New Methodology for Control of Nonlinear Unstable Multivariable Systems

Abstract

In this paper, a new methodology for control of nonlinear unstable multivariable systems is developed. The method involves stabilization of the nonlinear plant followed by generation of sinusoidal input describing function (SIDF) models of the stabilized closed-loop system. With the known SIDF model of the closed-loop system and the known stabilizing controller, the model of the unstable nonlinear multivariable system is extracted; then a controller for the model is designed. Finally, the design is verified by simulation. Stability is demonstrated by successful generation of SIDF models of the designed closed-loop system for various amplitudes of excitation. The method is applied to a two-input/two-output (TITO) model of a nonlinear unstable robotic arm, and the results are compared with an alternative approach.