Direct adaptive control of non-minimum phase linear distributed parameter models of large flexible structures

Mark J. Balas; Susan A. Frost

doi:10.1117/12.2512596

21 March 2019 Direct adaptive control of non-minimum phase linear distributed parameter models of large flexible structures

Mark J. Balas, Susan A. Frost

Author Affiliations +

Proceedings Volume 10967, Active and Passive Smart Structures and Integrated Systems XIII; 1096707 (2019) https://doi.org/10.1117/12.2512596
Event: SPIE Smart Structures + Nondestructive Evaluation, 2019, Denver, Colorado, United States

Abstract

Linear Distributed Parameter Systems are governed by partial differential equations. They are linear infinite dimensional systems described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on a general Hilbert space of states and are controlled via a finite number of actuators and sensors. Many distributed applications are included in this formulation, such as large flexible aerospace structures, adaptive optics, diffusion reactions, smart electric power grids, and quantum information systems. Using a recently developed normal form for these systems, we have developed the following stability result: an infinite dimensional linear system is Almost Strictly Dissipative (ASD) if and only if its high frequency gain CB is symmetric and positive definite and the open loop system is minimum phase, i.e. its transmission zeros are all exponentially stable. In this paper, we focus on infinite dimensional linear systems that are non-minimum phase because a finite number of transmission zeros are unstable. Several methods to compensate for this issue modify the output of the infinite dimensional plant and then control this modified output rather than the original control output. Here we use a finite dimensional residual mode filter to modify the output to produce a fully minimum phase system. Then direct adaptive control for the infinite dimensional plant can use this modified output rather than the original output, to achieve ASD and produce asymptotically stability of the states on the Hilbert space. These results are illustrated by application to direct adaptive control of general linear systems on a Hilbert space that are described by operators with compact resolvent.

Conference Presentation

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Mark J. Balas and Susan A. Frost "Direct adaptive control of non-minimum phase linear distributed parameter models of large flexible structures", Proc. SPIE 10967, Active and Passive Smart Structures and Integrated Systems XIII, 1096707 (21 March 2019); https://doi.org/10.1117/12.2512596

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