Control of Flexible Structures Governed by the Wave Equation Using Infinite Dimensional Transfer Functions

[+] Author and Article Information
Yoram Halevi

Faculty of Mechanical Engineering, Technion - Israel Institute of Technology, Haifa 32000, Israelmerhy01@tx.technion.ac.il

J. Dyn. Sys., Meas., Control 127(4), 579-588 (Dec 06, 2004) (10 pages) doi:10.1115/1.2098895 History: Received February 27, 2004; Revised December 06, 2004

A method of noncollocated controller design for flexible structures, governed by the wave equation, is proposed. First an exact, infinite dimension, transfer function is derived and its properties are investigated. A key element in that part is the existence of time delays due to the wave motion. The controller design consists of two stages. The first one is an inner collocated rate loop. It is shown that there exists a controller that leads to a finite dimensional plus delay inner closed loop, which is the equivalent plant for the outer loop. In the second stage an outer noncollocated position loop is closed. It has the structure of an observer-predictor control scheme to compensate for the response delay. The resulting overall transfer function is second order, with arbitrarily assigned dynamics, plus delay.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 1

The general control scheme

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Figure 2

The flexible system

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Figure 3

The four time delays in G(x,s)

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Figure 4

Impulse response of θ(L) of the system (upper left) and three FEM models (normalized time)

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Figure 5

Root locus of a free-free rod with collocated actuation and measurement at an end (A=k∕ϕ)

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Figure 6

Angular velocity control closed loop system

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Figure 7

Step response of the system in Fig. 6 with gains 1.5ϕ, ϕ, and 0.5ϕ

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Figure 8

The general control scheme

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Figure 9

Step response of the nominal system and deviations of ±20% in the shear Young’s modulus G



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