On the feedback control of the wave equation

摘要

This paper addresses the problem of design of collocated andnoncollocated controllers for a uniform bar without structural damping.The bar whose dynamics are described by the wave equation is required toperform a rest-to-rest maneuver. A time delay controller whose gains aredetermined using the root-locus technique is used to control thenoncollocated system. The effect of sensor locations on the stability ofthe system is investigated when the actuator is located at one end ofthe bar. The critical gains which correspond to a pair of poles enteringthe right-half of the s-plane and the optimal gains which correspondingto locating the closed-loop poles at the left extreme of the root-locusfor each vibration modes are determined. The gain which minimizes aquadratic cost, in the range of the critical gains, is selected as theoptimum gain