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

Abstract

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