I am working on designing controller for a MIMO system, the system is undereducated i.e. number of inputs are less that Degrees of Freedom. What I have done so far is:
1. Designed state space model for desired system. Matrix Dimensions of the designed system are A(12x12), B(12x4), C(6x12).
2. Designed controller through pole placement method.
3. Justified that the response was stable but there was steady state error.
4. I found out that steady state error can be removed by designing integral action.
5. Tried to design integral control but failed in that.
The reason why I am failing is, I found two approaches to design integral action, both approaches are quite similar with only difference how to start up. Since I am dealing with MIMO system so I decided to use approach described in modern control engineering by Ogata 3rd edition (servo system design, page no. 849 and onwards). Here B’ = [B; 0] and A’ = [A B; C 0], the resultant A’ matrix should be square matrix but I get A’(18x16) matrix, if I add zeros with B matrix to make A’ a square matrix, the system doesn’t remain controllable (rank of the system comes to be 16). I don’t know how to deal with this problem, it would be really helpful if anyone can guide me how to resolve this issue.
Attached file has matrices (copied from MATLAB).
1. Designed state space model for desired system. Matrix Dimensions of the designed system are A(12x12), B(12x4), C(6x12).
2. Designed controller through pole placement method.
3. Justified that the response was stable but there was steady state error.
4. I found out that steady state error can be removed by designing integral action.
5. Tried to design integral control but failed in that.
The reason why I am failing is, I found two approaches to design integral action, both approaches are quite similar with only difference how to start up. Since I am dealing with MIMO system so I decided to use approach described in modern control engineering by Ogata 3rd edition (servo system design, page no. 849 and onwards). Here B’ = [B; 0] and A’ = [A B; C 0], the resultant A’ matrix should be square matrix but I get A’(18x16) matrix, if I add zeros with B matrix to make A’ a square matrix, the system doesn’t remain controllable (rank of the system comes to be 16). I don’t know how to deal with this problem, it would be really helpful if anyone can guide me how to resolve this issue.
Attached file has matrices (copied from MATLAB).
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