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Research Papers

An Online Tuning Method for Robust Control of Multivariable Nonlinear Processes With Nonanalytical Modules and Time Delay

[+] Author and Article Information
Jiqiang Wang

Jiangsu Province Key Laboratory
of Aerospace Power Systems,
College of Energy and Power Engineering,
Nanjing University of Aeronautics
and Astronautics,
29 Yudao Street,
Nanjing 210016, China;
e-mails: jiqiang.wang@nuaa.edu.cn;
jiqiang_wang@hotmail.com

Hao Shen, Zhitao Song

Shanghai Aircraft Airworthiness
Certification Center of CAAC,
Shanghai 200335, China

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received July 2, 2015; final manuscript received October 18, 2016; published online February 2, 2017. Assoc. Editor: Sergey Nersesov.

J. Dyn. Sys., Meas., Control 139(4), 041001 (Feb 02, 2017) (7 pages) Paper No: DS-15-1299; doi: 10.1115/1.4035088 History: Received July 02, 2015; Revised October 18, 2016

Control design for multivariable nonlinear systems has cultivated into a mature research area. A variety of control design methodologies have been well established. In most of the approaches, however, it is implicitly assumed that an analytically mathematical model can be available. This is not always feasible since in many practical control problems, system dynamics may be represented by nonanalytical modules, such as look-up tables, c or Fortran codes, etc. As a consequence, conventional methods can only be performed after analytical models are obtained. In this paper, an approach is proposed where the nonanalytical modules can be handled directly. Important results are obtained on optimal control laws and their implementation; robust control is achieved using a new online tuning method; input saturation and stability issues are also discussed. A numerical study is provided to validate the effectiveness of the proposed method.

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Figures

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Fig. 1

Block diagram for control of general nonlinear systems

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Fig. 2

Optimal control signal as generated through Eq. (22)

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Fig. 3

Optimal control signal as generated through Eq. (23)

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Fig. 4

Optimal signal generation with anticausal parameters (Fck−1Pc). One-step ahead prediction is augmented into the usual implementation without anticausal choice of (Fck−1Pc). (a) Optimal control signal as generated through Eq. (23) and (b) optimal control signal with augmented predictive action as generated through Eq. (24).

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Fig. 5

Robusify nominal controller: tuning the parameter Nac to reduce the residue signal ξ(t). The resulting controller will counteract the detrimental effect of the system uncertainties.

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Fig. 6

Two-link robotic manipulator

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Fig. 7

Separation of two-link robot model

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Fig. 8

Position control of the two-link robotic manipulator: PD and proposed optimal control designs—(a) q1 and control τ1 and (b) q2 and control τ2

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Fig. 9

Robust control of the two-link robotic manipulator: optimal control with uncertainty and optimal control with predictive action for counteracting the detrimental effects of uncertainty—(a) q1 and control τ1 and (b) q2 and control τ2

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