Timothy asked . 2020-11-23

Why do AnalysisPoints change the results of systune optimization?

I am wondering why additional analysis points change the outcome of the optimization with the systune command. The results are quite similar, but I would have expected identical results, since - as far as I understood - analysis points should not affect the system dynamics.

%  Define Laplace variable
s = tf('s');

%  Define all single transfer functions
k12 = 0.5; 
k21 = -0.1;

G11 = 2/(s^2 + 3*s + 2);
G12 = k12/(s+1);
G21 = k21/(s^2 + 2*s + 1);
G22 = 6/(s^2 + 5*s + 6);
%  Concatenate MIMO system
G = [G11, G12; G21, G22];

%  Create tunable state-space system
C = tunableSS('C', 4, 2, 2);

%  Define some analysi points
X = AnalysisPoint('X', 2);
E = AnalysisPoint('E', 2);
U = AnalysisPoint('U', 2);

%  Closed loop WITH analysis points
Gw1 = feedback(E*C*U*G, X, -1);
Gw1.InputName = 'w';
Gw1.OutputName = 'y';

%  Closed loop WITHOUT analysi points
Gw2 = feedback(C*G, X, -1);
Gw2.InputName = 'w';
Gw2.OutputName = 'y';

%  Make sure the bode plots are identical before the optimiziation with
%  systune
figure; bode(Gw1, Gw2); legend;

%  Specify tuning goal
Rtrack = TuningGoal.StepTracking('w', 'y', 0.5/3);

%  Tune both closed loop systems with the same tuning goal
CL1 = systune(Gw1, Rtrack);
CL2 = systune(Gw2, Rtrack);

%  Review bode plots of the optimization results
figure; bode(CL1, CL2); legend;

matlab , control system , Analysis