A sequential linear least square algorithm for tracking dynamic shapes of smart structures

Abstract

SUMMARYThis paper presents a sequential linear least square algorithm for tracking dynamic shapes of piezoelectric smart structures. The dynamic shape discussed in this paper is defined as a host structural shape varying with time, and the tracking technique is to find an electric voltage history for each piezoelectric device over a time period so that the desired structural movements can be achieved. In the theoretical formulation, dynamic equations of piezoelectric smart structures are introduced by finite element analysis, and then a solution procedure for a set of time-dependent electric voltages is derived by combining the linear least square method and the Houbolt numerical integration scheme. The formulation indicates that this algorithm can be used to find the time-dependent voltages for tracking structural movements of piezoelectric smart structures. The present novel formulation is then demonstrated through numerical examples for tracking dynamic shapes of piezoelectric smart beams and plates. The numerical results for the smart beam are compared with the experimental ones. It is shown that the present sequential linear least square algorithm is capable of efficiently simulating dynamic shape tracking for smart structures.

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

“…With reference to the SLLS algorithm (Luo and Tong 2006b), a structural shape, at an arbitrary point of time, may be expressed as:…”

“…where {Y c (t)} is the computed structural shape at time t, [R V (t)] is the coefficient matrix, which is the constant matrix in linear analysis and {V (t)} is a voltage distribution vector at time t. The vector {Y ρ (t)} represents the structural movement state and the mechanical force at time t, which is referred to as the inertial shape in Luo and Tong (2006b). The shape error at time t is defined as:…”

“…Irschik et al (2006) studied dynamic displacement tracking of smart beams. Luo and Tong (2006b) formulated a sequential linear least squares algorithm (SLLS) for tracking the dynamic shapes of PZT smart structures. Being different from vibration suppression or attenuation, dynamic shape tracking of smart flexible structures controls their designated dynamic movements, including deformation, vibration or other motion states over a given time period.…”

Fast frequency response computation for Rayleigh damping

“…Rayleigh damping is a physical model that has been actively studied over a long period [4][5][6]. The most popular method for solving models with Rayleigh damping is modal superposition, i.e.…”

Integrated design optimization of voltage channel distribution and control voltages for tracking the dynamic shapes of smart plates

“…The host structure and its actuators, as well as electric fields required, are used as design variables. Luo and Tong [16] formulated a sequential linear least-squares algorithm (SLLS) for tracking the dynamic shapes of PZT smart structures. In their later work [17], a segment-based sequential least-squares algorithm (SSLLS) is proposed to track the dynamic shapes of smart structures considering both tracking precision and electrical energy consumption.…”