Robust Decentralized Controller Synthesis in Flexure-Linked H-Gantry by Iterative Linear Programming

The dual-drive H-gantry is widely used for high-speed, high-precision Cartesian motion. Compared with the conventional rigid-linked design, the flexure-linked counterpart is able to prevent the damage of joints for its smaller interaxial coupling force. However, there are still barriers to further push up its precision, such as parametric uncertainties due to the inaccurate dynamical model, the possible induced vibration during high-speed motion, and the decentralized control structure required by industries. To maintain the tracking precision of carriages and minimize the vibration of the end effector, we aim to optimize parameters in decentralized controllers with choices of flexure pieces. We find that such decentralized feedback structure yields some uncontrollable but stabilizable states in the closed-loop system, and no direct solution from solving the algebraic Riccati equation is available in this case. Such structural constraint, together with constraints due to stability requirement and model uncertainties facilitates us to formulate an H2guaranteed cost control problem within a projected convex domain. From here, efficient numerical procedures are developed to obtain the global optimum by iterative linear programming. The real-time experiment validates the optimality and the robustness of the proposed method.