Output feedback controller design for polynomial linear parameter varying system via parameter-dependent Lyapunov functions

Xiaobao Han,Zhenbao Liu,Huacong Li,Xianwei Liu

doi:10.1177/1687814017690327

Abstract

This article presents a new output feedback controller design method for polynomial linear parameter varying model with bounded parameter variation rate. Based on parameter-dependent Lyapunov function, the polynomial linear parameter varying system controller design is formulated into an optimization problem constrained by parameterized linear matrix inequalities. To solve this problem, first, this optimization problem is equivalently transformed into a new form with elimination of coupling relationship between parameter-dependent Lyapunov function, controller, and object coefficient matrices. Then, the control solving problem was reduced to a normal convex optimization problem with linear matrix inequalities constraint on a newly constructed convex polyhedron. Moreover, a parameter scheduling output feedback controller was achieved on the operating condition, which satisfies robust performance and dynamic performances. Finally, the feasibility and validity of the controller analysis and synthesis method are verified by the numerical simulation.

Highlights

Most physical systems have significant nonlinear characteristics, which cannot be ignored in many control designs and brought great complexity in system analysis and synthesis.[1,2,3]
Based on Lyapunov theory, the analysis and synthesis methods for linear parameter varying (LPV) control are typically focused on the construction of Lyapunov functions
For the polynomial linear parameter varying (PLPV) model with bounded parameter variation rate, the parameterized linear matrix inequality (PLMI) conditions guaranteeing robust performance are studied for parameterdependent Lyapunov function (PLF)-based controller design

Summary

Introduction

Most physical systems have significant nonlinear characteristics, which cannot be ignored in many control designs and brought great complexity in system analysis and synthesis.[1,2,3] In gain-scheduling control for nonlinear objects, classical gain-scheduling controller is constructed from interpolation of local linear controller gains designed by linear time-invariant control theory. For the PLPV model with bounded parameter variation rate, the parameterized linear matrix inequality (PLMI) conditions guaranteeing robust performance are studied for PLF-based controller design. Based on Theorems 2 and 3, the global controller design can be achieved by satisfying equation (15) on the constructed convex polyhedron vertex set. The controller design problem for PLPV model in Theorem 1 with constraints (11) can be reduced to a normal LMI constrained convex optimization problem as follows. According to the aforesaid theory, following are the steps of output feedback controller design method for PLPV model using PLF: Control system HN performance analysis.

À0:991 10:516 5 1:909

Findings

Conclusion