Simulate a 2-input linear system with with ode45

Hello everyone,

I am new to ode45, I know how I should use ode45 to simulate a SISO system, but now I am trying to use it on a 2-input 2-output system.

The state space equations are as followed:

And here is my code trying to define the odefunction, the plot is not matching the result using lsim(), so it should not be correct.

t = [0 50]
x0 = [0 0 0 0 0];
[t,y] = ode45(@odefun,t,x0);
plot (t,y,'green');
grid on;

function dxdt = odefun(t,x)
x1 = x(1);
x2 = x(2);
x3 = x(3);
%input u
u1 =10;
u2 =10;
dxdt = zeros(5,1);
dxdt(1) = -1/6*x1-1/3*x3+1/6*u1+1/3*u2;
dxdt(2) = x3;
dxdt(3) = 0.5*x1-0.5*x2-0.5*x3;
dxdt(4) = x1-x2-x3;
dxdt(5) = 0.5*u1 -0.5*x1;
end

Answer 1

[Alan Stevens]

More like this:

tspan = [0 50];
x0 = [0; 0; 0];
u = [10; 10];
[t,x] = ode45(@(t,x) odefun(t,x,u),tspan,x0);
x = x';
My = [1 -1 -1; -1/2 0 0];
Ky = [0 0; 1/2 0];

y = My*x + Ky*u;
plot (t,y,'green');
grid on;

function dxdt = odefun(~,x,u)

        M = [-1/6 0 -1/3; 0 0 1; 1/2 -1/2 -1/2];
        K = [1/6 1/3; 0 0; 0 0];
        
        dxdt = M*x + K*u;
end

[Tianyi Zhu]

Ahh, I see. Thank you.