Journal of Electrical and Computer Engineering Innovations (JECEI)
مقاله 10 ، دوره 7، شماره 1 ، فروردین 2019، صفحه 83-94 1.07 M )
نوع مقاله: Original Research Paper
شناسه دیجیتال (DOI): 10.22061/jecei.2020.5744.253 نویسندگان
H. Nasiri Soloklo ؛ N. Bigdeli*
تاریخ دریافت : 09 فروردین 1397 ،
تاریخ بازنگری : 27 تیر 1397 ،
تاریخ پذیرش : 29 آبان 1397
چکیده Background and Objectives: In this paper, a predictive functional control based on Laguerre functions is designed for control of an industrial heating furnace. The fractional order model (FOM) of the heating furnace is assumed as the plant model.Methods: For designing the predictive functional controller (PFC), a reduced integer order approximation of the fractional order heating furnace model is derived. The order of the reduced integer model is determined based on Hankel singular values of the original system. Coefficients of the reduced integer model are assumed to be unknown. Unknown parameters are then obtained by minimizing a many-objective fitness function including weighted summation of differences of step responses, steady state errors, maximum overshoots as well as magnitude of frequency responses of the original and reduced systems. Routh-Hurwitz criteria are used as stability criteria and added to optimization problem as its constraints. The optimization tool is Genetic algorithm.Results: Advantages of the proposed method are preserving stability and focusing on various important features of both time and frequency responses of system. In addition, it uses a direct order reduction method without the need to intermediated approximations such as Oustaloup approximation.Conclusion: Laguerre-based PFC controller has been evaluated via two scenarios and the obtained results represent the satisfactory performance of the proposed controller.کلیدواژهها
Fractional order system ؛ Genetic Algorithm ؛ Model Predictive control ؛ Model order reduction ؛ Predictive functional control
مراجع
[1] A. D. Shakib Joo, “A comparison of different control design methods for the linearized CSTR temperature model,” Journal of Electrical and Computer Engineering Innovations, 1(2): 107-114, 2013.
[2] A. Basu, S. Mohanty, R. Sharma, “Introduction of fractional elements for improvising the performance of PID controller for heating furnace using AMIGO tuning technique,” Perspectives in Science, 8: 323-326, 2016.
[3] M. Ranjkesh, E. F. Choolabi, M. pourjafari, “Optimum design of a SRM using FEM & PSO,” Journal of Electrical and Computer Engineering Innovations, 2(1): 29-35, 2014.
[4] A. Tepljakov, Fractional-order modelling and control of dynamic systems, Springer International Publishing, 2017.
[5] W. Tan, J. Liu, T. Chen, H. J. Marquez, “Comparison of some well-known PID tuning formulas,” Computers and Chemical Engineering, 30(9): 1416-1423, 2006.
[6] M. Unal, A. Ak, V. Topuz, H. Erdal, Optimization of PID controllers using ant colony and genetic algorithms, Springer-Verlag Berlin Heidelberg, 2013.
[7] I. Podlubny, L. Dorcak, I. Kostial, “On fractional derivatives, fractional-order dynamic systems and PIλDμ controllers,” in Proc. The 36th IEEE Conference on Decision and Control, 5: 4985-4990, 1997.
[8] A. Dumlu, K. Erenturk, “Trajectory tracking control for a 3-DOF parallel manipulator using fractional-order PIλDμ control,” IEEE Transactions on Industrial Electronics, 61(7): 3417-3426, 2014.
[9] Y. M. Wang, Y. J. Liu, R. Z. Yan, Z. Zhang, “Fractional-order PID controller of a heating furnace system,” Advanced Materials Research, 490:495: 1145-1149, 2012.
[10] A. Basu, S. Mohanty, R. Sharma, “Dynamic modelling of heating furnace & enhancing the performance with PIλDµ controller for fractional order model using optimization techniques,” in Proc. International Conference on Emerging Trends in Electrical, Electronics and Sustainable Energy Systems: 164-168, 2016.
[11] D. Zhenhaia, S. Lianyun, “Design of temperature controller for heating furnace in oil field,” Physics Procedia, 24: 2083-2088, 2012.
[12] S. Dequan, G. Guili, G. Zhiwei, X. Peng, “Application of expert fuzzy PID method for temperature control of heating furnace,” Procedia Engineering, 29: 257-261, 2012.
[13] B. Kouvaritakis, M. Cannon, Model predictive control: classical, robust and stochastic, Springer International Publishing, 2015.
[14] J. D. Gibson, “A direct search approach to optimization for nonlinear model predictive control,” Optimal Control, Applications and Methods, 36(2): 139-157, 2015.
[15] S. Shamaghdari, M. Haeri, “Model predictive control of nonlinear discrete time systems with guaranteed stability,” Asian Journal of Control, 22(1): 1-10, 2020.
[16] N. Bigdeli, “The design of non-minimal state space fractional-order predictive functional controller for fractional systems of arbitrary order,” Journal of Process Control, 29(1): 45-56, 2015.
[17] W. Xu, J. Zhang, R. Zhang, “Application of multi-model switching predictive functional control on the temperature system of an electric heating furnace,” ISA Transactions, 68): 287-292, 2017.
[18] Y. Wang, H. Zou, J. Tao, R. Zhang, “Predictive Fuzzy PID control for temperature model of a heating furnace,” in Proc. The 36th Chinese Control Conference: 4523-4527, 2017.
[19] Q. Xu and S. Dubljevic, “Model predictive control of solar thermal system with borehole seasonal storage,” Computers & Chemical Engineering, 101): 59-72, 2017.
[20] J. Holaza, M. Klauco, J. Drgona, J. Oravec, M. Kvasnica, M. Fikar, “MPC-based reference governor control of a continuous stirred-tank reactor,” Computers & Chemical Engineering, 108: 289-299, 2018.
[21] V. Meidanshahi, B. Corbett, T. A. Adams, P. Mhaskar, “Subspace model identification and model predictive control based cost analysis of a semi continuous distillation process,” Computers & Chemical Engineering, 103: 39-57, 2017.
[22] Q. Zhang, Q. Wang, G. Li, “Nonlinear modeling and predictive functional control of Hammerstein system with application to the turntable servo system,” Mechanical Systems and Signal Processing, 72: 383-394, 2016.
[23] J. Rossiter, R. Haber, K. Zabet, “Pole-placement predictive functional control for over-damped systems with real poles,” ISA transactions, 61: 229-239, 2016.
[24] R. Haber, J. Rossiter, K. Zabet, “An alternative for PID control: predictive functional control- a tutorial,” in Proc. American Control Conference (ACC): 6935-6940, 2016.
[25] J. Richalet, D. O'Donovan, Predictive functional control: principles and industrial applications, Springer Science & Business Media, 2009.
[26] M. Abdullah, J. Rossiter, R. Haber, “Development of constrained predictive functional control using Laguerre function based prediction,” IFAC-PapersOnLine, 50: 10705-10710, 2017.
[27] M. Abdullah, Rossiter, “Utilising Laguerre function in predictive functional control to ensure prediction consistency,” in Proc. The 11th International Conference on Control: 1-6, 2016.
[28] A. Dzieliński, D. Sierociuk, “ Stability of discrete fractional order state space systems," IFAC Proceedings, 39(11): 505-510, 2006.
[29] A. Oustaloup, F. Levron, B. Mathieu, F. M. Nanot, “Frequency-band complex non integer differentiator: characterization and synthesis,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 47(1): 25-39, 2000.
[30] K. Matsuda, H. Fuji, “H∞ optimized wave-absorbing control: Analytical and experimental results,” Journal of Guidance, Control and Dynamics, 16(6): 1146-1153, 1993.
[31] G. Carlson, C. Halijak, “Approximation of fractional capacitors (1/s)1/n by a regular Newton process,” IEEE Transactions on Circuit Theory, 11(2): 210-213, 1964.
[32] E. J. Davison, “A method for simplifying linear dynamic systems,” IEEE Transactions on Automatic Control, 11: 93-101, 1966.
[33] B. C. Moore, “Principal component analysis in linear systems: controllability, observability and model reduction,” IEEE Transactions on Automatic Control, 26: 17–32, 1981.
[34] K. Glover, “All optimal Hankel norm approximation of linear multivariable systems and their L∞ error bounds,” International Journal of Control, 39): 1115-1193, 1984.
[35] W. A. H. Schilders, H. A. Van der Vorst, and J. Rommes, Model order reduction: Theory, research aspects and applications, Springer-Verlag Berlin Heidelberg, 2008.
[36] A. B. H. Adamou-Mitiche, L. Mitiche, “Multivariable systems model reduction based on the dominant modes and genetic algorithm,” IEEE Transactions on Industrial Electronics, 64(2): 1617-1619, 2017.
[37] H. Nasiri Soloklo, R. Hajmohammadi, M. M. Farsangi, “Model order reduction based on moment matching using Legendre wavelet and harmony search algorithm,” Iranian Journal of Science and Technology Transactions of Electrical Engineering, 39: 39-54, 2015.
[38] Z-Y. Qiu, Y-L. Jiang, “Piecewise polynomial model reduction method for nonlinear systems in time domain,” Asian Journal of Control, 22(2): 1-10, 2020.
[39] M. Rewieński, J. White, “Model order reduction for nonlinear dynamical systems based on trajectory piecewise-linear approximations,” Linear Algebra and its Applications, 415(2–3): 426-454, 2006.
[40] P. Yanga, Y-L. Jiang, K-L. Xu, “A trust-region method for H2 model reduction of bilinear systems on the Stiefel manifold,” Journal of the Franklin Institute, 356(4): 2258-2273, 2019.
[41] M. I. Ahmad, P. Benner, L. Feng, “Interpolatory model reduction for quadratic-bilinear systems using error estimators,” Engineering Computations, 36(1): 25-44, 2018.
[42] M. Sanatizade, N. Bigdeli, “The design of a coprime‐factorized predictive functional controller for unstable fractional order systems,” Asian Journal of Control, 21(5): 1-14, 2019.
[43] D. Wang, H. Zou, J. Tao, “A new design of fractional-order dynamic matrix control with proportional–integral–derivative-type structure,” Measurement and Control: SAGE Journal, 52(5-6): 567-576, 2019.
[44] R. Zhang, Q. Zou, Z. Cao, F. Gao, “Design of fractional order modelling based extended non-minimal state space MPC for temperature in an industrial electric heating furnace,” Journal of Process Control, 56: 13-22, 2017.
[45] A. Rhouma, B. Bouzouita, F. Bouani, “Practical application of model predictive control to fractional thermal system,” in Proc. Second International Conference on Informatics & Applications (ICIA): 23-25, 2013.
[46] R. Stanisławski, M. Rydel, K. J. Latawiec, M. Łukaniszyn, M. Gałek, “A comparative analysis of two methods for model predictive control of fractional-order systems,” in Proc. The 22nd International Conference on Methods and Models in Automation and Robotics (MMAR): 159-163, 2017.
[47] Q. Zou, Q. Jin, R. Zhang, “Design of fractional order predictive functional control for fractional industrial processes,” Chemometrics and Intelligent Laboratory Systems, 152: 34–41, 2016.
[48] C. A. Monje, Y. Q. Chen, B. M. Vinagre, D. Xue, V. Feliu, Fractional-order systems and control: fundamentals and applications, Springer-Verlag, London, 2010.
[49] M. S. Tavazoei, M. Haeri, “A note on the stability of fractional order systems,” Mathematical and Computers in Simulation, 79: 1566-1576, 2009.
[50] D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley Professional, 1989.
[51] Y. Y. Lepar, Y. C. Wang, C. T. Chang, “Automatic generation of interlock designs using genetic algorithms,” Computers & Chemical Engineering, 101: 167-192, 2017.
[52] S. Skogestad, I. Postethwaite, Multivariable feedback control, analysis and design, 2nd ed., John Wiley Press, 2005.
[53] M. A. Farahani, M. Haeri, “Design and implementation of extended predictive functional control for boiler-turbine unit of power plant,” in Proc. The 24th Mediterranean Conference on Control and Automation: 131-134, 2016.
[54] B. Wahlberg, “System identification using Laguerre models,” IEEE Trans on Automatic Control, 36(5): 551-562, 1991.
[55] L. Wang, “Discrete model predictive controller design using Laguerre functions,” Process Control, 14(2): 131-142, 2004.
[56] A. Basu, “Meliorating the performance of heating furnace system using proportional integral derivative controller with fractional element,” M. Tech. thesis, ITM University, Gwalior, 2016.
[57] H. M. Pandey, A. Chaudhary, D. Mehrotra, “A comparative review of approaches to prevent premature convergence in GA,” Applied Soft Computing, 24): 1047–1077, 2014.
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