s = tf('s'); T1 = 1 / (s+1); T2 = 1 / (s^2 + 0.1*s + 1);
A = [-0.3, -1; 1, 0]; B = [1; 0]; C = [0, 1]; D = 0; S3 = ss(A, B, C, D);
bode(T1, 'b-', T2, 'g', S3, 'r--'); grid on;
roots(T2.den{:})
eig(S3.a)
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) bode(L)
clp_den = L.den{:} + L.num{:}; roots(clp_den)
%-- 9/18/2014 1:06 PM --% t = [1 2 3] u = [1;2;3] V = [1 2 3; 4 5 6; 7 8 9] t' t'*t who k=0:0.1:10: k=0:0.1:10; y = sin(k); whos plot(x,y) plot(k,y) foo print -djpeg sin.jpg s = tf('s'); T1 = 1/(s+1) T2 = 1/(s^2+0.1*s+1); A = [-0.3, -1; 1, 0]; B = [1; 0]; C = [0, 1]; D = 0; S3 = ss(A, B, C, D); A B S3 bode(T1, 'b-', T2, 'g', S3, 'r--'); grid on; T2 T3 = tf(S3); T3 T2 T2.num T2.num{:} T2.den{:} roots(T2.den{:}) S3 S3.a eig(S3.a) mod0918_1 bode(T1, 'b-', T2, 'g', S3, 'r--'); grid on; roots(L.den{:}) L L = 1/(s^3+1.5*s^2+1.5*s+1); L roots(L.den{:}) nyquist(L) bode(L) grid on nyquist(L) L clp_den = L.den{:} + L.num{:}; clp_den roots(clp_den) mod0918_2
A = [1, 2; 0, -1]; % unstable plant B = [0; 1]; Uc = ctrb(A,B); det(Uc) % should be nonzero C = eye(2); % dummy D = zeros(2,1); % dummy F = [0, 0]; % without control x0 = [1; 1]; % initial state Q = eye(2); R = 1; P = are(A, B/R*B', Q); P-P' % should be zero eig(P) % should be positive F = R\B'*P;
%-- 9/25/2014 2:17 PM --% A = [1, 2; 0, -1]; % unstable plant B = [0; 1]; Uc = ctrb(A,B); Uc det(Uc)] det(Uc) C = eye(2); % dummy D = zeros(2,1); % dummy F = [0, 0]; % without control x0 = [1; 1]; % initial state mod0925 Q = eye(2); R = 1; P = are(A, B/R*B', Q); P-P' % should be zero eig(P) % should be positive F = R\B'*P; F J x0 x0'*P*x0
!!! the remaining page is under construction (the contents below are from 2013) !!!
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)
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ex1010_1 ex1010_2 WT] WT P0 P0_jw ex1010_3 mod1010
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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
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... sorry for missing to take photo ... mini report #1: write by hand; submit at the beginning of the next lecture; You will have a mini exam #1 related to this report on 31st Oct.
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... SSR of generalized plant#ref(): File not found: "ex1024_4.m" at page "授業/制御工学特論2014"
ex1024_1 ex1024_2 ex1024_3 ex1024_4
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%-- 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
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ex1024_2 ex1024_3 ex1024_4 ex1024_5 ex1031_1 gam ex1024_3 gam ex1031_2 help lft ex1031_2 ex1031_1 ex1031_2
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ex1024_2 ex1024_3 gam ex1024_4 ex1031_1 gam ex1031_2 ex1114_1 gam
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due to the difficulty of the inverted and short pendulum, the control target has been changed to an non-inverted and longer pendulum (I'm sorry)#ref(): File not found: "frdata_0.5mm.dat" at page "授業/制御工学特論2014"
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>> weight_ex2 >> cont_ex2
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... n4sid is not available IPC! (19 Dec.)#ref(): File not found: "weight_ex3.m" at page "授業/制御工学特論2014"
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>> nominal_ex3 >> weight_ex3 >> cont_ex3
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>> weight_ex4 >> cont_ex4
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[IMPORTANT] Due to unavailability of n4sid in IPC which is used in cont_ex3.m, please compare your controller and example 2 (not 3) in your report. The explanation of the report has been modified due to this change. See above.
freqresp_fixed frdata check_pcont weight_ex2 freqresp_fixed weight_ex2 cont_ex2 nominal_ex3 weight_ex4 cont_ex4 compare
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