Optimal control strategy of an induction motor for loss minimization using Pontryaguin principle

Abstract

This paper presents a new design of loss-minimization optimization control for Induction Machine (IM) drives. It describes a closed-loop optimal control law and exploits the Pontryagin principle to get optimal energy consumption. This proposal is based on the Optimal Control Problem (OCP) which focuses on minimizing a cost function given as an integral of a weighted sum of the mechanical power, copper losses and magnetic power of the IM. In order to minimize the IM energy consumption, we consider a normalized cost function with respect to the optimization finite-interval [0,T]. This functional is subjected to dynamic constraints which are developed from a reduced IM model. The system depends on two state variables: the rotor flux and the motor speed. The proposed method provides an optimal rotor flux that performs the minimal energy consumption of an IM along a given torque and velocity. This OCP conducts to a system of combined nonlinear differential equations of state and co-state variables. Long and hard developments lead to many calculus steps. Finally, an optimal time-varying rotor flux is successfully turned out. This OCP satisfies also abrupt torque conditions and can cover dynamic operations when the proposed solution fulfills some criteria of sub-optimality. The validity of the suggested optimal control design is tested via simulation and then via experimental results by comparing a dynamic control law using the proposed optimal rotor flux trajectory with a conventional control utilizing the rated flux value.