A segment based sequential least squares algorithm with optimum energy control for tracking the dynamic shapes of smart structures

摘要

This paper presents a segment based sequential least squares algorithm with optimum energy control for tracking the dynamic shapes of piezoelectric smart structures. In this algorithm, integration of the square difference between the desired and achieved dynamic shapes over a time period is employed as an error function. The total electrical energy consumption of all actuators is used as the other control target. Two control schemes are studied: (a) minimization of the square error over a time period with energy constraint and (b) minimization of control energy with specified square error constraint. The Lagrange multiplier technique is used to consider the constraint, in which the properties of the characteristic matrix and polynomials of the Lagrange multiplier are analysed. Based on the present analysis, a simple and efficient algorithm is proposed; the relationship between permissible energy constraint and achievable minimum square error is investigated. Numerical results are presented for tracking twisting shape variations of a smart plate. Optimum energy control for reducing conflicting effects of the applied actuation voltages is also discussed.