CHAOS SUPPRESSION IN FRACTIONAL ORDER PERMANENT MAGNET SYNCHRONOUS MOTOR BY ROBUST ADAPTIVE CONTROL

Abstract

In this paper we investigate the control of three-dimensional non-autonomous fractional-order uncertain model of a permanent magnet synchronous motor (PMSM) via a one input control technique. We derive a dimensionless fractional order model of the PMSM from the integer order presented in the literatures. Various dynamic properties of the fractional order model like eigen values, Lyapunov exponents, bifurcation and bicoherence are investigated. The system chaotic behavior for various orders of fractional calculus are presented. A robust adaptive one input controller is derived to suppress the chaotic oscillations of the fractional order model. As the direct Lyapunov stability analysis of the robust controller is difficult for a fractional order first derivative, we have derived a new lemma to analyze the stability of the system. Numerical simulations of the proposed chaos suppression methodology are given to prove the analytical results derived through which we show that for the derived robust adaptive controller and the parameter update law, the origin of the system for any bounded initial conditions is asymptotically stable.