MIMO differential models, State Space representaion problem

Hello all,

I've a MIMO(multi input, multi output) system model & I want it's representaion in State Space form. Following is the diffrential equation:

Now the problem is coeffients M, G, Kss, B & Ki are already in (4x4)Matrix form & "q" is a vector.

Hence, when I try to compute its state space representation using "ss(A,B,C,D)" , It gives me an error.

I want to know, Is there any way that I could represnt my System in Matlab using State Space Representaion.

Your contribution will be highly appreciated.

Answer 1

[Mauro Fusco]

ss(A,B,C,D) refers to the form x_dot = A_ss x+B_ss u; y = C_ss x + D_ss u (i used _ss to distinguish these matrices for the ss() command from the matrices of your system). You can cast your system in this form defining your state vector as:

x = [x1 x2]';

x1 = q;

x2 = q_dot;

then you can write the dynamics of x as: x1_dot = x2; x2_dot = - inv(M)*G*x_2 + inv(M)*B * u.

The first part (x1 dynamics) is a simple integrator (i leave to you to write the A_ss,B_ss matrices for this equation). The second part of the dynamics have: A_ss = - inv(M)*G, B_ss = inv(M)*B.

C_ss you can select based on hat you want to see in the output (which state). You do not need D_ss (set it to 0).