A nonlinear optimal control approach for permanent magnet AC motors with non-sinusoidal back EMF

The present article proposes a nonlinear optimal control approach for permanent magnet AC machines with non-sinusoidal back electromotive force being fed by three-phase inverters. Such AC machines are also known as permanent magnet brushless DC motors (PMBLDC) and find use in several traction and actuation systems. First, by applying an extended park transformation, the dynamic model of the electric motor is expressed in the dq rotating reference frame. Next, the nonlinear dynamic model of the electric motor 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 electric motor’s 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 electric motor, an H-infinity feedback controller is designed. This controller stands for the solution of the nonlinear optimal control problem for the considered type of electric motor under model uncertainty and external perturbations. For the computation of the controller’s feedback gains, an algebraic Riccati equation is iteratively solved at each time-step of the control scheme. The global asymptotic stability properties of the control scheme are proven through Lyapunov analysis. Finally, the nonlinear optimal control method is compared against flatness-based control and sliding-mode control.