Low-complexity model predictive control of electromagnetic actuators with a stability guarantee

Electromagnetically driven mechanical systems are characterized by fast nonlinear dynamics that are subject to physical and control constraints, which makes controller design a challenging problem. This paper presents a novel model predictive control (MPC) scheme that can handle both the performance/physical constraints and the strict limits on computational complexity required in control of general electromagnetic (EM) actuators. The 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. In this way feasibility of the MPC algorithm is improved considerably. While the MPC scheme uses a full nonlinear model, which improves performance, we show that the resulting MPC problem can still be transformed into a low-complexity linear program that can be solved by modern microprocessors within tenths of milliseconds. Moreover, an even simpler piecewise affine explicit controller can be obtained via multiparametric programming. Simulation results are reported and compared with the results achieved by state-of-the-art explicit MPC based on a piecewise affine model.