){&color(black,red){Please use LMI based H infini...
[K, clp, gopt] = hinfsyn(G, 1, 1, 'DISPLAY', 'on', 'METH...
&color(red){There were some numerical problems in the exe...
#ref(cont.png);
&color(red){You can also check if the design result is OK...
>> cont
Test bounds: 0.0000 < gamma <= 0.9051
gamma hamx_eig xinf_eig hamy_eig yinf_eig nrh...
0.905 4.1e-03 -2.2e-08 1.5e-03 -1.9e-20 0.0...
0.453 4.1e-03# ******** 1.5e-03 -3.8e-05# ****...
0.679 4.1e-03# ******** 1.5e-03 -1.5e-04# ****...
0.792 4.1e-03 -2.2e-08 1.5e-03 -3.9e-04# 0.00...
0.849 4.1e-03 -2.2e-08 1.5e-03 -9.0e-04# 0.00...
0.877 4.1e-03 -2.2e-08 1.5e-03 -2.1e-03# 0.01...
0.891 4.1e-03 -2.2e-08 1.5e-03 -5.3e-03# 0.03...
0.898 4.1e-03 -2.2e-08 1.5e-03 -2.2e-02# 0.13...
Gamma value achieved: 0.9051
>> norm(clp, 'inf')
ans =
1.2593
&color(red){In the above result, the closed-loop H infini...
** 2009.12.24 Speed control of two inertia system with se...
- Control experiment
[[participant list]]
#ref(cont_fixed.m)
#ref(cont_lmi.m)
#ref(compare.m)
#ref(load_cont_data.m)
** 2009.12.25 [#t6f1b7a7]
- program sources for frequency response experiment
#ref(freqresp.h)
#ref(freqresp_module.c)
#ref(freqresp_app.c)
- program sources for control experiment
#ref(hinf.h)
#ref(hinf_module.c)
#ref(hinf_app.c)
- format of result.dat file
-- 1st column: time [sec]
-- 2nd column: motor speed [rad/sec] (measured output)
-- 3rd column: load speed [rad/sec]
-- 4th column: motor torque [Nm] (control input)
-- 5th column: reference speed [rad/sec]
- configuration of control experiment
-- reference signal is generated as described in hinf_mod...
if((t > 5)&&(t < 15)){
r = 15.0;
}else{
r = 5;
}
-- 30% of rated torque is loaded from 10 to 12 sec as spe...
if((t > 10.)&&(t < 12.)){
daconv(0, bit16_conv(torq_volt_conv(RATED_TORQ*-0.3)));
}else{
daconv(0, bit16_conv(torq_volt_conv(0)));
}
** 2009.12.28 [#bfcaad4f]
- 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...
There are some ways to tackle the problem:
-- Use loose weight WT(s) (over estimate of modeling erro...
-- Loop shaping design procedure
-- sampled-data H infinity control design
-- Evaluate of control input u with a high pass filter
-- ...
The final option will be explained below:
- [[Design example with evaluation of control input u]]
**related links [#od998635]
//-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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