0
Research Papers

A New Structured Multimodel Control of Nonlinear Systems by Integrating Stability Margin and Performance

[+] Author and Article Information
Mahdi Ahmadi

Advanced Control Systems Lab,
Electrical Engineering,
Sharif University of Technology,
Tehran 11155-4363, Iran
e-mail: mahdiahmadi@ee.sharif.edu

Mohammad Haeri

Advanced Control Systems Lab,
Electrical Engineering,
Sharif University of Technology,
Tehran 11155-4363, Iran
e-mail: haeri@sharif.ir

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received August 26, 2016; final manuscript received February 7, 2017; published online June 5, 2017. Assoc. Editor: Dumitru I. Caruntu.

J. Dyn. Sys., Meas., Control 139(9), 091014 (Jun 05, 2017) (10 pages) Paper No: DS-16-1416; doi: 10.1115/1.4036069 History: Received August 26, 2016; Revised February 07, 2017

This paper deals with a new systematic multimodel controller design for nonlinear systems. The design of local controllers based on performance requirements is incorporated with the concept of local models selection as an optimization problem. Gap metric and stability margin are used as measuring tool and operation space dividing criterion, respectively. The developed method provides support to design a simple structured multiple proportional-integral (PI) controller which guarantees both robust stability and time-domain performance specifications. The main advantages of the proposed method are avoiding model redundancy, not needing a priori knowledge about system, having simple structure, and easing the implementation. To evaluate the presented multimodel controller design procedure, three benchmark nonlinear systems are studied. Both simulations and experimental results prove the effectiveness of the proposed method in set point tracking and disturbance rejection.

FIGURES IN THIS ARTICLE
<>
Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Du, J. , and Johansen, T. A. , 2014, “ Integrated Multimodel Control of Nonlinear Systems Based on Gap Metric and Stability Margin,” Ind. Eng. Chem. Res., 53(24), pp. 10206–10215. [CrossRef]
Du, J. , Song, C. , and Li, P. , 2012, “ Multimodel Control of Nonlinear Systems: An Integrated Design Procedure Based on Gap Metric and H Loop Shaping,” Ind. Eng. Chem. Res., 51(9), pp. 3722–3731. [CrossRef]
Galán, O. , Romagnoli, J. A. , Palazočlu, A. , and Arkun, Y. , 2003, “ Gap Metric Concept and Implications for Multilinear Model-Based Controller Design,” Ind. Eng. Chem. Res., 42(10), pp. 2189–2197. [CrossRef]
Haj Salah, A. A. , Garna, T. , Ragot, J. , and Messaoud, H. , 2016, “ Transition and Control of Nonlinear Systems by Combining the Loop Shaping Design Procedure and the Gap Metric Theory,” Trans. Inst. Meas. Control, 38(8), pp. 1004–1020. [CrossRef]
Zhang, R. , Alleyne, A. G. , and Carter, D. E. , 2005, “ Generalized Multivariable Gain Scheduling With Robust Stability Analysis,” ASME J. Dyn. Syst. Meas. Control, 127(4), pp. 668–687. [CrossRef]
Tao, X. , Li, D. , Wang, Y. , Li, N. , and Li, S. , 2015, “ Gap Metric Based Multiple-Model Predictive Control With Polyhedral Stability Region,” Ind. Eng. Chem. Res., 54(45), pp. 11319–11329. [CrossRef]
Porfı́rio, C. R. , Almeida Neto, E. , and Odloak, D. , 2003, “ Multi-Model Predictive Control of an Industrial C3/C4 Splitter,” Control Eng. Pract., 11(7), pp. 765–779. [CrossRef]
Yang, Z. , Li, Y. , and Seem, J. E. , 2015, “ Multi-Model Predictive Control for Wind Turbine Operation Under Meandering Wake of Upstream Turbines,” Control Eng. Pract., 45, pp. 37–45. [CrossRef]
Martin, P. A. , Odloak, D. , and Kassab, F. , 2013, “ Robust Model Predictive Control of a Pilot Plant Distillation Column,” Control Eng. Pract., 21(3), pp. 231–241. [CrossRef]
Du, J. , Song, C. , and Li, P. , 2009, “ Application of Gap Metric to Model Bank Determination in Multilinear Model Approach,” J. Process Control, 19(2), pp. 231–240. [CrossRef]
Du, J. , and Johansen, T. A. , 2014, “ A Gap Metric Based Weighting Method for Multimodel Predictive Control of MIMO Nonlinear Systems,” J. Process Control, 24(9), pp. 1346–1357. [CrossRef]
Toscano, R. , 2007, “ Robust Synthesis of a PID Controller by Uncertain Multimodel Approach,” Inf. Sci., 177(6), pp. 1441–1451. [CrossRef]
Arslan, E. , Çamurdan, M. C. , Palazoglu, A. , and Arkun, Y. , 2004, “ Multimodel Scheduling Control of Nonlinear Systems Using Gap Metric,” Ind. Eng. Chem. Res, 43(26), pp. 8275–8283. [CrossRef]
Murray-Smith, R. , and Johansen, T. , 1997, Multiple Model Approaches to Nonlinear Modelling and Control, Taylor & Francis, London.
Rodrigues, M. , Sahnoun, M. , Theilliol, D. , and Ponsart, J. C. , 2013, “ Sensor Fault Detection and Isolation Filter for Polytopic LPV Systems: A Winding Machine Application,” J. Process Control, 23(6), pp. 805–816. [CrossRef]
Rodrigues, M. , Theilliol, D. , Adam-Medina, M. , and Sauter, D. , 2008, “ A Fault Detection and Isolation Scheme for Industrial Systems Based on Multiple Operating Models,” Control Eng. Pract., 16(2), pp. 225–239. [CrossRef]
Liu, J. , Djurdjanovic, D. , Marko, K. , and Ni, J. , 2009, “ Growing Structure Multiple Model Systems for Anomaly Detection and Fault Diagnosis,” ASME J. Dyn. Syst. Meas. Control, 131(5), p. 051001. [CrossRef]
Tan, W. , Marquez, H. J. , Chen, T. , and Liu, J. , 2004, “ Multimodel Analysis and Controller Design for Nonlinear Processes,” Comput. Chem. Eng, 28(12), pp. 2667–2675. [CrossRef]
Du, J. , Song, C. , and Li, P. , 2009, “ Multilinear Model Control of Hammerstein-Like Systems Based on an Included Angle Dividing Method and the MLD-MPC Strategy,” Ind. Eng. Chem. Res., 48(8), pp. 3934–3943. [CrossRef]
Du, J. , Song, C. , Yao, Y. , and Li, P. , 2013, “ Multilinear Model Decomposition of MIMO Nonlinear Systems and Its Implication for Multilinear Model-Based Control,” J. Process Control, 23(3), pp. 271–281. [CrossRef]
Zribi, A. , Chtourou, M. , and Djemal, M. , 2016, “ A Systematic Determination Approach of Model's Base Using Gap Metric for Nonlinear Systems,” ASME J. Dyn. Syst. Meas. Control, 138(3), p. 031008. [CrossRef]
Jalali, A. A. , and Golmohammad, H. , 2012, “ An Optimal Multiple-Model Strategy to Design a Controller for Nonlinear Processes: A Boiler-Turbine Unit,” Comput. Chem. Eng., 46, pp. 48–58. [CrossRef]
Du, J. , and Johansen, T. A. , 2015, “ Integrated Multilinear Model Predictive Control of Nonlinear Systems Based on Gap Metric,” Ind. Eng. Chem. Res., 54(22), pp. 6002–6011. [CrossRef]
Mahdianfar, S. O. H. , and Momeni, H. R. , 2011, “ Robust Multiple Model Adaptive Control: Modified Using v-Gap Metric,” Int. J. Robust Nonlinear Control, 21(18), pp. 2027–2063. [CrossRef]
Toscano, R. , and Lyonnet, P. , 2009, “ Heuristic Kalman Algorithm for Solving Optimization Problems,” IEEE Trans. Syst. Man Cybern., Part B, 39(5), pp. 1231–1244. [CrossRef]
Toscano, R. , and Lyonnet, P. , 2009, “ Robust PID Controller Tuning Based on the Heuristic Kalman Algorithm,” Automatica, 45(9), pp. 2099–2106. [CrossRef]
Toscano, R. , 2013, Structured Controllers for Uncertain Systems: A Stochastic Optimization Approach, Springer, London.
El-Sakkary, A. , 1985, “ The Gap Metric: Robustness of Stabilization of Feedback Systems,” IEEE Trans. Autom. Control, 30(3), pp. 240–247. [CrossRef]
Georgiou, T. T. , and Smith, M. C. , 1990, “ Optimal Robustness in the Gap Metric,” IEEE Trans. Autom. Control, 35(6), pp. 673–686. [CrossRef]
Zhou, K. , and Doyle, J. C. , 1998, Essentials of Robust Control, Prentice Hall, Upper Saddle River, NJ.
Rodriguez, J. A. , Romagnoli, J. A. , and Goodwin, G. C. , 2003, “ Supervisory Multiple Regime Control,” J. Process Control, 13(2), pp. 177–191. [CrossRef]
Angelis, G. Z. , 2001, “ System Analysis, Modelling and Control With Polytopic Linear Models,” Ph.D. thesis, Eindhoven University of Technology, Eindhoven, The Netherlands.
Galán, O. , Romagnoli, J. A. , and Palazoglu, A. , 2004, “ Real-Time Implementation of Multi-Linear Model-Based Control Strategies—An Application to a Bench-Scale pH Neutralization Reactor,” J. Process Control, 14(5), pp. 571–579. [CrossRef]
Van de Wal, M. , Van Baars, G. , Sperling, F. , and Bosgra, O. , 2002, “ Multivariable H/μ Feedback Control Design for High-Precision Wafer Stage Motion,” Control Eng. Pract., 10(7), pp. 739–755. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

The standard feedback system

Grahic Jump Location
Fig. 2

(a) The steady-state curve and (b) the gaps between the local models

Grahic Jump Location
Fig. 3

Set point tracking test of the pH system in Eq. (23)

Grahic Jump Location
Fig. 4

Disturbance rejection in the closed-loop pH system

Grahic Jump Location
Fig. 10

Reference tracking control of real two tanks plant

Grahic Jump Location
Fig. 11

Disturbance rejection in the two-tank system

Grahic Jump Location
Fig. 8

Set point tracking test of the uncertain nonlinear CSTR in Eq. (24) with ω2=0.2 l/min

Grahic Jump Location
Fig. 9

Laboratory two tanks implementation setup

Grahic Jump Location
Fig. 5

(a) Steady-state description of nonlinear CSTR (24) and (b) gap between linearized models

Grahic Jump Location
Fig. 6

Set point tracking test of the nonlinear CSTR in Eq. (24)

Grahic Jump Location
Fig. 7

Set point tracking test of the uncertain nonlinear CSTR in Eq. (24) with Cb2=8 kmol/m3

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In