Integrated Mechatronic Design in the Flexure-Linked Dual-Drive Gantry by Constrained Linear–Quadratic Optimization

A dual-drive H-gantry is commonly used in many industrial processes to meet the requirement of high-precision Cartesian motion. Unlike the rigid-linked gantry stage, the flexure-linked counterpart allows a small degree of rotation of the crossarm to prevent possible damages. However, by this design, the chattering of control signals and inappropriate stiffness of the flexure may induce the resonant modes of the gantry. Hence, to maintain the precision tracking of the midpoint position and the orientation of the gantry, as well as to minimize the vibration on the end effector, we seek the most suitable flexure stiffness and controller parameters by formulating a constrained linear-quadratic optimization problem. Since such a mechatronic design problem is not solvable via standard linear-quadratic regulator formulas, we convert it to a constrained projection gradient-based optimization problem, which can be efficiently solved by direct computation of projection gradient and line search of optimal step length. A fast convergence of parameters is achieved after first several iterations. Through a series of comparative experiments, the effectiveness of the proposed method is validated.