Solve state space equation by ODE45

Kshitij Singh answered . 2024-12-21 16:30:19

In order to solve an ODE using ode45, you need to first define the function to describe the complete dynamics. In the linear state space system you provided, the definition of u is missing. In general, u can be designed as a linear feedback control law, such as u = Kx, where K is a 50-by-50 matrix. Let me give you a simpler example here. Suppose we have A = [0 1; -2 3]; B = [0;1]; K = [-1 -1]; Then, the system function can be constructed as:

function  dx = sys(t, x)
   A = [0 1; -2 3]; B = [0;1]; K = [-1 -1]; 
   u = K*x
   dx = A*x + B*u;
end

Please save the above function in an MATLAB file and name is as sys.m

Then, in a separate MATLAB script file or in the command window, you can simulate the system by executing the following

>> tspan = [0 10];
>> iniCon = [1;-1]
>> [t, y] = ode45(@sys, tspan, iniCon);

If you would like to show the simulation result in a figure, try executing >> plot(t,y)

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