State Space system and PID Controller Implementation

Hello,

I'm stil a struggling a bit with Matlab and Simulink trying to combine both to implement a PID Controller to my state space model.

I have set up matrices A, B, C,D to give me a 4x4 state space model which I can transform into a series of transfer functions. I understand that for my PID controller analysis I need to decouple my model to be able to select 1 dimension, 1 control input of motion to give me 1 output for me to analyse this with a PID controller.

Another difficulty is how do I define the error and gains I need to render my model stable: which is the objective of this exercice. I have found some values of static gain although I do not know how they connect to my model and where I should implement these after.

On another note, I am confused between the difference between the tf and ss2tf functions.

% A, B, C, D Matrices

A = [0 0 0 1 0 0 0 0 0 0 0 0;
    0 0 0 0 1 0 0 0 0 0 0 0;
    0 0 0 0 0 1 0 0 0 0 0 0;
    0 0 0 -0.0855 0 0 0 -9.81 0 0 0 0;
    0 0 0 0 -0.0855 0 9.81 0 0 0 0 0;
    0 0 0 0 0 0 0 0 0 0 0 0;
    0 0 0 0 0 0 0 0 0 1 0 0;
    0 0 0 0 0 0 0 0 0 0 1 0;
    0 0 0 0 0 0 0 0 0 0 0 1;
    0 0 0 0 0.7415 0 0 0 0 0 0 0;
    0 0 0 0.7415 0 0 0 0 0 0 0 0;
    0 0 0 0 0 0 0 0 0 0 0 0];

B = [0 0 0 0;
    0 0 0 0;
    0 0 0 0;
    0 0 0 0;
    0 0 0 0;
    -0.01435 -0.01435 -0.01435 -0.01435;
    0 0 0 0;
    0 0 0 0;
    0 0 0 0;
    0 -124.4 0 124.4;
    124.4 0 -124.4 0;
    -0.01999 0.01999 -0.01999 0.01999];

C = [1 0 0 0 0 0 0 0 0 0 0 0;
    0 1 0 0 0 0 0 0 0 0 0 0;
    0 0 1 0 0 0 0 0 0 0 0 0;
    0 0 0 0 0 0 0 0 1 0 0 0];

D = zeros(4, 4);

G = ss(A, B, C, D);
I = tf(G);
J = ss2tf(A, B, C, D, 4);

Coming back to simulink, how do I simplify my model for it to hold true and facilitate a Simulink analysis?

If you could elaborate, or give me any advice/information, I would be extremely grateful!

Regards,

Maxence