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How can I convert a state-space representation of a system into an equivalent transfer function (symbolic variables)?

Hello, guys, I hope you are well! I have a question: how can I convert a state-space representation of a system into an equivalent transfer function (symbolic variables)?
Example:
%----------------- Arrays (state-space) -----------------%
A=[0 1 0 0; -(Kw+Ks)/Mw -(Cs+Cw)/Mw Ks/Mw Cs/Mw; 0 0 0 1; Ks/Mc Cs/Mc -Ks/Mc -Cs/Mc];
B=[0; Kw/Mw; 0; 0];
C=[1 0 0 0; 0 0 1 0; -1 0 1 0; 0 -1 0 1];
D=[0; 0; 0; 0];
Thanks!

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1 Answer


The answer is:
syms Kw Ks Mw Mc Cs Cw s
%------ Arrays (state-space) ------%
A=[0 1 0 0; -(Kw+Ks)/Mw -(Cs+Cw)/Mw Ks/Mw Cs/Mw; 0 0 0 1; Ks/Mc Cs/Mc -Ks/Mc -Cs/Mc];
B=[0; Kw/Mw; 0; 0];
C=[1 0 0 0; 0 0 1 0; -1 0 1 0; 0 -1 0 1];
D=[0; 0; 0; 0];
%----- Find State Transition -------%
Phi=inv(s*eye(4)-A);
%----- Find transfer function ------%
H=C*Phi*B+D;
%----- Display -----%
pretty(simple(H))
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