A nonlinear optimal control approach for voltage source inverter-fed three-phase PMSMs

Voltage-source inverter-fed Permanent Magnet Synchronous Machines are widely used in industry (for instance for the actuation of robotic and mechatronic systems, of cranes, in water pumping stations) as well as in transportation systems (for the traction of trains and electric vehicles). The present article proposes a nonlinear optimal control approach for voltage source inverter-fed Permanent Magnet Synchronous Machines (VSI-PMSMs). The nonlinear dynamic model of VSI-PMSMs undergoes approximate linearization around a temporary operating point which is recomputed at each iteration of the control method. This temporary operating point is defined by the present value of the voltage source inverter-fed PMSM state vector and by the last sampled value of the machine's control inputs vector. The linearization relies on Taylor series expansion and on the calculation of the system's Jacobian matrices. For the approximately linearized model of the voltage source inverter-fed PMSM an H-infinity feedback controller is designed. This controller stands for the solution of the nonlinear optimal control problem for the voltage source inverter-fed PMSM under model uncertainty and external perturbations. For the computation of the controller's feedback gain an algebraic Riccati equation is iteratively solved at each time-step the control method. The global asymptotic stability properties of the control method are proven through Lyapunov analysis.