授業/制御工学特論2013
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*Advanced Automation [#zc0d6c13]
** &color(green){[lecture #1]}; 2013.9.5 outline of the l...
- outline of this lecture
-- syllabus
-- map
#ref(map_v1.0.pdf);
-- evaluation
--- mini report #1 ... 10%
--- mini exam #1 ... 10%
--- mini report #2 ... 10%
--- mini exam #2 ... 10%
--- final report ... 60%
- review
#ref(2013.09.05-1.jpg,left,noimg,whiteboard #1);
#ref(2013.09.05-2.jpg,left,noimg,whiteboard #2);
... missed (derivation of G(s) = 1/(ms^2+cs+k) by Laplace...
#ref(2013.09.05-3.jpg,left,noimg,whiteboard #3);
#ref(2013.09.05-4.jpg,left,noimg,whiteboard #4);
** &color(green){[lecture #2]}; 2013.9.12 CACSD introduct...
+ 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...
//
+ How to define open-loop system
//
++ &color(black,cyan){TF};
s = tf('s');
G1 = 1 / (s+1);
G2 = 1 / (s^2 + 0.1*s + 1);
++ &color(black,lightgreen){SSR};
A = [-0.3, -1; 1, 0];
B = [1; 0];
C = [0, 1];
D = 0;
G3 = ss(A, B, C, D);
-- Bode plot
bode(G1, 'b-', G2, 'g', G3, 'r--');
grid on;
//
+ open-loop stability can be checked by
//
++ &color(black,cyan){poles of TF};
roots(G2.den{:})
++ &color(black,lightgreen){eigenvalues of A-matrix in SS...
eig(G3.a)
++ also by simulation
#ref(mod0912_1.mdl);
//
+ closed-loop stability
//
L = 1/(s^3+1.5*s^2+1.5*s+1); % example of open-loop system
roots(L.den{:}) % confirm the open-loop system is stable
//
++ graphical test by &color(black,yellow){Nyquist stabili...
nyquist(L)
//
bode(L)
++ numerical test by closed-loop system
clp_den = L.den{:} + L.num{:};
roots(clp_den)
++ simulation
#ref(mod0912_2.mdl);
a = 1
ver
t = [1 2 3]
pwd
ls
foo
pwd
bar
s = tf('s')
G1 = 1 / (s+1);
G2 = 1 / (s^2 + 0.1*s + 1);
G1
G2
A = [-0.3, -1; 1, 0];
B = [1; 0];
C = [0, 1];
D = 0;
G3 = ss(A, B, C, D);
G3
bode(G1, 'b-', G2, 'g', G3, 'r--');
grid on;
G2
G2.den
G2.den{:}
roots(G2.den{:})
G3.a
eig(G3.a)
mod0912_1
L = 1/(s^3+1.5*s^2+1.5*s+1); % example of open-loop system
roots(L.den{:}) % confirm the open-loop system is stable
nyquist(L)
nyquist(L*1.25)
nyquist(L)
clp_den = L.den{:} + L.num{:};
roots(clp_den)
ex0912_2
mod0912_2
L = 1.5*L
#ref(2013.09.12-1.jpg,left,noimg,whiteboard #1);
#ref(2013.09.12-2.jpg,left,noimg,whiteboard #2);
** &color(green){[lecture #3]}; 2013.9.19 CACSD introduct...
+ LQR problem
+ ARE and quadratic equation
#ref(J.pdf);
+ (semi)-positive definiteness
+ example
#ref(mod0919.mdl);
mod0919
A = [1, 2, 3; 4, 5, 6; 7, 8, 9]
eig(A)
B = [1; 1; 1]
Uc = ctrb(A, B)
det(Uc)
B = [1; 0; 0]
Uc = ctrb(A, B)
det(Uc)
help are
P = are(A, B/R*B', Q)
Q = eye(3)
R = 1
P = are(A, B/R*B', Q)
P = are(A, B*inv(R)*B', Q)
P - P'
eig(P)
x(0)
x0 = [1; 1; 1]
x0'*P*x0
F = R\B'*P
C = eye(3)
D = [0; 0; 0]
J
#ref(2013.09.19-1.jpg,left,noimg,whiteboard #1);
#ref(2013.09.19-2.jpg,left,noimg,whiteboard #2);
#ref(2013.09.19-3.jpg,left,noimg,whiteboard #3);
#ref(2013.09.19-4.jpg,left,noimg,whiteboard #4);
** &color(green){[lecture #4]}; 2013.9.26 Intro. to robus...
+ Typical design problems
++ robust stabilization
++ &color(black,yellow){performance optimization};
++ robust performance problem (robust stability and perfo...
//
+ H infinity norm
-- definition
-- example
//
+ H infinity control problem
-- definition
-- application example : reference tracking problem
--- relation to the sensitivity function S(s) (S(s) -> 0 ...
--- given control system
#ref(ex0926_1.m)
--- controller design with H infinity control theory
#ref(ex0926_2.m)
s = tf('s')
G = 1/(s+1)
norm(G, 'inf')
G = s/(s+1)
norm(G, 'inf')
G = 1/(s^2+0.1*s+1)
bodemag(G)
norm(G, 'inf')
bodemag(G, 'b', ss(10.0125), 'r--')
G = 1/(s^2+0.5*s+1)
norm(G, 'inf')
bodemag(G, 'b', ss(2.0656), 'r--')
ex0926_1
ex0926_2
eig(K_hinf)
#ref(2013.09.26-1.jpg,left,noimg,whiteboard #1);
#ref(2013.09.26-2.jpg,left,noimg,whiteboard #2);
#ref(2013.09.26-3.jpg,left,noimg,whiteboard #3);
#ref(2013.09.26-4.jpg,left,noimg,whiteboard #4);
** &color(green){[lecture #5]}; %% 2013.10.3 Intro. to Ro...
** &color(green){[lecture #5]}; 2013.10.10 Intro. to Robu...
+ Typical design problems
++ &color(black,yellow){robust stabilization};
++ performance optimization
++ robust performance problem (robust stability and perfo...
//
+ connection between [H infinity control problem] and [ro...
-- small gain theorem
-- normalized uncertainty \Delta
-- sketch proof ... Nyquist stability criterion
+ How to design robust stabilizing controller with H infi...
-- practical example : unstable plant with perturbation
#ref(ex1010_1.m)
-- how to use uncertainty model (multiplicative uncertain...
#ref(ex1010_2.m)
-- how to set generalized plant G ?
#ref(ex1010_3.m)
-- simulation
#ref(mod1010.mdl)
ex1010_1
ex1010_2
WT]
WT
P0
P0_jw
ex1010_3
mod1010
#ref(2013.10.10-1.jpg,left,noimg,whiteboard #1);
#ref(2013.10.10-2.jpg,left,noimg,whiteboard #2);
#ref(2013.10.10-3.jpg,left,noimg,whiteboard #3);
#ref(2013.10.10-4.jpg,left,noimg,whiteboard #4);
** &color(green){[lecture #6]}; 2013.10.17 Intro. to robu...
+ review
-- robust stabilization ... (1) ||WT T||_inf < 1 (for mul...
-- performance optimization ... (2) ||WS S||_inf < gamma ...
-- &color(black,yellow){mixed sensitivity problem}; ... s...
+ a sufficient condition for (1) and (2) ... (*) property...
+ definition of singular value
+ mini report #1
+ meaning of singular value ... singular value decomposit...
+ proof of (*)
+ example
#ref(ex1017.m);
//#ref(mod1017.mdl);
j
A = [1, j; 0, 2]
A'
eig(A'*A)
sqrt(ans)
3+sqrt(5)
sqrt(3+sqrt(5))
sqrt(3-sqrt(5))
A
[U,S,V] = svd(A)
U'*U
U*U'
help svd
ex1017
#ref(2013.10.17-1.jpg,left,noimg,whiteboard #1);
#ref(2013.10.17-2.jpg,left,noimg,whiteboard #2);
#ref(2013.10.17-3.jpg,left,noimg,whiteboard #3);
... sorry for missing to take photo ... &color(red){&size...
#ref(2013.10.17-4.jpg,left,noimg,whiteboard #4);
#ref(2013.10.17-5.jpg,left,noimg,whiteboard #5);
#ref(2013.10.17-6.jpg,left,noimg,whiteboard #6);
** &color(green){[lecture #7]}; 2013.10.24 review of SVD,...
- review of SVD
#ref(ex1024_1.m);
- motivation of robust performance
#ref(ex1024_2.m);
#ref(ex1024_3.m);
... SSR of generalized plant
#ref(ex1024_4.m);
ex1024_1
ex1024_2
ex1024_3
ex1024_4
#ref(2013.10.24-1.jpg,left,noimg,whiteboard #1);
#ref(2013.10.24-2.jpg,left,noimg,whiteboard #2);
#ref(2013.10.24-3.jpg,left,noimg,whiteboard #3);
#ref(2013.10.24-4.jpg,left,noimg,whiteboard #4);
** &color(green){[lecture #8]}; 2013.10.31 Robust perform...
+ review of mini report #1
+ review of the limitation of mixed sensitivity problem
+ a solution of conservative design
-- example based on the one given in the last lecture
#ref(ex1031_1.m);
-- a check of the conservativeness
#ref(ex1031_2.m);
+ mini exam #1
#ref(exam1.pdf);
%-- 10/31/2013 1:02 PM --%
A = [j, 0; -j, 0]
A = [j, 0; -j, 1]
svd(A)
sqrt((3+sqrt(5))/2)
sqrt((3-sqrt(5))/2)
ex1024_2
ex1024_3
ex1024_4
ex1031_1
#ref(2013.10.31-1.jpg,left,noimg,whiteboard #1);
#ref(2013.10.31-2.jpg,left,noimg,whiteboard #2);
#ref(2013.10.31-3.jpg,left,noimg,whiteboard #3);
** &color(green){[lecture #9]}; 2013.11.14 Robust perform...
- map
- review of #8
- Q1 and Q2
- ex1031_2.m
- scaled H infinity control problem
#ref(ex1114_1.m);
- mini report #2
ex1024_2
ex1024_3
ex1024_4
ex1024_5
ex1031_1
gam
ex1024_3
gam
ex1031_2
help lft
ex1031_2
ex1031_1
ex1031_2
#ref(2013.11.14-1.jpg,left,noimg,whiteboard #1);
#ref(2013.11.14-2.jpg,left,noimg,whiteboard #2);
#ref(2013.11.14-3.jpg,left,noimg,whiteboard #3);
#ref(2013.11.14-4.jpg,left,noimg,whiteboard #4);
#ref(2013.11.14-5.jpg,left,noimg,whiteboard #5);
** &color(green){[lecture #10]}; 2013.11.21 Robust perfor...
- effect of scaling
- mini report #2
- practical design procedure
- derivation of generalized plant in SSR for mixed sensit...
ex1024_2
ex1024_3
gam
ex1024_4
ex1031_1
gam
ex1031_2
ex1114_1
gam
#ref(2013.11.21-1.jpg,left,noimg,whiteboard #1);
#ref(2013.11.21-2.jpg,left,noimg,whiteboard #2);
#ref(2013.11.21-3.jpg,left,noimg,whiteboard #3);
#ref(2013.11.21-4.jpg,left,noimg,whiteboard #4);
#ref(2013.11.21-5.jpg,left,noimg,whiteboard #5);
** &color(green){[lecture #11]}; 2013.11.28 Robust stabil...
- plant model for perturbed unstable poles
- LFT(Linear Fractional Transformation)
- a simple example
- inverted pendulum (penddemo.m)
- design example
- references:
--[[How to control objects>/:~kobayasi/easttimor/2009/ind...
---[[stabilization of 1-link inverted pendulum>/:~kobayas...
--[[情報処理演習および考究 II MATLAB コース ホームページ ...
---[[倒立振子の安定化>/:~kobayasi/i/Matlab/ex/1link.html]...
#ref(ex1128_1.m);
#ref(mod1128_1.mdl);
#ref(2013.11.28-1.jpg,left,noimg,whiteboard #1);
#ref(2013.11.28-2.jpg,left,noimg,whiteboard #2);
#ref(2013.11.28-3.jpg,left,noimg,whiteboard #3);
#ref(2013.11.28-4.jpg,left,noimg,whiteboard #4);
//#ref(ex_penddemo.m);
//#ref(mod_penddemo.mdl);
** &color(green){[lecture #12]}; 2013.12.5 Robust control...
- review of report #2
- introduction of experimental setup
#ref(photo1.jpg,left,noimg,photo1);
#ref(photo2.jpg,left,noimg,photo2);
#ref(photo3.jpg,left,noimg,photo3);
#ref(photo4.jpg,left,noimg,photo4);
#ref(photo5.jpg,left,noimg,photo5);
-- linear motor : Oriental motor EZC4D005M-A / stepping m...
-- Potentio meter : Midori Precisions Model QP-2H / input...
-- PC : Dell PowerEdge840 (RTAI3.6.1/Linux kernel 2.6.20....
-- Parallel input and output board : CONTEC PIO-32/32T(PC...
-- A/D : CONTEC AD12-16 (PCI) 12bit, 10us
- Objective of control system
++ to attenuate vibration due to pendulum oscillation
++ robust stability against modelling error due to plant ...
- physical model
- frequency response experiment
#ref(freqresp.m);
#ref(frdata_0_2.dat);
#ref(frdata_0_3.dat);
#ref(frdata_0_4.dat);
#ref(2013.12.5-1.jpg,left,noimg,whiteboard #1);
#ref(2013.12.5-2.jpg,left,noimg,whiteboard #2);
#ref(2013.12.5-3.jpg,left,noimg,whiteboard #3);
** &color(green){[lecture #13]}; 2013.12.12 Robust contro...
- mini exam #2
- pendulum No.2 ... l = 8.5cm
#ref(pendulum2.jpg,left,noimg);
due to the difficulty of the inverted and short pendulum,...
- modelling based on frequency response experiment
#ref(frdata_0.5mm.dat);
#ref(freqresp_fixed.m);
- control objective
- design example 1 : proportional control
-- negative feedback always stabilizes the closed loop th...
#ref(check_pcont.m);
-- control experiment
#ref(cont_P.dat,,,`cont.dat' file for P control);
#ref(cont_P_order.dat,,,`cont_order.dat' file for P contr...
#ref(result_P.dat);
#ref(result_openloop.dat);
#ref(openloop.mp4);
#ref(ex1.mp4);
- design example 2 : H infinity control (nominal performa...
-- m-files
#ref(weight_ex2.m);
#ref(cont_ex2.m);
>> weight_ex2
>> cont_ex2
-- control experiment
#ref(cont_ex2.dat,,,`cont.dat' file for ex2);
#ref(cont_ex2_order.dat,,,`cont_order.dat' file for ex2);
#ref(cont_ex2.mat,,,`cont.mat' file for ex2);
#ref(result_ex2.dat);
- design example 3 : H infinity control (nominal performa...
-- m-files
#ref(nominal_ex3.m);
... &size(25){&color(red){n4sid is not available IPC! (19...
#ref(weight_ex3.m);
#ref(cont_ex3.m);
>> nominal_ex3
>> weight_ex3
>> cont_ex3
-- control experiment
#ref(cont_ex3.dat,,,`cont.dat' file for ex3);
#ref(cont_ex3_order.dat,,,`cont_order.dat' file for ex3);
#ref(cont_ex3.mat,,,`cont.mat' file for ex3);
#ref(result_ex3.dat);
#ref(ex3.mp4);
- design example 4 : H infinity control (robust performan...
-- m-files
#ref(weight_ex4.m);
#ref(cont_ex4.m);
>> weight_ex4
>> cont_ex4
-- control experiment
#ref(cont_ex4.dat,,,`cont.dat' file for ex4);
#ref(cont_ex4_order.dat,,,`cont_order.dat' file for ex4);
#ref(cont_ex4.mat,,,`cont.mat' file for ex4);
#ref(result_ex4.dat);
#ref(ex4.mp4);
- summary of design examples : comparison of designed con...
#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: 31th(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 &size(25){&color(red){cont.dat, cont_order....
- 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: potentio meter's output (V)
--- 3rd column: theta (rad)
--- 4th column: x (m)
--- 5th column: reference position for linear motor (numb...
-program sources for generating linear motor's pulse
#ref(pulse.h);
#ref(pulse_module.c);
-common header
#ref(common.h);
#ref(2013.12.12-1.jpg,left,noimg,whiteboard #1);
#ref(2013.12.12-2.jpg,left,noimg,whiteboard #2);
#ref(2013.12.12-3.jpg,left,noimg,whiteboard #3);
// ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■
// &color(black,red){&size(20){#################### the r...
** &color(green){[lecture #14]}; 2013.12.19 Robust contro...
- review of the design examples
&color(red){&size(25){[IMPORTANT] Due to unavailability o...
- preparation of your own controller(s)
[[participant list2013]]
freqresp_fixed
frdata
check_pcont
weight_ex2
freqresp_fixed
weight_ex2
cont_ex2
nominal_ex3
weight_ex4
cont_ex4
compare
#ref(2013.12.19-1.jpg,left,noimg,whiteboard #1);
#ref(2013.12.19-2.jpg,left,noimg,whiteboard #2);
** &color(green){[lecture #15]}; 2013.12.26 Robust contro...
-preparation of your own controller(s)
//**related links [#g1a68a2b]
//-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/~...
終了行:
*Advanced Automation [#zc0d6c13]
** &color(green){[lecture #1]}; 2013.9.5 outline of the l...
- outline of this lecture
-- syllabus
-- map
#ref(map_v1.0.pdf);
-- evaluation
--- mini report #1 ... 10%
--- mini exam #1 ... 10%
--- mini report #2 ... 10%
--- mini exam #2 ... 10%
--- final report ... 60%
- review
#ref(2013.09.05-1.jpg,left,noimg,whiteboard #1);
#ref(2013.09.05-2.jpg,left,noimg,whiteboard #2);
... missed (derivation of G(s) = 1/(ms^2+cs+k) by Laplace...
#ref(2013.09.05-3.jpg,left,noimg,whiteboard #3);
#ref(2013.09.05-4.jpg,left,noimg,whiteboard #4);
** &color(green){[lecture #2]}; 2013.9.12 CACSD introduct...
+ 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...
//
+ How to define open-loop system
//
++ &color(black,cyan){TF};
s = tf('s');
G1 = 1 / (s+1);
G2 = 1 / (s^2 + 0.1*s + 1);
++ &color(black,lightgreen){SSR};
A = [-0.3, -1; 1, 0];
B = [1; 0];
C = [0, 1];
D = 0;
G3 = ss(A, B, C, D);
-- Bode plot
bode(G1, 'b-', G2, 'g', G3, 'r--');
grid on;
//
+ open-loop stability can be checked by
//
++ &color(black,cyan){poles of TF};
roots(G2.den{:})
++ &color(black,lightgreen){eigenvalues of A-matrix in SS...
eig(G3.a)
++ also by simulation
#ref(mod0912_1.mdl);
//
+ closed-loop stability
//
L = 1/(s^3+1.5*s^2+1.5*s+1); % example of open-loop system
roots(L.den{:}) % confirm the open-loop system is stable
//
++ graphical test by &color(black,yellow){Nyquist stabili...
nyquist(L)
//
bode(L)
++ numerical test by closed-loop system
clp_den = L.den{:} + L.num{:};
roots(clp_den)
++ simulation
#ref(mod0912_2.mdl);
a = 1
ver
t = [1 2 3]
pwd
ls
foo
pwd
bar
s = tf('s')
G1 = 1 / (s+1);
G2 = 1 / (s^2 + 0.1*s + 1);
G1
G2
A = [-0.3, -1; 1, 0];
B = [1; 0];
C = [0, 1];
D = 0;
G3 = ss(A, B, C, D);
G3
bode(G1, 'b-', G2, 'g', G3, 'r--');
grid on;
G2
G2.den
G2.den{:}
roots(G2.den{:})
G3.a
eig(G3.a)
mod0912_1
L = 1/(s^3+1.5*s^2+1.5*s+1); % example of open-loop system
roots(L.den{:}) % confirm the open-loop system is stable
nyquist(L)
nyquist(L*1.25)
nyquist(L)
clp_den = L.den{:} + L.num{:};
roots(clp_den)
ex0912_2
mod0912_2
L = 1.5*L
#ref(2013.09.12-1.jpg,left,noimg,whiteboard #1);
#ref(2013.09.12-2.jpg,left,noimg,whiteboard #2);
** &color(green){[lecture #3]}; 2013.9.19 CACSD introduct...
+ LQR problem
+ ARE and quadratic equation
#ref(J.pdf);
+ (semi)-positive definiteness
+ example
#ref(mod0919.mdl);
mod0919
A = [1, 2, 3; 4, 5, 6; 7, 8, 9]
eig(A)
B = [1; 1; 1]
Uc = ctrb(A, B)
det(Uc)
B = [1; 0; 0]
Uc = ctrb(A, B)
det(Uc)
help are
P = are(A, B/R*B', Q)
Q = eye(3)
R = 1
P = are(A, B/R*B', Q)
P = are(A, B*inv(R)*B', Q)
P - P'
eig(P)
x(0)
x0 = [1; 1; 1]
x0'*P*x0
F = R\B'*P
C = eye(3)
D = [0; 0; 0]
J
#ref(2013.09.19-1.jpg,left,noimg,whiteboard #1);
#ref(2013.09.19-2.jpg,left,noimg,whiteboard #2);
#ref(2013.09.19-3.jpg,left,noimg,whiteboard #3);
#ref(2013.09.19-4.jpg,left,noimg,whiteboard #4);
** &color(green){[lecture #4]}; 2013.9.26 Intro. to robus...
+ Typical design problems
++ robust stabilization
++ &color(black,yellow){performance optimization};
++ robust performance problem (robust stability and perfo...
//
+ H infinity norm
-- definition
-- example
//
+ H infinity control problem
-- definition
-- application example : reference tracking problem
--- relation to the sensitivity function S(s) (S(s) -> 0 ...
--- given control system
#ref(ex0926_1.m)
--- controller design with H infinity control theory
#ref(ex0926_2.m)
s = tf('s')
G = 1/(s+1)
norm(G, 'inf')
G = s/(s+1)
norm(G, 'inf')
G = 1/(s^2+0.1*s+1)
bodemag(G)
norm(G, 'inf')
bodemag(G, 'b', ss(10.0125), 'r--')
G = 1/(s^2+0.5*s+1)
norm(G, 'inf')
bodemag(G, 'b', ss(2.0656), 'r--')
ex0926_1
ex0926_2
eig(K_hinf)
#ref(2013.09.26-1.jpg,left,noimg,whiteboard #1);
#ref(2013.09.26-2.jpg,left,noimg,whiteboard #2);
#ref(2013.09.26-3.jpg,left,noimg,whiteboard #3);
#ref(2013.09.26-4.jpg,left,noimg,whiteboard #4);
** &color(green){[lecture #5]}; %% 2013.10.3 Intro. to Ro...
** &color(green){[lecture #5]}; 2013.10.10 Intro. to Robu...
+ Typical design problems
++ &color(black,yellow){robust stabilization};
++ performance optimization
++ robust performance problem (robust stability and perfo...
//
+ connection between [H infinity control problem] and [ro...
-- small gain theorem
-- normalized uncertainty \Delta
-- sketch proof ... Nyquist stability criterion
+ How to design robust stabilizing controller with H infi...
-- practical example : unstable plant with perturbation
#ref(ex1010_1.m)
-- how to use uncertainty model (multiplicative uncertain...
#ref(ex1010_2.m)
-- how to set generalized plant G ?
#ref(ex1010_3.m)
-- simulation
#ref(mod1010.mdl)
ex1010_1
ex1010_2
WT]
WT
P0
P0_jw
ex1010_3
mod1010
#ref(2013.10.10-1.jpg,left,noimg,whiteboard #1);
#ref(2013.10.10-2.jpg,left,noimg,whiteboard #2);
#ref(2013.10.10-3.jpg,left,noimg,whiteboard #3);
#ref(2013.10.10-4.jpg,left,noimg,whiteboard #4);
** &color(green){[lecture #6]}; 2013.10.17 Intro. to robu...
+ review
-- robust stabilization ... (1) ||WT T||_inf < 1 (for mul...
-- performance optimization ... (2) ||WS S||_inf < gamma ...
-- &color(black,yellow){mixed sensitivity problem}; ... s...
+ a sufficient condition for (1) and (2) ... (*) property...
+ definition of singular value
+ mini report #1
+ meaning of singular value ... singular value decomposit...
+ proof of (*)
+ example
#ref(ex1017.m);
//#ref(mod1017.mdl);
j
A = [1, j; 0, 2]
A'
eig(A'*A)
sqrt(ans)
3+sqrt(5)
sqrt(3+sqrt(5))
sqrt(3-sqrt(5))
A
[U,S,V] = svd(A)
U'*U
U*U'
help svd
ex1017
#ref(2013.10.17-1.jpg,left,noimg,whiteboard #1);
#ref(2013.10.17-2.jpg,left,noimg,whiteboard #2);
#ref(2013.10.17-3.jpg,left,noimg,whiteboard #3);
... sorry for missing to take photo ... &color(red){&size...
#ref(2013.10.17-4.jpg,left,noimg,whiteboard #4);
#ref(2013.10.17-5.jpg,left,noimg,whiteboard #5);
#ref(2013.10.17-6.jpg,left,noimg,whiteboard #6);
** &color(green){[lecture #7]}; 2013.10.24 review of SVD,...
- review of SVD
#ref(ex1024_1.m);
- motivation of robust performance
#ref(ex1024_2.m);
#ref(ex1024_3.m);
... SSR of generalized plant
#ref(ex1024_4.m);
ex1024_1
ex1024_2
ex1024_3
ex1024_4
#ref(2013.10.24-1.jpg,left,noimg,whiteboard #1);
#ref(2013.10.24-2.jpg,left,noimg,whiteboard #2);
#ref(2013.10.24-3.jpg,left,noimg,whiteboard #3);
#ref(2013.10.24-4.jpg,left,noimg,whiteboard #4);
** &color(green){[lecture #8]}; 2013.10.31 Robust perform...
+ review of mini report #1
+ review of the limitation of mixed sensitivity problem
+ a solution of conservative design
-- example based on the one given in the last lecture
#ref(ex1031_1.m);
-- a check of the conservativeness
#ref(ex1031_2.m);
+ mini exam #1
#ref(exam1.pdf);
%-- 10/31/2013 1:02 PM --%
A = [j, 0; -j, 0]
A = [j, 0; -j, 1]
svd(A)
sqrt((3+sqrt(5))/2)
sqrt((3-sqrt(5))/2)
ex1024_2
ex1024_3
ex1024_4
ex1031_1
#ref(2013.10.31-1.jpg,left,noimg,whiteboard #1);
#ref(2013.10.31-2.jpg,left,noimg,whiteboard #2);
#ref(2013.10.31-3.jpg,left,noimg,whiteboard #3);
** &color(green){[lecture #9]}; 2013.11.14 Robust perform...
- map
- review of #8
- Q1 and Q2
- ex1031_2.m
- scaled H infinity control problem
#ref(ex1114_1.m);
- mini report #2
ex1024_2
ex1024_3
ex1024_4
ex1024_5
ex1031_1
gam
ex1024_3
gam
ex1031_2
help lft
ex1031_2
ex1031_1
ex1031_2
#ref(2013.11.14-1.jpg,left,noimg,whiteboard #1);
#ref(2013.11.14-2.jpg,left,noimg,whiteboard #2);
#ref(2013.11.14-3.jpg,left,noimg,whiteboard #3);
#ref(2013.11.14-4.jpg,left,noimg,whiteboard #4);
#ref(2013.11.14-5.jpg,left,noimg,whiteboard #5);
** &color(green){[lecture #10]}; 2013.11.21 Robust perfor...
- effect of scaling
- mini report #2
- practical design procedure
- derivation of generalized plant in SSR for mixed sensit...
ex1024_2
ex1024_3
gam
ex1024_4
ex1031_1
gam
ex1031_2
ex1114_1
gam
#ref(2013.11.21-1.jpg,left,noimg,whiteboard #1);
#ref(2013.11.21-2.jpg,left,noimg,whiteboard #2);
#ref(2013.11.21-3.jpg,left,noimg,whiteboard #3);
#ref(2013.11.21-4.jpg,left,noimg,whiteboard #4);
#ref(2013.11.21-5.jpg,left,noimg,whiteboard #5);
** &color(green){[lecture #11]}; 2013.11.28 Robust stabil...
- plant model for perturbed unstable poles
- LFT(Linear Fractional Transformation)
- a simple example
- inverted pendulum (penddemo.m)
- design example
- references:
--[[How to control objects>/:~kobayasi/easttimor/2009/ind...
---[[stabilization of 1-link inverted pendulum>/:~kobayas...
--[[情報処理演習および考究 II MATLAB コース ホームページ ...
---[[倒立振子の安定化>/:~kobayasi/i/Matlab/ex/1link.html]...
#ref(ex1128_1.m);
#ref(mod1128_1.mdl);
#ref(2013.11.28-1.jpg,left,noimg,whiteboard #1);
#ref(2013.11.28-2.jpg,left,noimg,whiteboard #2);
#ref(2013.11.28-3.jpg,left,noimg,whiteboard #3);
#ref(2013.11.28-4.jpg,left,noimg,whiteboard #4);
//#ref(ex_penddemo.m);
//#ref(mod_penddemo.mdl);
** &color(green){[lecture #12]}; 2013.12.5 Robust control...
- review of report #2
- introduction of experimental setup
#ref(photo1.jpg,left,noimg,photo1);
#ref(photo2.jpg,left,noimg,photo2);
#ref(photo3.jpg,left,noimg,photo3);
#ref(photo4.jpg,left,noimg,photo4);
#ref(photo5.jpg,left,noimg,photo5);
-- linear motor : Oriental motor EZC4D005M-A / stepping m...
-- Potentio meter : Midori Precisions Model QP-2H / input...
-- PC : Dell PowerEdge840 (RTAI3.6.1/Linux kernel 2.6.20....
-- Parallel input and output board : CONTEC PIO-32/32T(PC...
-- A/D : CONTEC AD12-16 (PCI) 12bit, 10us
- Objective of control system
++ to attenuate vibration due to pendulum oscillation
++ robust stability against modelling error due to plant ...
- physical model
- frequency response experiment
#ref(freqresp.m);
#ref(frdata_0_2.dat);
#ref(frdata_0_3.dat);
#ref(frdata_0_4.dat);
#ref(2013.12.5-1.jpg,left,noimg,whiteboard #1);
#ref(2013.12.5-2.jpg,left,noimg,whiteboard #2);
#ref(2013.12.5-3.jpg,left,noimg,whiteboard #3);
** &color(green){[lecture #13]}; 2013.12.12 Robust contro...
- mini exam #2
- pendulum No.2 ... l = 8.5cm
#ref(pendulum2.jpg,left,noimg);
due to the difficulty of the inverted and short pendulum,...
- modelling based on frequency response experiment
#ref(frdata_0.5mm.dat);
#ref(freqresp_fixed.m);
- control objective
- design example 1 : proportional control
-- negative feedback always stabilizes the closed loop th...
#ref(check_pcont.m);
-- control experiment
#ref(cont_P.dat,,,`cont.dat' file for P control);
#ref(cont_P_order.dat,,,`cont_order.dat' file for P contr...
#ref(result_P.dat);
#ref(result_openloop.dat);
#ref(openloop.mp4);
#ref(ex1.mp4);
- design example 2 : H infinity control (nominal performa...
-- m-files
#ref(weight_ex2.m);
#ref(cont_ex2.m);
>> weight_ex2
>> cont_ex2
-- control experiment
#ref(cont_ex2.dat,,,`cont.dat' file for ex2);
#ref(cont_ex2_order.dat,,,`cont_order.dat' file for ex2);
#ref(cont_ex2.mat,,,`cont.mat' file for ex2);
#ref(result_ex2.dat);
- design example 3 : H infinity control (nominal performa...
-- m-files
#ref(nominal_ex3.m);
... &size(25){&color(red){n4sid is not available IPC! (19...
#ref(weight_ex3.m);
#ref(cont_ex3.m);
>> nominal_ex3
>> weight_ex3
>> cont_ex3
-- control experiment
#ref(cont_ex3.dat,,,`cont.dat' file for ex3);
#ref(cont_ex3_order.dat,,,`cont_order.dat' file for ex3);
#ref(cont_ex3.mat,,,`cont.mat' file for ex3);
#ref(result_ex3.dat);
#ref(ex3.mp4);
- design example 4 : H infinity control (robust performan...
-- m-files
#ref(weight_ex4.m);
#ref(cont_ex4.m);
>> weight_ex4
>> cont_ex4
-- control experiment
#ref(cont_ex4.dat,,,`cont.dat' file for ex4);
#ref(cont_ex4_order.dat,,,`cont_order.dat' file for ex4);
#ref(cont_ex4.mat,,,`cont.mat' file for ex4);
#ref(result_ex4.dat);
#ref(ex4.mp4);
- summary of design examples : comparison of designed con...
#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: 31th(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 &size(25){&color(red){cont.dat, cont_order....
- 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: potentio meter's output (V)
--- 3rd column: theta (rad)
--- 4th column: x (m)
--- 5th column: reference position for linear motor (numb...
-program sources for generating linear motor's pulse
#ref(pulse.h);
#ref(pulse_module.c);
-common header
#ref(common.h);
#ref(2013.12.12-1.jpg,left,noimg,whiteboard #1);
#ref(2013.12.12-2.jpg,left,noimg,whiteboard #2);
#ref(2013.12.12-3.jpg,left,noimg,whiteboard #3);
// ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■
// &color(black,red){&size(20){#################### the r...
** &color(green){[lecture #14]}; 2013.12.19 Robust contro...
- review of the design examples
&color(red){&size(25){[IMPORTANT] Due to unavailability o...
- preparation of your own controller(s)
[[participant list2013]]
freqresp_fixed
frdata
check_pcont
weight_ex2
freqresp_fixed
weight_ex2
cont_ex2
nominal_ex3
weight_ex4
cont_ex4
compare
#ref(2013.12.19-1.jpg,left,noimg,whiteboard #1);
#ref(2013.12.19-2.jpg,left,noimg,whiteboard #2);
** &color(green){[lecture #15]}; 2013.12.26 Robust contro...
-preparation of your own controller(s)
//**related links [#g1a68a2b]
//-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/~...
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