# State Feedback Integral Control Design

#### abdullah8391

Joined Sep 6, 2015
103
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.

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).

#### Attachments

• 12 KB Views: 1

#### MrAl

Joined Jun 17, 2014
11,276
Hi,

Just some general questions...

Did you ever do a simpler system before this?
Did you ever use State Space methods for control system design before?

#### abdullah8391

Joined Sep 6, 2015
103
Hi,

Just some general questions...

Did you ever do a simpler system before this?
Did you ever use State Space methods for control system design before?
Yes, did all the examples and exercise problems of Norman chap. 12 and Ogata servo motor example.

#### MrAl

Joined Jun 17, 2014
11,276
Yes, did all the examples and exercise problems of Norman chap. 12 and Ogata servo motor example.
Hi,

Then i guess they all worked out ok except for this one.
This is a little more involved than i usually like to get in these forums but if i can i will take a closer look.
The 12x12 matrix makes it a little more time consuming
Too bad i dont have that book either.

#### abdullah8391

Joined Sep 6, 2015
103
Hi,

Then i guess they all worked out ok except for this one.
This is a little more involved than i usually like to get in these forums but if i can i will take a closer look.
The 12x12 matrix makes it a little more time consuming
Too bad i dont have that book either.
No need to do by hand, start MATLAB, it hardly takes 5 minutes.
I am weak in control system concepts that's why I need help!

Last edited:

#### abdullah8391

Joined Sep 6, 2015
103
Hi,

Then i guess they all worked out ok except for this one.
This is a little more involved than i usually like to get in these forums but if i can i will take a closer look.
The 12x12 matrix makes it a little more time consuming
Too bad i dont have that book either.
Also this is not any book problem, it is a question related to my project.

#### MrAl

Joined Jun 17, 2014
11,276
Hi,

Wow the whole book in pdf format that's amazing.
What is funny is that so many of these books have the words "Modern Control" in the title.

I dont have Matlab though that might be a problem, but i'll look it over anyway.

Is this problem in the book somewhere?

#### abdullah8391

Joined Sep 6, 2015
103
Hi,

Wow the whole book in pdf format that's amazing.
What is funny is that so many of these books have the words "Modern Control" in the title.

I dont have Matlab though that might be a problem, but i'll look it over anyway.

Is this problem in the book somewhere?
This is not a book problem, this is a problem related to my project. I am designing dynamic model for quadcopter and I followed this paper. Though the system is stable but it has steady state error. In easy terms I want to remove this steady state error, for that I only know one approach, that is, insert an integral action. I know the basic procedure of designing from Ogata book (I did read some other books and MIT lecture, procedure was same with different notations) but for some this procedure isn't applicable for my problem.
My query is:
1. If you know some other way of removing steady state error from state feedback control design, please let me know.
2. Or tell me where I am wrong in following the procedures mentioned in book.

#### abdullah8391

Joined Sep 6, 2015
103
This is not a book problem, this is a problem related to my project. I am designing dynamic model for quadcopter and I followed this paper. Though the system is stable but it has steady state error. In easy terms I want to remove this steady state error, for that I only know one approach, that is, insert an integral action. I know the basic procedure of designing from Ogata book (I did read some other books and MIT lecture, procedure was same with different notations) but for some this procedure isn't applicable for my problem.
My query is:
1. If you know some other way of removing steady state error from state feedback control design, please let me know.
2. Or tell me where I am wrong in following the procedures mentioned in book.
Also I have the complete research paper in PDF form, I don't know if posting a paper here would be good idea or not.

#### MrAl

Joined Jun 17, 2014
11,276
Also I have the complete research paper in PDF form, I don't know if posting a paper here would be good idea or not.
Hi,

Why would you not be able to post it, is it copyrighted or something?

But i read over some of your posts, are you saying that you used pole placement not state variable control methods?
Also, are you saying that some states are not observable? If so then you have to construct an estimator.

It might be better to start with a smaller system and work with that first then i could work it with my current software too.