Simple Adaptive Tracking Control of Systems with Bounded Nonlinear Disturbances

Copyright © IFAC System Identification, Kitakyushu, Fukuoka,Japan,1997

SIMPLE ADAPTIVE TRACKING CONTROL OF SYSTEMS WITH BOUNDED NONLINEAR DISTURBANCES Kazuya SATO· Toshihiro KOBAYASHI*· Masahiro OYA··

• Department of Mechanical Engineering, Saga University, 1 Honjyo-machi, Saga 840, JAPAN •• Department of Control Engineering, Kyushu Institute of Technology, Sensui-cho, Tobata, Kitakyushu 804, JAPAN

Abstract. In this paper a simple adaptive control of plants with bounded nonlinear disturbances is proposed. The proposed controller is applicable to all those plants whose relative degree is less than four, the upper bound of the high frequency gain and the function type of the disturbances are known. Experimental results also demonstrates that the method is very effective. Keywords. Adaptive control, Disturbance rejection, Tracking systems

1. INTRODUCTION

Recently, there have been researched about an adaptive control which does not rely on the plant order (BarKana and Kaufman, 1985; Bar-Kana and Kaufman, 1988; Iwai and Mizumoto, 1992; Iwai and Mizumoto, 1993; Mareels, 1984) . But only the boundedness of all state variables and plant output can be guaranteed when it is applied to a plant with bounded nonlinear disturbances. This paper proposes a new adaptive control method under the assumption that the relative degree is less than four, the upper bound of the high frequency gain and the function type of the bounded nonlinear disturbances are known. This method does not depend on the plant order and guarantee that the plant output converges to the reference signal. To show the effectiveness of the proposed method, experimental results are also shown.

where A(p) and B(p) are monic polynomials of degree n and m, respectively (n - m is the relative degree). B(p)/A(p) denotes the response corresponding to the initial state of the plant and y(O) = bn - 1 . In this paper, 'p' treats as MikusiIiski's differential operator. Besides for notational simplicity, for example, denote the function {!(t)} as f(t). In (1), the available signal is only input and output. w(t) is the bounded nonlinear disturbances of the form I

w(t)

= LWi X Wi(y(t))

(2)

i=l

where Wi are unknown constants and Wi(y(t)) are known bounded non linear functions. 2. SYSTEM DESCRIPTION

Here, make following assumptions. Assumption 1: 1/B(p) is asymptotically stable. Assumption 2: The sign of bm and its upper bound

Consider the following SISO plant

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