Nonsmooth-Optimization-Based Bandwidth Optimal Control for Precision Motion Systems

Abstract: Precision motion systems are at the core of various manufacturing equipment. The rapidly increasing demand for higher productivity necessitates higher control bandwidth in the motion systems to effectively reject disturbances while maintaining excellent positioning accuracy. However, most existing optimal control methods do not explicitly optimize for control bandwidth, and the classic loop-shaping method suffers from conservative designs and fails to address cross-couplings, which motivates the development of new control solutions for bandwidth optimization. This paper proposes a novel bandwidth optimal control formulation based on nonsmooth optimization for precision motion systems. Our proposed method explicitly optimizes the system's MIMO control bandwidth while constraining the H-infinity norm of the closed-loop sensitivity function for robustness. A nonsmooth optimization solver, GRANSO, is used to solve the proposed program, and an augmented quadratic programming (QP)--based descent direction search is proposed to facilitate convergence. Simulation evaluations show that the bandwidth optimal control method can achieve a 23% higher control bandwidth than conventional loop-shaping design, and the QP-based descent direction search can reduce iteration number by 60%, which illustrates the effectiveness and efficiency of the proposed approach.