A constrained linear quadratic optimization approach to jerk decoupling cartridge design for vibration suppression

Linear direct feed drives are widely used in high performance equipment and machine tools, but the abrupt counter force to the machine frame from the secondary part of the linear motor induces possible residue vibration. The jerk decoupling cartridge (JDC) provides a buffer to reduce such an impact. However, no existing JDC design considers the factors of closed-loop control together with mechanical parameters, as well as how to obtain optimal parameters under various mechanical and electrical design constraints. This paper presents a systematic methodology to seek optimal control parameters and mechanical parameters for high-speed feed drive positioning. At the starting phase with some simplification, the optimization problem is categorized as a hybrid Linear Quadratic Tracking (LQT) and Linear Quadratic Regulator (LQR) optimization problem. Through a series of simulation, the correctness of obtained optimal parameters is verified.