A Methodology for Determination of Piezoelectric Actuator and Sensor Location on Beam Structures

Abstract

In the design of actively controlled structures, the determination of the actuators and sensors location is a very important issue. In this way, the purpose of this paper is to propose a new approach to "nd the optimal location of piezoelectric actuators and sensors on beam structures. More precisely, "rst the optimization criteria are de"ned: it is proposed here to "nd the optimal actuators location by minimizing the mechanical energy integral of the system and the optimal sensors location by maximizing the energy of the state output. In the two cases, a sensitivity method applied to the discrete equations is used. Several results are presented. This methodology is used to "nd the optimal location of one actuator and one sensor on a cantilever beam, and on a three-beam structure. When there are di!erent optimal locations, several performance measures are considered in order to keep one location.

Recent Advances in Optimization of Smart Structures and Actuators

“…The optimization problem is solved analytically using a closed form solution of the optimality conditions. Bruant et al (2001) optimize both sensor and actuator locations, but consider them separately. The actuator length and location are found first by minimizing the mechanical energy integral, then the sensor location is found by maximizing a measure of the observability Grammian.…”

The state of the art of sensor placement methods in structural health monitoring

“…However, few investigators take the influence of loading situations into consideration when a method of placing sensors is being developed [43,44] , even though implicitly. The authors noted that sensors should place at different positions if the loadings vary with positions and frequencies during modal experiments [45] .…”

Robust vibration control of uncertain flexible structures based on model reduction

“…Bruant I. [8] proposed an approach to find the optimal actuator location by minimizing the mechanical energy integral of the system and the optimal sensor location by maximizing the energy of the state output. Michael A. Demetriou [9] used an analytical bound approach to place collocated actuators and sensors in structural systems so that the H infinity norm of the transform function whose input is disturbance is the smallest.…”

“…Several optimization criteria for optimal placement were proposed in [7][8][9]. Li Bin [7] used maximal modal force rule for optimal placement of This work is supported by National Natural Science Foundation (NNSF) of China under Grants 61225013 and 11332001. point piezoelectric actuators for plates.…”