How to create an input that is a function of State

I have a mechanical system with:

2 Inputs (i, fs)

4 states(x1, x2, x3, x4)

2 outputs(y1=x1 and y2=x3)

I want the input 'fs' as a function of two states x2 and x4. How can i do that?...

Does this problem require state feedback and how can I use it for a practical problem.

Thanks

Shilp

Answer 1

[Azzi Abdelmalek]

In your SS block, initialy c=[1 0 0 0;0 0 1 0] and d=[0 0;0 0]

If you want to use x2 and x4, set c=eye(4) and d=zeros(4,2), you will obtain 4 output in this order x1, x2, x3 and x4. use x1 and x3 as output, and do whatever you want with x2 and x4

[Shilp Dixit]

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

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

This is my code and document. I came across the concept of state feedback and 'reachability' from http://www.cds.caltech.edu/~murray/amwiki/index.php/State_Feedback Can this concept be used for my problem?...

Thanks Shilp

[Azzi Abdelmalek]

Shilp, what about my suggestion, have you tried it?

[Azzi Abdelmalek]

Shilp, your question was, how to use x2 and x4, what did you get?

[Shilp Dixit]

Hi,

I will be trying out your suggestion tomorrow. Will provide an updated report. It is too late in the night right now. :)

Thanks again.

[Shilp Dixit]

Hi,

I have made the changes as suggested by you.So now the state space model is a 2 input, 4 state and 4 output model. Now I can use the two outputs x1 and x3 to give feedback and x2 and x4 to build one of the input functions. I have a couple of questions that branch out from this approach.

1. Is is advisable and ok to have a system where the states and outputs represent the same physical quantity. Will it create any problems in terms of stability etc.

2. My input function is made up of two signals [i; fs]. fs is a function of the two outputs x2 and x4. How can I code this in matlab?

[Azzi Abdelmalek]

Hi, From your question, you said that output1=x1 and output2=x3 What we 've added will not affect anything, the states x2 and x4 exist and are computed even we did'nt make change. We have just acces to the values.

[Shilp Dixit]

Yes, I understood that we have access to these values as O/p. One of my input function fs(semi-active damper force) now has to compute dynamically from these values of Output2=x2 and output4=x4. How do I go about achieving this:

1. Create individual feedback loops for each o/p stream based on the individual transfer functions that we obtain.

OR

2. Is there any other way form the function fs as fs(x2,x4,t)?

thanks.

[Azzi Abdelmalek]

Shilp, Now you are asking another question. I don't know which method you are using to control your system. In real application, sometimes we have'nt acces to states measurment, the states x2 and x4 are estimated (Kalman filter for example).

[Shilp Dixit]

Hi,

I think I got all my doubts cleared. Will work on creating the control algorithm. Will approach if I have any more doubts. I have had no formal education in the field of dynamics and control and hence the numerous doubts.

Thanks for your patience.

Regards

Shilp