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Research Papers

Adaptive Augmenting Control Design for Time-Varying Polytopic Systems

[+] Author and Article Information
Hessam Mahdianfar

Control and Instrumentation Group,
Department of Engineering,
University of Leicester,
Leicester LE1 7RH, UK
e-mail: hessam.mahdianfar@gmail.com

Emmanuel Prempain

Control Research Group,
Department of Engineering,
University of Leicester,
Leicester LE1 7RH, UK
e-mail: ep26@leicester.ac.uk

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received September 12, 2015; final manuscript received August 3, 2016; published online September 22, 2016. Assoc. Editor: M. Porfiri.

J. Dyn. Sys., Meas., Control 139(1), 011005 (Sep 22, 2016) (6 pages) Paper No: DS-15-1440; doi: 10.1115/1.4034420 History: Received September 12, 2015; Revised August 03, 2016

To increase the performance of closed-loop controlled systems in off-nominal conditions and in the presence of inevitable faults and uncertainties, a systematic approach based on robust convex optimization for adaptive augmenting control design is discussed in this paper. More specifically, this paper addresses the problem of adaptive augmenting controller (AAC) design for systems with time-varying polytopic uncertainty. First, a robust state-feedback controller is designed via robust convex optimization as a baseline controller. The closed-loop polytopic system with the baseline controller is considered as the desired time-varying reference model for the design of a direct state-feedback adaptive controller. Next using Lyapunov arguments, global stability of combined robust baseline and adaptive augmenting controllers is established. Furthermore, it is proved that tracking error converges to zero asymptotically. A case study for a generic nonminimum phase nonlinear pitch-axis missile autopilot is conducted. Simulation tests are performed to evaluate stability and performance of nonlinear time-varying closed-loop system in the presence of uncertainties in pitching moment and normal force coefficients, and unmodeled time delays. In addition, results of the simulations indicate satisfactory robustness in case of severe loss of control effectiveness event.

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Figures

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Fig. 1

Adaptive augmenting control system schematic

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Fig. 2

Bode diagrams of linearized models at different operating points

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Fig. 3

Performance of adaptive augmenting control in the presence of time-delay in input channel td=35 ms, and +25% simultaneous perturbation in pitch aerodynamic coefficients

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Fig. 4

A −40% independent perturbation in pitch aerodynamic coefficients: adaptive augmenting control (dashed) versus robust baseline controller (solid)

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Fig. 5

Evolution of adaptive gains. A −40% independent perturbation in pitch aerodynamic coefficients.

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Fig. 6

A 70% loss of control effectiveness at t = 3 s and −20% and +10% independent perturbations in pitch and normal force aerodynamic coefficients, respectively: adaptive augmenting control (dashed) versus baseline controller (solid)

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Fig. 7

A 70% loss of control effectiveness at t = 3 s and −20% and +10% independent perturbations in pitch and normal force aerodynamic coefficients

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