How to take feedback from a state for a MIMO design

Hi,

How can i create a control system model with feedback taken from state instead of output i.e. State Feedback?

I have 4 states, 2 inputs and 2 outputs.

• Feedback from state 2,x(2) and state 4, x(4) to be used to create input function for u(2) = fs. u(1) does not depend on state.
• I have another concern. While creating the state space model i had my input vector as a 2 X N matrix. However while using a lsim function I had to provide input in the form N X 2. Is there something deeply wrong with my approach?...

Code and document in the links below.

http://sdrv.ms/X0IJVR (Document)

http://pastebin.com/1UEgD5KU (Code)

Thanks for all the help...

Regards

Shilp

Answer 1

[Arkadiy Turevskiy]

You can add 2 more rows to your C and D matrices:

for C: [0 1 0 0;

0 0 0 1];

for D: [0 0;

0 0];

This would give you 4 outputs and 2 inputs, with outputs 3 and 4 being your states 2 and 4.

Arkadiy

[Shilp Dixit]

Hi,

Thank you for your reply. I was wondering if it is possible to do it using the concept of state feedback. I came across it while searching for possible methods. http://www.cds.caltech.edu/~murray/amwiki/index.php/State_Feedback

Any comments on my 2nd point/query.

Thanks again.

Regards Shilp

[Arkadiy Turevskiy]

Not sure what you mean when you are asking about state feedback. State feedback simply means that you use the state vector to create the control signal, u=k*x.

To get access to states, x, you need a unity C matrix and zero D matrix. If it helps, think about it as a second, different state space system.

In regards to dimensions of u, lsim wants it as Nx2, as you already know. In your code this is handled correctly.

HTH. Arkadiy

[Shilp Dixit]

Thank you very much for the help.

I am still a bit confused about the explanation of matrix C and D. 1. Do I create another pseudo system with states as input and my dependent input as the output.

OR

1. Modify my current matrix C and D to accommodate the control signal.

How can I achieve the same result by working on transfer functions?

[Mr. NailGuy]

If I want to get the step response of the output of the system instead of the state variables and plot it using Simulink, how can I get it? Same as this problem posted, I was able to feedback the state to the system but when I check the output of the system it shows the graph of my state instead of my output. Can you help me on this?