compensator with pole in RHS of s-plane

Dear colleagues,

I am working on a project where i am trying to decouple the internal interaction of 2x2 industrial plant transfer function matrix aiming to get diagonal dominant matrix (Q(s)= G(s)K(s) where G(s) is the plant transfer function matrix and K(s) is the claculated compensators matrix) . I am getting 4 second and first order compensators each with a pole located in the right hand side of the s-plane. Can I acknowledge such compensators? Will the pole located in the RHS of s-plane be a potential of troubles or difficulties for controlling the resulted decoupled transfer function matrix Q(s)?

Thank you in advance

Basim Touqan

[Sam Chak]

Have you successfully designed some controllers to stabilize the "decoupled plants"?

[Basim Touqan]

Dear Mr. Sam,

Yes, I used PID controllers for the individual decoupled loops and got satisfactor output responses, i.e. stable responses, no oscillation around the steady state value, very small steady state error, small percentage of coupling between the outputs, etc. So is it fine to employ compensators with unstable poles? is there any restrictions with compensators with unstable poles?

Thanks & regards

[Sam Chak]

Hi @Basim Touqan

I usually won't design compensators with unstable poles because their role is to stabilize the system. But if your compensators merely serve as "decouplers" and then the entire decoupled system Q(s) = G(s)*K(s) to be stabilized using PID controllers, then it's a different story.

[Basim Touqan]

Thank you sir for your valuable contribution, the issuue remains whether you have a valid reference like a book or a paper or any other valid document that confirmes this conclusion so I can enhance it with such reference as a valid verification. At the end the work needs to be published in a scopus ranked journal where every conclusion must be referenced.

Answer 1

[Sam Chak]

Basim, you should run a few more simulations under different conditions to verify if the approach works. After that, you should rigorously prove that your designed systems are stable, according to some stability theories.

Multivariable Feedback Control: Analysis and Design

Book by Ian Postlethwaite and Sigurd Skogestad

[Basim Touqan]

Thank you again for your interaction, I will follow your approach and rationalise this conclusion