Linear Simulation Tool Problem

Hello,

I am trying to produce graphs showing me how my state-space model responds to a sine function.

Unfortunately when using the Linear Simulation Tool, importing the system G and trying a linear analysis with time t = [0:0.1:10] and signal u=sin(t).

The program tells me "None of the systems have a complete set of inputs." Is there a way to solve this?

Regards,

Maxence

Here is my code:

% 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 = 0;

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

Answer 1

[Star Strider]

This works for me:

t = 0:0.1:10;
u = ones(size(B,2),1)*sin(t);

y = lsim(G, u', t);

figure
plot(t, u, '--')
hold on
plot(t, y)
hold off
grid

Experiment to get the result you want.

[Maxence Luneau]

Dear Star Strinder,

Thank you very much for you solution from which I can now simulate plots while changing the signal!

I was wondering if you could perhaps give me further information as to the "None of the systems have a complete set of inputs." error if you know about it? Is it due to my previous u matrice not being of the correct size, as you specified here size(B, 2).

Thank you again!

[Star Strider]

As always, my pleasure!

To use any state space representation of a system, the input signal has to be compatible with the size of the B and D matrices. That has everything to do with matrix operations and linear algebra. I used the state space representation, rather than the transfer function representation, to do the simulation, because the state space representation more accurately represents the system and is easier to change (pole placement, etc.) if necessary. The input signal does not necessarily have to feed into every input in B and D (zero vectors are certainly permitted), although it must be compatible with matrix multiplication with B and D. That discrepancy was likely throwing the error.

[Maxence Luneau]

Hello again,

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.

Using the same 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.

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!

Cheers

[Star Strider]

I have not done anything with Simulink in a long time, so I cannot help you with it.

If possible, do everything in state space. It is much easier. I have no idea how you are supposed to approach this problem, however pole placement, state feedback, and such in state space is preferable. With respect to the tf and ss2tf functions, tf accepts numerator and denominator polynomials to produce a system object defined initially by a transfer function. The ss2tf function converts a state space model to a transfer function model. You can find good descriptions of that process in all good modern control textbooks. (I prefer state space for many reasons, some of which I mentioned here. I do not remember much about classical control.)