Investigation of Frequency-Shaped Final-State Control Design Focusing on Softening Spring Characteristics of Machine-Stand Vibration

Fast and high-precision positioning is key in various industrial fields. In industrial machines with positioning mechanisms, drive systems are generally installed on the machine stands which are installed on the floor with support mechanisms. The machine-stand vibrations caused by the drive systems' high acceleration/deceleration motion deteriorate the positioning performance. Frequency-shaped final-state control (FFSC) is a method to suppress machine-stand vibration. In FFSC, the frequencies to be suppressed must be determined in advance. However, machine-stand vibrations have softening spring characteristics owing to the strong influence of the contact factors. It is unclear which amplitude is utilized when frequency characteristics are acquired in systems with softening spring characteristics because of their amplitude dependence. Here, a non-linear spring model that reproduces the softening spring characteristics is developed, and the frequency characteristics and positioning response are verified. Furthermore, the parameters of the FFSC in the non-linear model are optimized by the particle swarm optimization method, and the determination of the parameters is discussed.