Discrete optimization for actuator and sensor positioning for vibration control using genetic algorithms

Abstract

Research about actuator and sensor positioning is important to obtain smart structures that can achieve better performance, and studies concerning controller design techniques are also important. In some studies on smart structures, the positioning of sensors and actuators are defined by some physical criteria and, thereafter, the controller is designed to satisfy some requirements of the controlled system. However, the optimal number and placement of sensors and actuators can also be obtained through the solution of an optimization problem, taking into account, for example, the possible positions to allocate the active elements and the available number of these. This paper presents a discrete heuristic optimization technique in order to determine the discrete positions of the active elements in active control systems. Furthermore, a technique that involves the determination of the number of active elements and the positioning is shown. These techniques have been implemented based on the genetic algorithms. Depending on the desired number of the sensors and actuators, and the number of candidate positions, it is impractical to use a combinatorial algorithm, as this is very expensive in terms of computational time due to the number of possible combinations. Thus, the techniques developed here have the aim to obtain good solutions analyzing fewer combinations than the combinatorial method and in reduced computational time. In this paper, the controllers are designed based on the ${\mathcal{H}}_{\infty }$ control theory. The objective function used to solve the positioning problem of active elements is the ${\mathcal{H}}_{\infty }$ norm of the closed-loop system.