Robust polynomial eigenstructure assignment control of a class of nonlinear systems

Abstract

A nonlinear controller based on polynomial eigen-structure assignment (PEA) is presented for a class of nonlinear systems. In this paper, the PEA approach used for LTI and LPV models is extended to QLTV model to realize the desired control performance of closed-loop system. With PEA approach, the eigenstructure assignment for the controller can be completed without imposing any particular eigenvalues. Using a polynomial matrix eigenspace for system and a coprime factorization for desired closed-loop transfer function, the designer is only left to choose the controller structure and calculate the controller gains by several simple formulas to produce a flexible design method for nonlinear system. As simple functions of varying parameters, the controller gains enable to realized the independence between the closed-loop system and the operating point. The stability of nominal closed-loop system and robustness of uncertain system are analyzed by using Lyapunov theorem. Finally, PEA approach is applied to a nonlinear control system and the corresponding simulation is carried out to verify the performance of system.