Robust control of nonlinear uncertain systems

This paper presents a new control procedure for designing robust controllers for nonlinear time-varying systems that contain uncertain terms. The application of the Lyapunov theory allows us to avoid certain difficulties associated with the application of the Hamilton-Jacobi theory which leads to nonlinear two-point boundary-value problems. The solution is obtained by applying sufficient conditions for robust stability. The foundation of our algorithm, which allows one to solve the nonlinear robust control problem, is based upon the Lyapunov-based lemma, and nonquadratic Lyapunov candidates are used to synthesize nonlinear robust algorithms. The method is computationally attractive, and the reported concept makes it possible to design nonlinear controllers for high order uncertain systems. We illustrate the procedure by studying the multivariable electric motor with parameter variations. In particular, a robust regulator is synthesized to control the squirrel-cage induction motor, and robustness of the closed-loop system is verified. Experimental results are performed to validate the bounded controller as well as to analyze the system performance and dynamics