A novel constrained H₂ optimization algorithm for mechatronics design in flexure-linked biaxial gantry

The biaxial gantry is widely used in many industrial processes that require high precision Cartesian motion. The conventional rigid-link version suffers from breaking down of joints if any de-synchronization between the two carriages occurs. To prevent above potential risk, a flexure-linked biaxial gantry is designed to allow a small rotation angle of the cross-arm. Nevertheless, the chattering of control signals and inappropriate design of the flexure joint will possibly induce resonant modes of the end-effector. Thus, in this work, the design requirements in terms of tracking accuracy, biaxial synchronization, and resonant mode suppression are achieved by integrated optimization of the stiffness of flexures and PID controller parameters for a class of point-to-point reference trajectories with same dynamics but different steps. From here, an H₂ optimization problem with defined constraints is formulated, and an efficient iterative solver is proposed by hybridizing direct computation of constrained projection gradient and line search of optimal step. Comparative experimental results obtained on the testbed are presented to verify the effectiveness of the proposed method.