Advanced Automation

[lecture #1] 2012.9.6 review of classical control theory

[lecture #2] 2012.9.20 given by Prof. Kimura

[lecture #3] 2012.9.27 CACSD introduction with review of classical and modern control theory

  1. introduction of Matlab and Simulink
  2. relationship between TF and SSR
  3. open-loop stability can be checked by poles of TF and eigenvalues of A-matrix in SSR
  4. closed-loop stability
    • graphical test by Nyquist stability criterion and Bode plot with GM(gain margin) and PM(phase margin)
    • numerical test by poles of closed-loop TF and eigenvalues of A-matrix in closed-loop SSR
    • example: stabilization of unstable system
%-- 9/27/2012 1:07 PM --%
a = 1
pwd
G1 = 1/(s+1)
ex0927_1
G1 = 1/(s+1)
A
ex0927_2
G2_tf
G2_tf.den
G2_tf.den{:}
G2_tf.num{:}
eig(G2_tf)
G2_ss.a
eig(G2_ss.a)
G2_ss
G2_ss.a
G2_ss.b
ex0927_3
nyquist(1.5*G3_tf)
nyquist(-1.5*G3_tf)
bode(-1.5*G3_tf)
bode(1.5*G3_tf)
K
K = 1
ex0927_4
ex0927_5
A
eig(A)
K = 0
K=1
ex0927_5 

[lecture #4] 2012.10.4 Intro. to robust control theory (H infinity control theory)

  1. Typical design problems
    1. robust stabilization
    2. performance optimization
    3. robust performance problem (robust stability and performance optimization are simultaneously considered)
  2. H infinity norm
    • definition
    • example
  3. H infinity control problem
    • definition
    • application example : reference tracking problem
      • relation to the sensitivity function S(s) (S(s) -> 0 is desired but impossible)
      • given control system please change the line `K = 1' to `K = ss(1)'
%-- 10/4/2012 1:11 PM --%
s = tf('s')
G = 1/(s+1)
norm(G, 'inf')
help norm
ex1004_1
ex1004_2
K
K_hinf
size(K_hinf.a)

[lecture #5] 2012.10.11 Introduction to Robust Control (cont.)

  1. Typical design problems
    1. robust stabilization ... plant is given as class
    2. performance optimization; ... plant has no variation
    3. robust performance problem (robust stability and performance optimization are simultaneously considered)
  2. connection between H infinity control problem and robust stabilization
    • normalized uncertainty \Delta
    • small gain theorem
    • sketch proof ... Nyquist stability criterion
  3. How to design robust stabilizing controller with H infinity control problem ?
    • connection between \Delta and plant ?
    • generalized plant G ?
    • practical example of robust stabilization problem
%-- 10/11/2012 12:56 PM --%
ex1011_1
ex1011_2
ex1011_3
mod1011
ex1011_1
P
ex1011_2
1i
j
j = 2
1i = 2
ex1011_3
mod1011
c = 0.8
c = 1.2
c = 1.3
c = 2

[lecture #6] 2012.10.18 Introduction to Robust Control (cont.)

  1. review
    • robust stabilization ... ||WT T||_inf < 1 (for multiplicative uncertainty)
    • performance optimization ... ||WS S||_inf < gamma -> min
    • mixed sensitivity problem gives a sufficient condition such that both conditions hold ... nominal (not robust) performance problem
  2. proof of small gain theorem ... Nyquist stability criterion
  3. mixed sensitivity problem
%-- 10/18/2012 12:56 PM --%
mod1018
ex1018_1
input_to_P0
WT
WSgam
systemnames
ex1018_1
G
ex1018_1

[lecture #7] 2012.10.25 singular value decomposition(SVD)

%-- 10/25/2012 1:27 PM --%
A = [1, 2, 3; 4, 5, 6]
[U, Sigma, V] = svd(A)
U*U'
U'*U
V'*V
[U, Sigma, V] = svd(A')
A = [1, 2, 3; 4, 5, 1i]
[U, Sigma, V] = svd(A)

[lecture #8] 2012.11.1 Robust performance problem

%-- 11/1/2012 1:37 PM --%
ex1101_1
ex1101_2
K
ex1101_2
ex1101_3

[lecture #9] 2012.11.8 Robust performance problem (cont.)

%-- 11/8/2012 1:29 PM --%
ex1101_4
ex1101_1
ex1101_2
ex1101_3
ex1101_4
ex1101_5

[lecture #10] 2012.11.15 Robust performance problem (cont.)

%-- 11/15/2012 1:08 PM --%
ex1101_1
ex1101_2
ex1101_3
ex1101_4
ex1101_5
-13/20
10**-0.65
10^-0.65
ex1101_4
K
ex1101_4
ex1101_5
gam
K
d
gam
K
sigma(mdiag(1,1/gam)*lft(G,K))
sigma(mdiag(1/d,1/gam)*lft(G,K)*mdiag(d,1),'r')
sigma(mdiag(1,1/gam)*lft(G,K))
hold on
sigma(mdiag(1/d,1/gam)*lft(G,K)*mdiag(d,1),'r')

[lecture #11] 2012.11.22 will be given by Prof. Kimura

[lecture #12] 2012.11.29 will be given by Prof. Kimura

[lecture #13] 2012.12.6 Robust control design for a practical system (1/3) : Active vibration control of a pendulum using linear motor (loudspeaker) some mistakes fixed on 2012.12.13 [#k776c145]

  1. design your controller(s) so that the system performance is improved compared with the given example above
  2. Draw the following figures and explain the difference between two control systems (your controller and the example above):
    1. bode diagram of controllers
    2. gain characteristic of closed-loop systems
    3. time response of control experiment
  3. Why is the performance of your system improved(or unfortunately decreased)?
    • due date: 27th(Thu) Dec 17:00
    • submit your report(pdf or doc) by e-mail to kobayasi@nagaokaut.ac.jp
    • You can use Japanese
    • maximum controller order is 20
    • submit your cont.dat, cont_order.dat, and cont.mat to kobayasi@nagaokaut.ac.jp not later than 21th(Fri) 25th(Tue) Dec
freqresp
nominal
help n4sid
load result.dat
load result_no.dat
plot(result(:,1),result(:,3),'r',result_no(:,1),result_no(:,2),'g')
plot(result(:,1),result(:,3),'r',result_no(:,1),result_no(:,3),'g')

... please use the potentio meter output as the measured output instead the PSD output (2012.12.13)

[lecture #14] 2012.12.13 Robust control design for a practical system (2/3)

IMPOTANT:due to some change on experimental apparatus, please use the potentio meter output as the measured output instead of the PSD output. Moreover, some files have been re-uploaded due to this change. See previous links.

%-- 12/13/2012 12:59 PM --%
freqresp
pwd
freqresp
nominal
P0
weight
cont
compare
load result.dat
plot(result(:,1),result(:,3));
load result_no.dat
plot(result_no(:,1),result_no(:,3),'b',result(:,1),result(:,3),'r');
plot(result_no(:,1),result_no(:,2),'b',result(:,1),result(:,2),'r');
plot(result_no(:,1),result_no(:,4),'b',result(:,1),result(:,4),'r');

[lecture #15] 2012.12.20 Robust control design for a practical system (3/3)

participant list2012

related links


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Last-modified: 2012-12-21 (金) 19:15:18