An Applicable Control-Relevant Method for Nonlinearity Assessment using Gap Metric

Document Type : Power Article

Author

Assistant Professor,Faculty of Electrical and Computer Engineering, Esfarayen University of Technology, North-Khorasan, Iran.

Abstract

In this paper, an applicable control-relevant nonlinearity assessment method is proposed for nonlinear dynamic systems. In this method, nonlinear system is decomposed to a bank of linear systems using gap metric, a smart tool for measuring the distance between two linear systems. Then, the ability of each local linear model is investigated to stabilize all linear models. A criterion is proposed to measure the nonlinearity of nonlinear system based on gap metric and maximum stability margin values which bounded between 0 and 1. Unlike most of the current nonlinearity measurement, the proposed method could be used for both integrating and unstable nonlinear systems. Besides, the presented method supplies to distinguish that a single linear controller is adequate to control the nonlinear system or it is necessary to employ the multi-model based controllers design methods. Therefore, the redundancy problem could be avoided by employing the proposed method. A nonlinear Continues Stirred Reactor Tank (CSTR) process is studied that the results confirm the capability of presented nonlinearity assessment method.
.

Keywords

Main Subjects

References

[1] K. Elkhalil, and A. Zribi. "Linear controller design approach for nonlinear systems by integrating gap metric and stability margin." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 237, no. 10, (2023): 1-12.
[2] J. Xavier, S.K. Patnaik, and R.C. Panda. "Nonlinear Measure for Nonlinear Dynamic Processes Using Convergence Area: Typical Case Studies." Journal of Computational and Nonlinear Dynamics 16, no. 5, (2021): 051002.
[3] T. Schweickhardt, and F. Allgöwer. "Linear control of nonlinear systems based on nonlinearity measures." Journal of Process Control 17, no. 3, (2007): 273-284.
[4] M. Ahmadi, and M. Haeri. "A new structured multi-model control of nonlinear systems by integrating stability margin and performance." Journal of Dynamic Systems, Measurement, and Control 139, no. 9, (2017): 091014.
[5] C. Desoer, and Y.T. Wang. "Foundations of feedback theory for nonlinear dynamical systems." IEEE Transactions on Circuits and Systems 27, no. 2, (1980): 104-123.
[6] S.A. Eker, and M. Nikolaou. "Linear control of nonlinear systems: Interplay between nonlinearity and feedback." AIChE journal 48, no. 9, (2002): 1957-1980.
[7] M. Guay, R. Dier, J. Hahn, and P.J. McLellan. "Effect of process nonlinearity on linear quadratic regulator performance." Journal of process control 15, no. 1, (2005): 113-124.
[8] K.R Harris , M. Celeste Colantonio, and A. Palazoğlu. "On the computation of a nonlinearity measure using functional expansions." Chemical engineering science 55, no. 13, (2000): 2393-2400.
[9] A. Helbig, W. Marquardt, and F. Allgöwer. "Nonlinearity measures: definition, computation and applications." Journal of Process Control 10, no. 2-3, (2000): 113-123.
[10] A. Alaeddini, K.A. Morgansen, and M. Mesbahi. "Augmented state feedback for improving observability of linear systems with nonlinear measurements." Systems & Control Letters 133, (2019): 104520.
[11] J. Du, and Z. Tong. "An improved nonlinearity measure based on gap metric." in Proceedings of the 33rd Chinese Control Conference, pp. 1920-1923. IEEE, 2014.
[12] M. Ahmadi, and M. Haeri. "An integrated best–worst decomposition approach of nonlinear systems using gap metric and stability margin." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 235, no. 4, (2021): 486-502.
[13] M. Ahmadi, and M. Haeri. "A systematic decomposition approach of nonlinear systems by combining gap metric and stability margin." Transactions of the Institute of Measurement and Control 43, no. 9, (2021): 2006-2017.
[14] G.T. Tan, M. Huzmezan, and K. Ezra Kwok. "Vinnicombe metric as a closed-loop nonlinearity measure." in 2003 European Control Conference (ECC), pp. 751-756. IEEE, 2003.
[15] W. Tan, H.J. Marquez, T. Chen, and J. Liu. "Analysis and control of a nonlinear boiler-turbine unit." Journal of process control 15, no. 8, (2005): 883-891.
[16] J. Du, and T.A. Johansen. "Control-relevant nonlinearity measure and integrated multi-model control." Journal of Process Control 57, (2017): 127-139.
[17] M. Ahmadi. "Multi-Model Control of Nonlinear Systems Using an Improved Procedure for Nominal Local Models Selection." Journal of Mechanical Engineering 52, no. 2, (2022): 251-259 (in Persian).
[18] A. El-Sakkary. "The gap metric: Robustness of stabilization of feedback systems." IEEE Transactions on Automatic Control 30, no. 3, (1985): 240-247.
[19] K. Zhou, and J.C. Doyle. Essentials of robust control. Vol. 104. Upper Saddle River, NJ: Prentice hall, 1998.
[20] J. Du, C. Song, Y. Yao, and P. Li. "Multilinear model decomposition of MIMO nonlinear systems and its implication for multilinear model-based control." Journal of Process Control 23, no. 3, (2013): 271-281.
[21] J. Du, C. Song, and P. Li. "A gap metric based nonlinearity measure for chemical processes." in 2009 American Control Conference, pp. 4440-4445. IEEE, 2009.
[22] M. Ahmadi, P. Rikhtehgar, and M. Haeri. "A multi-model control of nonlinear systems: A cascade decoupled design procedure based on stability and performance." Transactions of the Institute of Measurement and Control 42, no. 7, (2020): 1271-1280.
[23] W. Tan, H.J. Marquez, T. Chen, and J. Liu. "Multimodel analysis and controller design for nonlinear processes." Computers & chemical engineering 28, no. 12, (2004): 2667-2675.
Journal of Modeling in Engineering
Volume 22, Issue 77
August 2024
Pages 261-271

Files

History

  • Receive Date: 17 June 2023
  • Revise Date: 24 November 2023
  • Accept Date: 26 December 2023

Share

How to cite

Statistics