Multiobjective control of a four-link flexible manipulator: A robust H_∞ approach

This paper presents a new approach to robust H_∞ control of a real multilink flexible manipulator via regional pole assignment. We first show that the manipulator system can be approximated by a linear continuous uncertain model with exogenous disturbance input. The uncertainty occurring in an operating space is assumed to be norm-bounded and enter into both the system and control matrices. Then, a multiobjective simultaneous realization problem is studied. The purpose of this problem is to design a state feedback controller such that, for all admissible parameter uncertainties, the closed-loop system simultaneously satisfies both the prespecified H_∞ norm constraint on the transfer function from the disturbance input to the system output and the prespecified circular pole constraint on the closed-loop system matrix. A new algebraic parameterized approach is developed to characterize the existence conditions as well as the analytical expression of the desired controllers. Third, by comparing with the traditional linear quadratic regulator (LQR) control method in the sense of robustness and tracking precision, we provide both the simulation and experimental results to demonstrate the effectiveness and advantages of the proposed approach.