Efficient Shape Control of Distributed Reflectors with Discrete Piezoelectric Actuators

Abstract

In the current article, a novel approach to the shape control problem with a limited number of discrete actuators is presented. In optimizing the actuator locations, first the reference input was expanded with a representative set of eigenfunctions. From the expansion coefficients, the dominant modes in the reference input were identified. Next the distributed parameter system was rewritten in modal coordinates and the irrelevant modes were truncated. Finally, the actuator locations were selected such that the singular values of the controllability matrix of the truncated system were maximized. The steady state actuation forces were optimized such that a cost function based on the absolute value of the steady state error is minimized. To improve the transient response, a hybrid of dynamic modal control algorithm and the optimization method is developed. Four discrete linear actuators for the one-dimensionally curved reflector and eight actuators for the two-dimensionally curved reflector are utilized. The structures are controlled and assessments for experimental implementation are made.

An investigation into shape and vibration control of space antenna reflectors

“…They found that the beam shaping increases the coverage area by 40% while a beam-steering scanning angle of 10°is achieved. Andoh et al (2004) investigated the problem of shape control in the antenna reflector with a minimum number of actuators. Locations of the actuators were optimized by removing the unnecessary modes from the modal coordinates.…”

Development of the En Masse Elimination Algorithm for Actuator Grouping Optimization

“…Background and Research Goal I N many adaptive structural system concepts, large numbers of actuators are utilized to achieve high authority and near distributed control actions. Many studies to date (Andoh et al, 2004;DeSmidt et al, 2006;Chen et al, 1991) have assumed that each actuator can be controlled individually. While ideally each actuator should be controlled by an individual power supply, at times it is not realistically feasible due to design, weight, or cost constraints.…”

Deflection model for corner-supported plates with segmented in-plane actuators

“…In [10,16], finite element models for simply supported rectangular PVDF laminates are studied. Control algorithms based on analytical and numerical laminate models are discussed in [2,3,13].…”