A sum of squares approach to robust PI controller synthesis for a class of polynomial multi-input multi-output nonlinear systems

Abstract

This paper presents a new algorithmic method to design PI controller for a general class of nonlinear polynomial systems. Design procedure can take place on certain or uncertain nonlinear model of plant and is based on sum of squares optimization.The so-called density function is employed to formulate the design problem as a convex optimization program in the sum of squares form. Robustness of design is guaranteed by taking parametric uncertainty into account with an approach similar to that of generalized \({\mathcal {S}}\)-Procedure. Validity and applicability of the proposed methods are verified via numerical simulations. The method presented here for PI controller design is not based on local linearization and works globally. Derived stability conditions overcome several drawbacks seen in previous results, such as depending on a linearized model or a stable model. Furthermore, employing sum of squares technique makes it possible to derive stability conditions with least conservatism and directly design controller for polynomial affine nonlinear systems.