MIMO differential models, State Space representaion problem
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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.
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Mauro Fusco
le 16 Avr 2019
Modifié(e) : Mauro Fusco
le 16 Avr 2019
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).
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