A Design Method of a Vibration Control System for Flexible Structures : Vibration Control with Control Energy Constraints

Abstract

This paper deals with a sensor/actuator placement problem in design of active vibration control system for flexible structures. This problem is formulated as a minimization problem of the total energy which is defined as a sum of a kinetic and strain energy in a colatrolled structure with a constraint of control effort. The inequality constraint on the variance of the closed loop control effort is adopted to represent the capacity of the actuator. Using a design algorithm which iteratively tunes the weighting matrix of the quadratic performance index in LQG problem, the controller which meets these specifications can be synthesized. The optimal location of the sensor/actuator is determined by calculating the total energy for each candidate of them under several energy constraints of the control effort. It is found that the optimal placement of the sensor/actuator depends on the input energy constraint. The simulation and a experiment for a cantilevered beam as a typical example of flexible structures are conducted. It is shown that these results of the optimization can be used as a guide to the design of active vibration control systems.