Fast Search Method for Stable NMPC by Objective Nondimensionalization of Mechatronic Systems

Many nonlinear model predictive controls (NM-PCs) are still suffering from the stability and the computational cost for mechanical and mechatronic systems. The paper provides a simple but general fast search method of design parameters for NMPCs. By applying the proposed method, the computational cost is reduced since the number of the (stable or unstable) closed-loop simulations is decreased and also each closed-loop simulation runs faster. First, we assume dimensions (SI units) for the objective function as well as the constraints. Second, we propose a fast search method of design parameters for NMPCs by introducing a new on-line nondimensionalization for the objective function instead of the standard nondimensionalization for the physical dynamics. Finally, the effectiveness of the proposed method is confirmed by numerical and real experiments using a mechatronic system. Almost 98 % reduction of the total search time is achieved to find good design parameters for the stable closed-loop experiment. Remarkably, the proposed method is applicable to many NMPCs and is not restricted to a specific one.