Flatness-based tracking control of nonlinear differential algebraic systems with geometric index one

Abstract

Flatness-based tracking control design with ob server is studied for nonlinear differential algebraic systems with geometric index one. It is shown that a concept of algebraic observability is useful for observer design of a flatness-based tracking control. Through a simple example of an algebraically observable system, it is demonstrated that a proposal flatness based tracking control design with observer is effective.

Algebraic Controllability and Observability of Nonlinear Differential Algebraic Systems with Geometric Index One

“…Remark 1. If the system (5)-(7) is differentially flat [5], [7], and if a flat output is known, a generation of a feasible trajectory is easy (see example 4).…”

“…the system (25)-(27) is differentially flat [5]. Therefore from the relation (39), for example, we have ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ i 1 (t) = cL 2 cos t + I 0 exp(kL 2 cos t) − 1 + sin t, i 2 (t) = sin t, e(t) = L 2 cos t, u(t) = (L 1 + L 2 ) cos t −L 1 L 2 (c + I 0 k exp(kL 2 cos t)) sin t.…”

“…This paper is partially based on conference paper [1] which discusses the relation between algebraic observability and local observability. Furthermore, conference paper [5] has demonstrated that algebraic observability serves for an observer design of a flatness-based trajectory tracking control. Note that although [1] and [5] have studied an algebraically observable DAS, they have not addressed on an algebraically controllable DAS.…”