A Parallel Control System for Continuous Architecture Using Finite Element Method

Abstract

In this paper, a parallel control system for continuous architecture formed by bimorph piezoelectric actuators has been developed and verified. Finite Element Method (FEM) is adopted as the control scheme for it is capable of expressing the behavior of the whole system by evaluating the stiffness equations. Conventional control system requires a slight change in its state equations, depending on the shape of a system or the quantity of the linked members. Although FEM is mainly a computational tool for analyzing structures, fluids, etc., the capability of expressing the whole continuous system can be applied to parallel control schemes, and may be practical if the computational time is reduced to real-time use. An inverse theory, which is simplified by using the linearity of the electric potential distribution in a bimorph piezoelectric actuator, is applied for calculating control voltage of the actuators. The algorithm using this theory consumes less computational memory, and runs faster than the numerical schemes using generalized inverse matrices. This paper seeks the reduction of dofs and thus the computational time, by implementing noncompatible four-node element to the FEM control program. The finite element allows in-plane bending mode by considering noncompatible mode in shape functions, and can obtain practical solutions by minimum number of elements. By examining the experiments on static displacement control of connected piezoelectric actuators, the validity of the FEM parallel control system has been confirmed.