Optimal Placement of an Actuator for Suppressing Vibrations

Abstract

Objective: To observe the effect of location of an actuator on the performance of a smart structure based on active vibration control scheme using an optimization criterion which is optimized by employing GA as a meta-heuristic optimization technique. Methods/Analysis: In this work a two degrees of freedom spring-mass-damper system has been considered with a hypothetical actuator placeable at three different locations. Equations of motion derived from free body diagrams are converted into a system of first order ordinary differential equations to get a state space model. Control gains for suppressing transient vibrations are obtained using Linear Quadratic optimal control. For optimal placement of hypothetical actuator, an optimization criterion (performance index) consisting of sum of transient displacements of both the masses is formulated. MATLAB optimization toolbox based Genetic Algorithm (GA) solver is employed to obtain optimal location of an actuator by minimizing the optimization criterion. Findings: It is found that optimal actuator location gives minimum value of performance index. By placing the actuator at 1st location performance index increases by 1.31 times and by placing at 2nd location it increases by 2.87 times the case when actuator is located at optimal location suggested by GA i.e. 3rd location. It is therefore concluded that an optimal location of an actuator plays a vital role in performance of an active vibration control scheme and GA can be easily employed for finding optimal actuator location. Novelty/Improvements: To optimally place an actuator in a typical actively controlled structure a strategy i.e. optimization criterion based on sum of transient vibrations of a smart structure has been suggested. GA can be used to solve this optimization problem.