Convex Optimization Based Design of Finite Impulse Response Filters for Reference Shaping

This paper explores design of finite impulse response (FIR) filters for controlling underdamped systems while dealing with uncertainties in model parameters. By setting magnitude constraints in the frequency domain within a convex programing framework, it ensures that dominant resonant modes are attenuated at the end of the maneuver, high-frequency unmodeled modes are not excited, and there is no inordinate accentuation of frequencies in the passband of the filter. A mobile platform with an attached flexible beam serves as a testbed to validate the designs for rest to rest maneuvers, demonstrating how different cost functions of error between the desired and optimized magnitude response affect the filter performance. The study also examines robustness in the notch area by shifting the natural frequencies of the system by shifting a tip mass at the free end of the beam. The total energy at the final maneuver time of the first three system modes is calculated as a vibration suppression metric and is used to compare established input shapers with the proposed finite impulse response filters.