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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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References

Isidori, A. , 1995, Nonlinear Control Systems, 3rd ed., Springer-Verlag, Berlin.
Van der Shaft, A. J. , 1996, L2 Gain and Passivity Techniques in Nonlinear Control, Springer-Verlag, Heidelberg, Germany.
Byrnes, C. I. , 2000, “ Toward a Nonequilibrium Theory for Nonlinear Control Systems,” Lecture Notes in Control and Information Sciences, Springer, Berlin.
Sepulchre, R. , Jankovic, M. , and Kokotovic, P. V. , 1997, Constructive Nonlinear Control, Springer-Verlag, New York.
Block, A. M. , Baillieul, J. , Crouch, P. , and Marsden, J. , 2003, Nonholonomic Mechanics and Control, Springer, New York.
Mayne, D. Q. , Rawlings, J. B. , Rao, C. V. , and Scokaet, P. O. M. , 2000, “ Constrained Model Predictive Control: Stability and Optimality,” Automatica, 36(6), pp. 787–814. [CrossRef]
Zhou, K. , Doyle, J. C. , and Glover, K. , 1996, Robust and Optimal Control, Prentice Hall, Englewood Cliffs, NJ.
Kristić, M. , Sun, J. , and Kokotović, P. V. , 1996, “ Robust Control of Nonlinear Systems With Input Unmodeled Dynamics,” IEEE Trans. Autom. Control, 41(6), pp. 913–920. [CrossRef]
Ahmadi, M. , Mojallali, H. , and Wisniewski, R. , 2012, “ Robust H Control of Uncertain Switched Systems Defined on Polyhedral Sets With Filippov Solutions,” ISA Trans., 51(6), pp. 722–731. [CrossRef] [PubMed]
de Best, J. , Bukkems, B. , van de Molengraft, M. , Heemels, W. , and Steinbuch, M. , 2008, “ Robust Control of Piecewise Linear Systems: A Case Study in Sheet Flow Control,” Control Eng. Pract., 16(8), pp. 991–1003. [CrossRef]
Franklin, G. F. , Powell, J. D. , and Emami-Naeini, A. , 2002, Feedback Control of Dynamical Systems, 4th ed., Addison-Wesley Longman Publishing, Englewood, CO.
Radke, A. , and Gao, Z. , 2006, “ A Survey of State and Disturbance Observers for Practitioners,” 2006 American Control Conference, Minneapolis, MN, June 14–16, pp. 5183–5188.
Li, S. , Yang, J. , Chen, W. , and Chen, X. , 2014, Disturbance Observer Based Control: Methods and Applications, CRC Press, London.
Choi, Y. , Yang, K. , Chung, W. K. , Kim, H. R. , and Suh, I. H. , 2003, “ On the Robustness and Performance of Disturbance Observers for Second-Order Systems,” IEEE Trans. Autom. Control, 48(2), pp. 315–320. [CrossRef]
Choi, H. T. , Kim, B. K. , Suh, I . H. , and Chung, W. K. , 2000, “ Design of Robust High-Speed Motion Controller for a Plant With Actuator Saturation,” ASME J. Dyn. Syst. Meas. Control, 122(3), pp. 535–541. [CrossRef]
Lee, K. B. , and Blaabjerg, F. , 2007, “ Robust and Stable Disturbance Observer of Servo System for Low-Speed Operation,” IEEE Trans. Ind. Appl., 43(3), pp. 627–635. [CrossRef]
Yang, J. , Zolotas, A. , Chen, W. , Michail, K. , and Li, S. , 2011, “ Robust Control of Nonlinear MAGLEV Suspension System With Mismatched Uncertainties Via DOBC Approach,” ISA Trans., 50(3), pp. 389–396. [CrossRef] [PubMed]
Han, J. , 2009, “ From PID to Active Disturbance Rejection Control,” IEEE Trans. Ind. Electron., 56(3), pp. 900–906. [CrossRef]
Zhang, Y. , and Jiang, J. , 2008, “ Bibliographical Review on Reconfigurable Fault-Tolerant Control Systems,” Annu. Rev. Control, 32(2), pp. 229–252. [CrossRef]
Jiang, J. , and Yu, X. , 2012, “ Fault-Tolerant Control Systems: A Comparative Study Between Active and Passive Approaches,” Annu. Rev. Control, 36(1), pp. 60–72. [CrossRef]
Dey, C. , and Mudi, R. , 2009, “ An Improved Auto-Tuning Scheme for PID Controllers,” ISA Trans., 48(4), pp. 396–409. [CrossRef] [PubMed]
Das, S. , Saha, S. , Das, S. P. , and Gupta, A. , 2011, “ On the Selection of Tuning Methodology of FOPID Controllers for the Control of Higher Order Processes,” ISA Trans., 50(3), pp. 376–388. [CrossRef] [PubMed]
Wang, J. , Hu, Z. , and Ye, Z. , 2014, “ Static Feedback Stabilization of Nonlinear Systems With Single Sensor and Single Actuator,” ISA Trans., 53(1), pp. 50–55. [CrossRef] [PubMed]
Slotine, J. J. E. , and Li, W. , 1991, Applied Nonlinear Control, Prentice Hall, Englewood Cliffs, NJ.

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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