Low-complexity model predictive control of ElectroMagnetic actuators

Electromagnetically driven mechanical systems are characterized by fast non-linear dynamics that are subject to physical and control constraints. This paper describes a Model Predictive Controller (MPC) for a general ElectroMagnetic (EM) actuator that satisfies both the performance constraints and the strict requirements on the computation time. Novel aspects of the MPC design are a one-step-ahead prediction horizon and an infinity-norm artificial Lyapunov function that is employed to drive the system to a desired reference. An additional optimization variable is introduced to relax the conditions on the Lyapunov function, which is not forced to decrease monotonically. This feature improves feasibility considerably. The resulting MPC problem is transformed into a low-complexity linear program that can be solved by modern microprocessors within tenths of milliseconds. An even simpler piecewise affine explicit controller is obtained via multiparametric programming. Simulation results are reported and compared with the results achieved by existing state-of-the-art explicit MPC.