Solve state space equation by ODE45
Hello everybody. I am new to state space representation. please help me to solve this question. I have state space equation for IM motor like this: xdot=A.x+B.u --> and their dimensions are : [50,1]=[50,50]*[50,1]+[50,50]*[50,1] I have calculated A & B and I need to get xdot. (there are no C & D) 1- how should I write my function? (I don't use Simulink) 2- I used my solver like this: >> [t,y] = ode45(@sys, tspan, zeros(50,1));
Kshitij Singh answered .
2025-11-20
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)