H∞ robust control synthesis for an undamped, non-colocated spring-mass system

An H^∞ control law design is presented for an undamped pair of spring-coupled masses with a sensor and actuator which are not colocated. This simple mechanical system captures many of the salient features of more complex aircraft and space structure vibration control problems. The H^∞ problem formulation enables the issue of stability robustness in the face of large mass and spring constant variation to be directly addressed. Constraints on closed-loop dominant pole locations and settling time are accommodated via the simple s-plane bilinear transform s = +/r+1. The parameter "σ" is found to be directly related to closed-loop disturbance settling time and controller open loop pole-zero locations, respectively. A 4-state H^∞ controller has been developed for each of three benchmark problems via this procedure. These controllers which are stable and minimum phase have met all the benchmark design specifications.