  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.
