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

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Chala Kedir
Chala Kedir 2022-4-8
Can any one help with matlab code for a harmonic osillator
function [x, u, Sf, tf] = ex3_3_5(a, b, r, x0)
om=0.8; del=0.1; b=1; r=1;
A= [0 1;-om^2 -2*del*om]; B= [0;b];
C= [1 0]; D= 0;
Q= [0.1 0;0 0.1]; R= 1;
% Control of a Harmonic Oscillator
% Compute the solution to Riccati Equation
[tb, S]=ode45(@HW3_4,[-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
subplot 221
plot(t,y(:,1),'b')
xlabel('time[s]');
legend('q=0.01','q=0.1','q=1');
title('state x_1');
hold on
subplot 222
plot(t,u,'b')
xlabel('time[s]');
legend('q=0.01','q=0.1','q=1');
title('control u');
hold on
subplot 223
range=[0 10];
ic=[0;0;0];
[t, S]=ode45(@HW3_4,range,ic);
plot(t,S(:,1),'k-',t,S(:,2),'b',t,S(:,3),'r')
legend('s(1)','s(2)','s(3)')
xlabel('time[s]');
title('q=0.01');
hold on
subplot 224
range=[0 10];
ic=[0;0;0];
[t, S]=ode45(@HW3_4,range,ic);
plot(t,S(:,1),'k-',t,S(:,2),'b',t,S(:,3),'r')
legend('s(1)','s(2)','s(3)')
xlabel('time[s]');
title('q=1');
function sd=HW3_4(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)];

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