11. Simulation Study of Model Predictive Vibration Control

This chapter presents the results of simulations performed with various computationally efficient model predictive control (MPC) strategies applied to the state space model of an active vibration control (AVC) demonstration device. A numerical study analyzing the minimal prediction horizon necessary to steer system state into equilibrium for the AVC demonstrator model suggests very long horizons, even for relatively small outside disturbances. Because infinite horizon cost dual-mode quadratic programming based MPC (QPMPC) with stability guarantees is assumed for this test, the feasibility of the online implementation with several hundred steps long horizon is unlikely due to excessive computation times. Through the computation of offline optimization times, number of regions and controller sizes, it is demonstrated here that the computational requirements of multi-parametric programming based MPC (MPMPC) also render it as an unlikely candidate for the AVC of lightly damped systems. From the viewpoint of computational complexity, Newton–Raphson MPC (NRMPC) is certainly a good choice for AVC, however, not without drawbacks. As the simulation results presented here suggest, invariance of the target set and therefore constraints can be violated due to numerical imprecision at the offline computational stage. Moreover, the suboptimality of this approach becomes troubling with increasing problem dimensionality. As the numerical tests demonstrate, the offline computational drawbacks can be partly remedied by performance bounds and proper solver settings, while the optimality is somewhat influenced by a suitable input penalty choice. The chapter is finished with a simulation comparison of the QPMPC, MPMPC and NRMPC algorithms, which shows input and output sequences in agreement with theoretical expectations.