Your browser does not support JavaScript!
http://iet.metastore.ingenta.com
1887

Nonlinear PID Predictive Controller

Nonlinear PID Predictive Controller

For access to this article, please select a purchase option:

Buy article PDF
£12.50
(plus tax if applicable)
Buy Knowledge Pack
10 articles for £75.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
IEE Proceedings - Control Theory and Applications — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

A new class of nonlinear PID controllers are derived for nonlinear systems using a nonlinear generalised predictive control (NGPC) approach. First, the disturbance decoupling ability of the NGPC is discussed. For a nonlinear system where the disturbance cannot be decoupled, a nonlinear observer is designed to estimate the offset. By selecting the nonlinear gain function in the observer, it is shown that the closed-loop system under optimal generalised predictive control with the nonlinear observer is asymptotically stable. It is pointed out that this composite controller is equivalent to a nonlinear controller with integral action. As a special case, for a nonlinear system with a low relative degree, the proposed nonlinear controller reduces to a nonlinear PI or PID predictive controller, which consists of a nonlinear PI or PID controller and a prediction controller. The design method is illustrated by an example nonlinear mechanical system.

References

    1. 1)
      • B. WITTENMARK , K.J. ÅSTRÖM , H. UNBEHAUEN . (1980) Simple self-tuning controllers, Methods and applications in adaptive control.
    2. 2)
      • J.W. GRIZZLE , M.D. DI BENEDETTO , F. LAMNABHI-LAGARRIGUE . Necessary conditions for asymptotic tracking in nonlinear systems. IEEE Trans. Autom. Control , 9 , 1782 - 1794
    3. 3)
      • H. NIJMEIJER , A. VAN DER SCHAFT . (1990) , Nonlinear dynamical control systems.
    4. 4)
      • M. Vidyasagar . On the stabilization of nonlinear systems using state detection. IEEE Trans. Autom. Control , 3 , 504 - 509
    5. 5)
      • D.W. Clarke , C. Mohtadi , P.S. Tuffs . Generalised predictive control. Part I: The basic algorithm. Automatica , 2 , 137 - 148
    6. 6)
      • CHEN, W.-H., BALLANCE, D.J., GAWTHROP, P.J., GRIBBLE, J.J., O'REILLY, J.: `A nonlinear disturbance observer for robotic manipulators', Proceedings of the 38th IEEE conference on Decision and control, Dec. 1999, Arizona, USA, Phoenix.
    7. 7)
      • P.J. GAWTHROP . Self-tuning PID controllers: Algorithms and implementation. IEEE Trans. Autom. Control , 3 , 201 - 209
    8. 8)
      • P. LU . Approximate nonlinear receding-horizon control laws in closed form. Int. J. Control , 1 , 19 - 34
    9. 9)
      • L.R. HUNT , M.S. VERMA . Observers for nonlinear systems in steady state. IEEE Trans. Autom. Control , 10 , 2113 - 2118
    10. 10)
      • GAWTHROP, P.J., DEMIRCIOGLU, H.: `GPC in a continuous-time context', Proceedings of the 1st European control conference, 1991, France, Grenoble, p. 55–74.
    11. 11)
      • R.R. BITMEAD , M. GEVERS , V. WERTZ . (1990) , Adaptive optimal control: The thinking man's GPC.
    12. 12)
      • D.W. CLARKE , C. MOHTADI , P.S. TUFFS . Generalised predictive control. Part II: Extensions and interpretations. Automatica , 2 , 149 - 160
    13. 13)
      • M. SOROUSH , C. KRAVARIS . A continuous-time formulation of non-linear model predictive control. Int. J. Control , 1 , 121 - 146
    14. 14)
      • D.W. CLARKE , A.J.F. HODGSON , P.S. TUFFS . Offset problem and k-incremental predictors in self-tuning control. IEE Proc. D Control Theory Appl. , 5 , 217 - 225
    15. 15)
      • A. ISIDORI . (1995) , Nonlinear control systems: An Introduction.
    16. 16)
      • CHEN, W.-H., BALLANCE, D.J., GAWTHROP, P.J.: `Nonlinear generalised predictive control and optimal dynamic inversion control', Preprints of the 14th IFAC World Congress, 1999, Beijing, PRC.
    17. 17)
      • M. SOROUSH , H.M. SOROUSH . Input-output linearising nonlinear model predictive control. Int. J. Control , 6 , 1449 - 1473
    18. 18)
      • D. ANGELI , E. MOSCA . Command governors for constrained nonlinear systems. IEEE Trans. Autom. Control , 4 , 816 - 820
    19. 19)
      • P.E. MORAAL , J.W. GRIZZLE . Observer design for nonlinear systems with discrete-time measurements. IEEE Trans. Autom. Control , 3 , 395 - 404
    20. 20)
      • F. CAMERON , D.E. SEBORG . A self-tuning controller with a PID structure. Int.J. Control , 3 , 401 - 407
    21. 21)
      • C.G. PROUDFOOT , P.J. GAWTHROP , O.L.R. JACOBS . Self-tuning control of a pH neutralisation process. IEE Proc. D Control Theory Appl. , 5 , 267 - 272
    22. 22)
      • D.W. CLARKE , C.J. HARRIS , S.A. BILLINGS . (1981) Self-tuning and adaptive control: theory and applications, Self-tuning and adaptive control: theory and applications.
    23. 23)
      • P.J. GAWTHROP , H. DEMIRCIOGLU , I. SILLER-ALCALA . Multivariable continuous-time generalised predictive control: A state-space approach to linear and nonlinear systems. IEE Proc. Control Theory Appl. , 3 , 241 - 250
    24. 24)
      • E.A. MISAWA . Discrete-time sliding mode control for nonlinear systems with unmatched uncertainties and uncertain control vectors. ASME J. Dynam. Syst. Meas. Control , 3 , 503 - 512
    25. 25)
      • B.L. WALCOTT , M.J. CORLESS , S.H. ZAK . Comparative study of nonlinear state-observation techniques. Int. J. Control , 6 , 2109 - 2132
    26. 26)
      • H. DEMIRCIOGLU , P.J. GAWTHROP . Continuous-time generalised predictive control. Automatica , 1 , 55 - 74
    27. 27)
      • P. LU . Tracking control of nonlinear systems with bounded controls and control rates. Automatica , 6 , 1199 - 1202
    28. 28)
      • A.W. ORDYS , D.W. CLARKE . A state-space description for GPC controllers. Int. J. Syst. Sci. , 9 , 1727 - 1744
    29. 29)
      • H. DEMIRCIOGLU , P.J. GAWTHROP . Multivariable continuous-time generalised predictive control. Automatica , 4 , 697 - 713
http://iet.metastore.ingenta.com/content/journals/10.1049/ip-cta_19990744
Loading

Related content

content/journals/10.1049/ip-cta_19990744
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address