robust_control/two_mass_system.m

@@ -1,182 +0,0 @@
-
-%% Plant definition
-% refer to to Sinha, FIGURE 5.1.1
-clear;
-
-k1 = ureal('k1', 100, 'Percentage', 20);
-k2 = ureal('k2', 500, 'Percentage', 20);
-m = ureal('m', 1, 'Percentage', 1);
-alpha = ureal('alpha', 1, 'Percentage', 5);
-
-A = [
-    0 0 1 0;
-    0 0 0 1;
-    -(k1+k2)/m k2/m -alpha/m 0;
-    k2/m -(k1+k2)/m 0 -alpha/m;
-    ];
-
-B = [0 0; 0 0; 1 0; 0 1];
-C = [eye(2) zeros(2)];
-D = zeros(2);
-
-G = uss(A, B, C, D);
-G_fullstate = uss(A, B, eye(4), zeros(4, 2));
-
-% multiplicative uncertainty
-w = logspace(0, 3, 40);
-systems = usample(G, 40);
-data = frd(systems, w)  ;
-[G2, Info] = ucover(data, G.NominalValue, 4, []);
-Im = tf(Info.W1);
-
-%% Controller Definition
-Gn = G.NominalValue;
-Gn_fullstate = G_fullstate.NominalValue;
-
-s = tf('s');
-
-%%%% loop invertion controller
-% K = inv(Gn);
-% K = K*1/s * 1/(1+10*s) * (1+0.7*s) * 100;
-% 
-% Gcl = feedback(G*K, eye(2));
-% L = Gn*K;
-
-%%%% PI diagonal controller
-% D = evalfr(inv(G), 0);
-% K = D*(s^2 + s + 100) / (1+s) / (1+s/10);
-% 
-% Gcl = feedback(G*K, eye(2));
-% L = Gn*K;
-
-%%%% LQI controller
-% state weight + integrators weight
-Q = blkdiag(1e3*eye(4), 1e9*eye(2));
-% input weight
-R = 1e-6*eye(2);
-K = -lqi(Gn, Q, R, zeros(6, 2));
-K = ss(K);
-K.InputName = {'x(1)', 'x(2)', 'x(3)', 'x(4)', 'e(1)', 'e(2)'};
-K.OutputName = 'u';
-G_fullstate.InputName = 'u';
-G_fullstate.OutputName = 'x';
-G_feedback = connect(G_fullstate, K, "e", "x");
-% only select first and second output
-G_feedback = G_feedback([1 2], [1 2]);
-G_feedback.OutputName = 'y';
-
-Gcl = feedback(G_feedback*1/s, eye(2));
-L = G_feedback.NominalValue*1/s;
-
-%%%% Sensitivity functions
-S = inv(eye(2)+L);
-T = eye(2) - S;
-
-if ~isstable(T)
-    disp('Nominal closed loop is not stable');
-else
-    disp('Nominal closed loop is stable');
-end
-
-%% Simulation
-t = 0:0.001:1;
-u1 = 0*t + 1;
-u2 = 0*t;
-
-y = lsim(T, [u1; u2], t);
-realizations = usample(Gcl, 20);
-ninputs = 2;
-y_unc = zeros(ninputs*length(realizations), length(t));
-for i=1:length(realizations)
-    p = lsim(realizations(:,:, i, 1), [u1; u2], t);
-    y_unc(ninputs*i, :) = p(:, 1);
-    y_unc(ninputs*i+1, :) = p(:, 2);
-end
-
-%% close figures
-close all;
-
-%% Plant sv and multiplicative uncertainty
-figure('Name', 'Open Loop System');
-subplot(2, 1, 1);
-sigma(G);
-hold on;
-title('Singular values of the system');
-
-subplot(2, 1, 2);
-sigma(Im);
-title('Multiplicative Uncertainty Magnitude');
-
-%% Singular value robustness and performance analysis
-figure('Name', 'Loop Analysis');
-subplot(2, 2, 1);
-w = logspace(-1, 10, 100);
-SV = sigma(eye(2) + inv(L), w);
-semilogx(w, 20*log10(min(SV, [], 1))); hold on;
-sigma(Im, w, 'r'); hold off;
-title('Robust stability analysis')
-
-% open loop performance specifications
-subplot(2, 2, 2);
-sigma(L);
-title('Open loop specifications: L');
-
-subplot(2, 2, 3);
-[SV, W] = sigma(S);
-semilogx(W, 20*log10(max(SV, [], 1)));
-title('Open loop specifications: S');
-
-subplot(2, 2, 4);
-[SV, W] = sigma(T);
-semilogx(W, 20*log10(max(SV, [], 1)));
-title('Open loop specifications: T');
-
-%% Structured singular value analysis
-opts = robOptions('VaryFrequency','on');
-[stabmarg,wcg,info] = robstab(Gcl,opts);
-semilogx(info.Frequency,info.Bounds)
-title('Stability Margin vs. Frequency');
-ylabel('Margin');
-xlabel('Frequency');
-legend('Lower bound','Upper bound');
-
-if stabmarg.LowerBound > 1
-    fprintf('Closed loop system is robustly stable: mu=%f-%f at %f rad/s\n', ...
-        stabmarg.LowerBound, stabmarg.UpperBound, stabmarg.CriticalFrequency);
-else
-    fprintf('Closed loop system is not robustly stable: mu=%f-%f at %f rad/s\n', ...
-        stabmarg.LowerBound, stabmarg.UpperBound, stabmarg.CriticalFrequency);
-end
-
-Twc = usubs(Gcl, wcg);
-y_wc = lsim(Twc, [u1; u2], t);
-
-%% Transient plot
-figure('Name', 'Transient simulation');
-subplot(2, 3, 1);
-plot(t, u1, '--b', t, y(:, 1), 'r');
-title('Nominal system response');
-subplot(2, 3, 4);
-plot(t, u2, '--b', t, y(:, 2), 'r');
-
-subplot(2, 3, 2);
-plot(t, u1, '--b'); hold on;
-for i=1:length(realizations)
-    plot(t, y_unc(ninputs*i, :), 'r');
-end
-hold off;
-title('Uncertain system response');
-
-subplot(2, 3, 5);
-plot(t, u2, '--b'); hold on;
-for i=1:length(realizations)
-    plot(t, y_unc(ninputs*i+1, :), 'r');
-end
-hold off;
-
-subplot(2, 3, 3);
-plot(t, u1, '--b', t, y_wc(:, 1), 'r');
-title('Worst case system response');
-
-subplot(2, 3, 6);
-plot(t, u2, '--b', t, y_wc(:, 2), 'r');