MATLAB code to use for the control of a harmonic oscillator.

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Chala Kedir
Chala Kedir 2022-4-9
function [x, u, Sf, tf] = ex3_3_5(a, b, r, x0)
% Control of a Harmonic Oscillator
% Compute the solution to Riccati Equation
[tb, S]=ode45(@fex3_3_5,[-10:0.1:0],zeros(3,1));
% Compute Optimal Feedback Gains
Sf=flipud(S);
tf=-flipud(tb);
K=-b/r*Sf(:,2:3);
x(:,1)=x0;
u(1)=K(1,:)*x(:,1) ;
% compute Closed-loop Response
for k=1:length(tf)-1,
% Harmonic Oscillator System State Equations
x(:,k+1) =expm((a+[0; b]*K(k,:))*(tf(k+1)-tf(k)))*x(:,k);
u(k+1)=K(k+1,:)*x(:,k+1);
end
function sd=fex3_3_5(t,s)
q=1*eye(2); om=0.8; del=0.1; b=1; r=1;
sd =[-2*om^2*s(2)-b^2*s(2)^2+q(1, 1);
s(1)-4*del*om*s(2)-om^2*s(3)-b^2*s(2)*s(3);
2*s(2)-4*del*om*s(3)-b^2*s(3)^2+q(2,2)];
please if anyone can help,
To output the following graph. Its from optimal control Frank Lewis.

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