A Unified Approach to Robust Control of Flexible Mechanical Systems Using H-Infinity Control Powered by PD Control

Abstract

This chapter presents a unified approach to robust control of a variety of flexible mechanical systems, which are not only systems having flexible structure themselves such as a robotic manipulator with a flexible structure and a crane system, but also systems not having flexible structure but handling flexible objects such as a liquid container system and a fishery robot. So far, a lot of research efforts have been devoted to solve control problems of such flexible systems, one of the most typical problems among which is the problem of flexible robotic manipulators, e.g., [Sharon & Hardt (1984); Spong (1987); Wang & Vidyasagar (1990); Torres et al., (1994); Magee & Book (1995); Nenchev et al., (1996); Nenchev et al., (1997)]. As other types of applications, the problems of a crane system [Kang et al. (1999)] and of a liquid container system [Yano & Terashima (2001); Yano et al., (2001)] have been investigated. The common control problem for flexible systems can be stated as “how to achieve required motion control with suppressing undesirable oscillation due to its flexibility”. From the control methodology point of view, let us review those previous works. For socalled micro-macro manipulators associated with large flexible space robots, [Torres et al (1994)] and [Nenchev et al., (1996); Nenchev et al., (1997)] have proposed path-planning based control methods using a coupling map and a reaction null-space respectively, which utilize the geometric redundancy. The control methods in [Sharon & Hardt (1984)] for a micro-macro manipulator and in [Kang et al., (1999)] for a crane system rely on the endpoint direct feedback, which require sensors to measure the endpoint. In [Wang & Vidyasagar (1990)], a passivity-based control method has been proposed for a single flexible link, and in [Spong (1987)] an exact-linearization method and an integral manifold method have been presented for a flexible-joint manipulator. The method in [Magee & Book (1995)] is based on input signal filtering where the underlying concept is pole-zero cancellation. [Ueda & Yoshikawa (2004)] has applied a mode-shape compensator based on acceleration feedback to a flexible-base manipulator. For a liquid container system, H∞ control in [Yano & Terashima (2001)] and a notch-type filter based control, that is, equivalent to pole-zero cancellation, in [Yano et al., (2001)] are utilized respectively. In general, most other works have focused on individual systems and hence their control methods are not directly available for various flexible systems. For example, the path-planning methods in [Torres et