Nonlinear optimal control for the nine-phase permanent magnet synchronous motor
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Industrial Systems Institute
Department of Management and Innovation Systems University of Salerno, Italy
Department of Electrical Engineering King Saud University, Saudi Arabia
Department of ECS Engineering Rensselaer Polytechnic Institute, USA
Department of Electrical Engineering University of Setif I, Algeria
Department of Electrical and Electronic Engineering Science University of Johanessburg, South Africa
Corresponding author
Gerasimos G. Rigatos   

Industrial Systems Institute
Power Electronics and Drives 2023;8(Special Section - Advanced Control Methods of Electrical Machines and Drives )
Multi-phase electric motors and in particular nine-phase permanent magnet synchronous motors (9-phase PMSMs) find use in electric actuation, traction and propulsion systems. They achieve high power and torque rates under moderate variations of phases voltage and currents, while also exhibiting fault tolerance. In this article a novel nonlinear optimal control method is developed for the dynamic model of nine-phase PMSMs. First it is proven that the dynamic model of these motors is differentially flat. Next, to apply the proposed nonlinear optimal control, the state-space model of the nine-phase PMSM undergoes an approximate linearization process at each sampling instance. The linearization procedure is based on first-order Taylor-series expansion and on the computation of the system's Jacobian matrices. It takes place at each sampling interval around a temporary operating point which is defined by the present value of the system's state vector and by the last sampled value of the control inputs vector. For the linearized model of the system an H-infinity feedback controller is designed. To compute the feedback gains of this controller an algebraic Riccati equation is repetitively solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis.