# Solve state space equation by ODE45

Hello everybody.

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));

NOTE:-

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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

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## Technical Source

Simple! That is me, a simple person. I am passionate about knowledge and reading. That’s why I have decided to write and share a bit of my life and thoughts to.