Potentials of Evolving Linear Models in Tracking Control Design for Nonlinear Variable Structure Systems

Document Type : Research Article

Authors

1 Assistant Professor, School of Electrical and Computer Engineering, University of Tehran

2 M.Sc. Student, Faculty of New Sciences and Technologies, University of Tehran

Abstract

Evolving models have found applications in many real world systems. In this paper, potentials of the Evolving Linear Models (ELMs) in tracking control design for nonlinear variable structure systems are introduced. At first, an ELM is introduced as a dynamic single input, single output (SISO) linear model whose parameters as well as dynamic orders of input and output signals can change through the time. Then, the potential of ELMs in modeling nonlinear time-varying SISO systems is explained. Next, the potential of the ELMs in tracking control of a minimum phase nonlinear time-varying SISO system is introduced. For this mean, two tracking control strategies are proposed respectively for (a) when the ELM is known perfectly and (b) when the ELM model has uncertainties but dynamic orders of the input and output signals are fixed. The methodology and superiority of the proposed tracking control systems are shown via some illustrative examples: speed control in a DC motor and link position control in a flexible joint robot.

Keywords

References

[1] Zames, G.; “Feedback and Optimal Sensitivity: Model Reference Transformations, Multiplicative Seminorms and Approximate Inverses,” IEEE Transaction on Automatic Control, Vol. 26, No. 2, pp. 301–320, 1981.
[2] Helton, J. W.; “Orbit Structure of the Mobius Transformation Semi-Group Action on H-Infinity (Broadband Matching),” Adv. in Math. Suppl. Stud., Vol. 3, pp. 129–197, 1978.
[3] Bakule, L.; Rehák, B. and Papík, M.; “Decentralized Image-Infinity Control of Complex Systems with Delayed Feedback,” Automatica, Vol. 67, No. 3, pp. 127–131, 2016.
[4] Rojas, C. R.; Oomen, T.; Hjalmarsson, H. and Wahlberg, B.; “Analyzing Iterations In Identification With Application To Nonparametric H∞-Norm Estimation,” Automatica, Vol. 48, No. 11, pp. 2776– 2790, 2012.
[5] Yang, C. D. and Taic, H. C.; “Synthesis of μ Controllers Using Statistical Iterations,” Asian Journal of Control, Vol. 4, No. 3, pp. 331–310, 2002.
[6] Taher, S. A.; Akbari, S.; Abdolalipour, A. and Hematti, R.; “Robust Decentralized Controller Design for UPFC Using μ–Synthesis,” Communications in Nonlinear Science and Numerical Simulation, Vol. 15, No. 8, pp. 2149–2161, 2010.
[7] Zinober, A. S. I.; “Deterministic Control of Uncertain Systems,” IEE Control Engineering Series, 1991.
 [8] Khalil, H. K.; “Nonlinear Systems,” Prentice Hall, NewJercy, 3rd Edition, 2002.
[9] Zhou, Q.; Yao, D.; Wang, J. and Wu, C.; “Robust Control of Uncertain Semi-Markovian Jump Systems Using Sliding Mode Control Method Original,” Applied Mathematics and Computation, Vol. 286, pp. 72–87, 2016.
[10] Barambones, O. and Alkorta, P.; “Vector Control for Induction Motor Drives Based on Adaptive Variable Structure Control Algorithm,” Asian Journal of Control, Vol. 12, No. 5, pp. 640–649, 2010.
[11] Ling, R.; Wu, M.; Dong, Y. and Chai, Y.; “High Order Sliding-Mode Control for Uncertain Nonlinear Systems with Relative Degree Three,” Communications in Nonlinear Science and Numerical Simulation, Vol. 17, No. 8, pp. 3406–3416, 2012.
[12] Nasiri, R. and Radan, A.; “Adaptive Ole- Placement Control of 4-Leg Voltage-Source Inverters for Standalone Photovoltaic Systems,” Renewable Energy, Vol. 36, No. 7, pp. 2032–2042, 2011.
[13] Yang, Q.; Xue, Y.; Yang, S. X. and Yang, W.; “An Auto-Tuning Method for Dominant-Pole Placement Using Implicit Model Reference Adaptive Control Technique,” Journal of Process Control, Vol. 22, No. 3, pp. 519–526, 2012.
[14] Madady, A.; “ A Self-Tuning Iterative Learning Controller for Time Variant Systems,” Asian Journal of Control, Vol. 10, No. 6, pp. 666–677, 2008.
[15] Ahmed, M. S.; “Neural Net Based MRAC for a Class of Nonlinear Plants,” Neural Networks, Vol. 13, No. 1, pp. 111–124, 2000.
[16] Guo, J.; Tao, G. and Liu, Y.; “A Multivariable MRAC Scheme with Application to a Nonlinear Aircraft Model,” Automatica, Vol. 47, No. 4, pp. 804–812, 2011.
[17] Mohideen, K. A.; Saravanakumar, G.; Valarmathi, K.; Devaraj, D. and Radhakrishnan, T. K.; “Real-Coded Genetic Algorithm for System Identification and Tuning of a Modified Model Reference Adaptive Controller for a Hybrid Tank System,” Applied Mathematical Modeling, Vol. 37, No. 6, pp. 3829–384, 2013.
[18] Rugh, W. J. and Shamma, J. S.; “Research on Gain Scheduling,” Automatica, Vol. 36, No. 10, pp. 1401–1425, 2000.
[19] Wu, F.; Packard, A. and Balas, G.; “Systematic Gain-Scheduling Control Design: A Missile Autopilot Example,” Asian Journal of Control, Vol. 4, No. 3, pp. 341–34, 2002.
[20] Horowitz, I.; Smay, J. and Shapiro, A.; “A Synthesis Theory for Self-Oscillating Adaptive Systems (SOAS) Original Research Article,” Automatica, Vol. 10, No. 4, pp. 381–392, 1974.
[21] Olivier, J. C.; Loron, L.; Auger, F. and Le- Claire, J. C.; “Improved Linear Model of Self Oscillating Systems Such as Relay Feedback Current Controllers,” Control Engineering Practice, Vol. 18, No. 8, pp. 927–935, 2010.
[22] Vargas, J. F. and Ledwich, G.; “Variable Structure Control for Power Systems Stabilization,” International Journal of Electrical Power and Energy Systems, Vol. 32, No. 2, pp. 101–107, 2010.
[23] Sumar, R.; Coelho, A. and Goedtel, A.; “Multivariable System Stabilization via Discrete Variable Structure Control,” Control Engineering Practice, Vol. 40, No. 4, pp. 71–80, 2015.
[24] Landau, I. D.; “Combining Model Reference Adaptive Controllers and Stochastic Self-Tuning Regulators,” Automatica, Vol. 18, No. 1, pp. 77–84, 1982.
[25] Landau, I. D. and Karimi, A.; “A Unified Approach to Model Estimation and Controller Reduction (Duality and Coherence),” European Journal of Control, Vol. 8, No. 6, pp. 561–572, 2002.
[26] Kasabov, N.; “DENFIS: Dynamic Evolving Neural Fuzzy Inference System and its Application for Time Series Prediction,” IEEE Transaction on Fuzzy Systems, Vol. 10, No. 2, pp. 144–154, 2002.
[27] Angelov, P. and Filev, D.; “An Approach to Online Identification of Takagi Sugeno Fuzzy Models,” IEEE Transaction on Systems, Man and Cybernetics Part B, Vol. 34, No. 1, pp. 484–498, 2004.
[28] Angelov, P. and Zhou, X.; “Evolving Fuzzy Systems from Data Streams in Real-Time,” International Symposium on Evolving Fuzzy Systems, pp. 29–35, 2006.
[29] Angelov, P.; Filev, D. and Kasabov, N.; “Evolving Intelligent Systems: Methodology and Applications,” John Wiley and Sons, Chapter 2, pp. 21–50, 2010.
[30] Lughofer, E. D.; “FLEXFIS: A Robust Incremental Learning Approach for Evolving Takagi–Sugeno Fuzzy Models,” IEEE Transaction Fuzzy Systems, Vol. 16, No. 6, pp. 1393–1410, 2008.
[31] Kalhor, A.; Araabi, B. N. and Lucas, C.; “Online Extraction of Main Linear Trends for Nonlinear Time Varying Processes,” Information Sciences, Vol. 220, pp. 22–33, 2013.
[32] Kalhor, A., Iranmanesh, H. and Abdollahzade, M.; “Online Modeling of Real-World Time Series through Evolving AR Models,” IEEE International Conference on Fuzzy systems, FUZIEEE, 2012.
[33] Kalhor, A.; Araabi, B. N. and Lucas, C.; “A New Systematic Design for Habitually Linear Evolving TS Fuzzy Model,” Journal of Expert Systems with Applications, Vol. 39, No. 2, pp. 1725–1736, 2012.
[34] Jang, R.; “ANFIS: Adaptive Network-Based Fuzzy Inference System,” IEEE Transaction on Systems, Man and Cybernetics, Vol. 23, No. 3, pp. 665–685, 1993.
[35] Nelles, O.; “Nonlinear System Identification,” Springer, New York, pp. 365–366, 2001.
[36] Kalhor, A.; Araabi, B. N. and Lucas, C.; “Reducing the Number of Local Linear Models in Neuro–Fuzzy Modeling: A Split and Merge Clustering Approach,” Applied Soft Computing, Vol. 11, No. 8, pp. 5582–5589, 2011.
[37] Robinson, J. C.; “An Introduction to Ordinary Differential Equations,” Cambridge University Press, Cambridge, UK, 2004.
[38] SIemon, G. R. and Straughen, A.; “Electric Machines, Addison,” Wesley, Reading, MA, 1980.
AUT Journal of Modeling and Simulation
Volume 48, Issue 2
November 2016
Pages 75-92

Files

Share

How to cite

Statistics