Controller Synthesis via Differential Game Theory Approach For Vibration Suppression

In this paper a differential game is developed for a forced vibration of two DOF spring-mass system. The active control system is developed to suppress the vibration of one of the masses against another mass's arbitrary bounded motion. It is desired to minimize the terminal miss distance for the mass under the control with the time of termination prescribed. In this vibration system, the noise is able to change itself unpredictablyin duration of time and only its effects on the system, i.e. transposition and velocity are measurable. The control system should be able to suppress the unpredictable second mass motion. This problem is interpreted as a differential game which the controller competes against noise and it has been solved by differential games method. The results show the effectiveness of the control system in noise and disturbance rejection.

Keywords:

game theory , differential games , optimal strategies , vibration suppression