H-infinity synthesis using a bilinear pole shifting transform

An H-inifinity control law design is presented for a benchmark problem consisting of an undamped pair of spring-coupled masses with a sensor and actuator that are not collocated. This simple mechanical system captures many of the salient features of more complex aircraft and space structure vibration control problems. The H-infinity 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 a simple s-plane bilinear transform. The transform parameter can give direct control of closed-loop disturbance settling time and controller open-loop pole-zero locations. A four-state H-infinity minimum phase controller was found to meet the given specifications of each design. Detailed analysis on the tradeoffs of sensor noise vs control energy are also presented.