PID non linear ode model

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Abdelmoumen Bacetti
编辑： Abdelmoumen Bacetti 2017-6-7
Hi guys
I've modeled a nonlinear system using ode function, but I don't see how can I use a PID controller alongside with this ode model in feedback function since this latter function requires inputs of type sys. Is there any way to make this work without linearization of the system.
Here is how the system looks like:
xdot(1) = c11*x(1) + c12*x(2) + c13*x(3) + u
xdot(2) = c21*x(1) + c22*x(2) + c23*x(3)
xdot(3) = c31*x(1) + c32*x(2) + c33*x(3) + NLterm
NLterm = c*x(3)/(c^2 + x(3)^2)
In SS form:
A= [c11 c12 c13;...
c21 c22 c23;...
c31 c32 c33 + c/(c^2 + x(3)^2)];
B = [1 0 0]';
C = [0 0 1];
But, this can't be done with "ss" function in Matlab.
Any ideas !!

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