Fuzzy state feedback with double integrator and anti-windup for the Van de Vusse reaction

• Autorzy: Márquez-Vera C. A. , Màrquez-Vera M. A. , Yakoub Z. , Ma’arif A. , Castro-Montoya A. J. , Cázarez-Castro N. R.

Identyfikatory

DOI

10.24425/acs.2022.141717

• Języki publikacji: EN

Abstrakty

EN

Chemical processes use to be non-minimum phase systems. Thereby, they are a challenge for control applications. In this paper, fuzzy state feedback is applied in the Van de Vusse reaction that has an inverse response. The control design has an integrator to enhance the control performance by eliminating the steady-state error when a step reference is applied. An anti-windup action is used to reduce the undershoot in the system response. In practice, it is not possible to have always access to all the state variables. Thus, a fuzzy state observer is implemented via LMIs. Frequently, the papers that show similar applications present some comments about disturbance rejection. To eliminate the steady-state error when a ramp reference is used, in this work, a second integrator is aggregated. Now, the anti-windup also reduces the overshoot generated due to the usage of two integrators in the final application.

Słowa kluczowe

EN

fuzzy state feedback; LMIs; Van de Vusse reaction; double integrator; anti-windup

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2022
• Tom: Vol. 32, No. 2
• Strony: 383--408
• Opis fizyczny: Bibliogr. 43 poz., rys., tab., wzory

Twórcy

autor

Márquez-Vera C. A.

• Universidad Veracruzana, Prolongación Venustiano Carranza S/N, Col. Revolución, Poza Rica 93390, Veracruz, Mexico

autor

Màrquez-Vera M. A.

• Polytechnic Universityof Pachuca, C. Pachuca-Cd. Sahagún Km 20, Ex-Hacienda de Santa Bárbara, Zempoala 43830, Hgo., Mexico

autor

Yakoub Z.

• University of Gabès, National Engineering School of Gabès, Rue Omar Ibn El Khattab, Zrig Eddakhlania, Gabès 6029, Tunisia

autor

Ma’arif A.

• Universitas Ahmad Dahlan, Jl. Kapas No. 9, Semaki, Kec. Umbulharjo, Yogyakarta 55166, Indonesia

autor

Castro-Montoya A. J.

• Universidad Michoacana de San Nicolás de Hidalgo, Edif. M, Ciudad Universitaria, Morelia 58030, Michoacán, Mexico

autor

Cázarez-Castro N. R.

• Instituto Tecnológico de Tijuana, Calz. Tecnológico S/N, Fracc. Tomás Aquino, Tijuana 22414, BC, Mexico

Bibliografia

• [1] P. Skupin, M. Metzger, P. Laszczyk and M. Niedzwiedz: Experimental and bifurcation analysis of a hybrid CSTR plant. Chemical Engineering Research and Design, 148 (2019), 191-201. DOI: 10.1016/ j.cherd.2019.06.010.
• [2] A. Simorgh, A. Razminia and V. Shiryaev: System identification and control design of a nonlinear continuously stirred tank reactor. Mathematics and Computers in Simulation, 173 (2020), 16-31. DOI: 10.1016/j.matcom.2020.01.010.
• [3] W. Chang: Nonlinear cstr control system design using an artificial bee colony algorithm. Simulation Modelling Practice and Theory, 31 (2013), 1-9. DOI: 10.1016/j.simpat.2012.11.002
• [4] L. Chen, S. Du, Y. He, M. Liang and D. Xu: Robust model predictive control for greenhouse temperature based on particle swarm optimization. Information Processing in Agriculture, 5 (2018), 329-338. DOI: 10.1016/j.inpa.2018.04.003.
• [5] A. Palencia-Díaz, J. Carpinteiro-Durangoand J. Fabregas-Villegas: Modeling, simulation and control of a reactor for the production of aluminum chloride. Prospectiva, 10 (2012), 31-36. DOI: 10.15665/rp.v10i2.230.
• [6] M. Kumarand R.S. Singh: Comparison of non-linear, linearized 2nd order and reduced to FOPDT models of CSTR using different tuning methods. Resource-Efficient Technologies, 2 (2016), S71-S75. DOI: 10.1016/j.reffit.2016.11.003.
• [7] M. Irshad and A. Ali: Optimal tuning rules for PI/PID controllers for inverse response processes. IFAC PapersOnLine, 51 (2018), 413-418. DOI: 10.1016/j.ifacol.2018.05.063.
• [8] M. Bahita and K. Belarbi: Model reference neural-fuzzy adaptive control of the concentration in a chemical reactor (CSTR). IFAC PapersOnLine, 49 (2016), 158-162. DOI: 10.1016/j.ifacol.2016.11.093.
• [9] K. Hagenmeyer and M. Zeitz: Van de Vusse CSTR as a benchmark problem for nonlinear feedforward control design techniques. In: IFAC Nonlinear Control Systems, Ed. Elsevier, Stuttgart, Germany, (2004), 1123-1128.
• [10] H. Perez, B. Ogunnaike and S. Devasia: Output tracking between operating points for nonlinear processes: Van de Vusse example. IEEE Transactions on Control Systems Technology, 10 (2002), 611-617. DOI: 10.1109/TCST.2002.1014680.
• [11] K. Vu: A model predictive controller for inverse response control systems. IFAC PapersOnLine, 48 (2015), 562-567. DOI: 10.1016/j.ifacol. 2015.09.02.
• [12] C. Mesén, E. Vargas and J. Torres: Sintonización y análisis del funcionamiento de un sistema CSTR. Proyecto Final: IE-0431 Sistems de Control, Diagnostic test, Universidad de Costa Rica, 2021.
• [13] V. Alfaro, P. Balaguer and O. Arrieta: Robustness considerations on pid tuning for regulatory control of inverse response processes. In: IFAC Conference on Advanced PID Control, Ed. Elsevier, Bresia, Italy, (2012), 193-198. DOI: 10.3182/20120328-3-IT-3014.00033
• [14] S. Kuntanapreeda and P. Marusak: Nonlinear extended output feedback control for CSTRs with Van de Vusse reaction. Computers & Chemical Engineering, 41 (2012), 10-23. DOI: 10.1016/j.compchemeng.2012.02.010.
• [15] A. Bertone, R. da M. Jafelice and B. Goes: Classic and fuzzy type-2 control for the Van de Vusse reactor: A comparative study. In: Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, Ed. S. de Matemática Aplicada e Computacional. 6 Sao Carlos, Brazil, (2018), 1-7. DOI: 10.5540/03.2018.006.02.0258.
• [16] R. Malar and T. Thyagarajan: Artificial neural networks based modeling and control of continuous stirred tank reactor. American Journal of Engineering and Applied Sciences, 2 (2009), 229-235. DOI: 10.3844/ajeassp.2009.229.235.
• [17] G. Cassol, G. Campos, D. Thomaz, B. Capron and A. Secchi: Reinforcement learning applied to process control: A Van de Vusse reactor case study. in: International Symposium on Process Systems Engineering-PSE, Eds. M.I. Mario and R. Eden, San Diego, California, United States of America, (2018), 1123-1128. DOI: 10.1016/B978-0-444-64241-7.50087-2.
• [18] W. Cargua, M. Gallegos, P. Leica, L. Guzmán-Beckmann and O. Camacho: Control schemes comparison for CSTR chemical reactors. Ciencia e Ingeniería, 39 (2018), 177-189.
• [19] M.A. Márquez-Vera, L.E. Ramos-Velasco and B.D. Balderrama-Hernández: Stable fuzzy control and observer via LMIs in a fermentation process. Journal of Computational Science, 27 (2018), 192-198. DOI: 10.1016/j.jocs.2018.06.002.
• [20] H. Ojeda-Elizarras, R. Maya-Yescas, S. Hernández-Castro, J. Segovia-Hernández and A.J. Castro-Montoya: Fuzzy control of a nonlinear system with inverse responce: Van de Vusse reaction. International Journal of Latest Research in Science and Technology, 2 (2013), 1-5. DOI: 10.1016/j.eswa.2010.09.158.
• [21] S. Tsai: Robust H∞ control for Van de Vusse reactor via T-S fuzzy bilinear scheme. Expert Systems with Applications, 38 (2011), 4935-4944. DOI: 10.1016/j.eswa.2010.09.158.
• [22] H. Lam, F. Leung and P. Tam: Fuzzy state feedback controller for nonlinear systems: Stability analysis and design. In: Ninth IEEE International Conference on Fuzzy Systems, FUZZ-IEEE. Ed. IEEE, San Antonio, United States of America, (2000), 677-681. DOI: 10.1109/FUZZY.2000.839102.
• [23] K. Tanaka and H. O. Wang: Fuzzy control systems design and analysis: A linear matrix inequality approach. Wiley-Intescience, New York, 2001.
• [24] I. Carrera-Flores: Diseno de sistemas de control para procesos aplicados a reactores continuos tipo tanque agitado (CSTR). Master’s thesis, Escuela Politécnica Nacional, Quito, Ecuador, 2014.
• [25] H. Chen, A. Kremling and F. Allgöwer: Nonlinear predictive control of a benchmark CSTR. In: Proceedings of 3rd European Control Conference, Rome, Italy, (1995), 3247-3252.
• [26] S. Engell and K. Klatt: Nonlinear control of a nonminimum-phase CSTR. In: Proceedings of the American Control Conference, (ed. IEEE), San Francisco, United States of America, (1993), 2941-2945. DOI: 10.23919/acc.1993.4793439.
• [27] J.G. van de Vusse: Plug-flow type reactor versus tank reactor. Chemical Engineering Science, 19(12), (1964), 994-996. DOI: 10.1016/0009- 2509(64)85109-5.
• [28] T. Ross: Fuzzy Logic with Engineering Applications. John Wiley & Sons, Ltd., West Sussex, 2008.
• [29] P. Woolf: Chemical Process Dynamics and Controls. Open textbook library, University of Michigan Engineering Controls Group, 2009.
• [30] J. Verhaegh, F. Kupper and F. Willem: Frequency response based multivariable feedback control design for transient RCCI engine operation. IFAC PapersOnLine, 53 (2020), 14008-14015. DOI: 10.1016/j.ifacol.2020.12.921.
• [31] J. Koo, D. Park, S. Ryu, G. Kimand Y. Lee: Design of a self-tuning adaptive model predictive controller using recursive model parameter estimation for real-time plasma variable control. Computers & Chemical Engineering, 123 (2019), 126-142. DOI: 10.1016/j.compchemeng.2019.01.002.
• [32] E. J. Herrera-López, B. Castillo-Toledo, J. Ramírez-Córdova and E. Ferreira: Takagi-Sugeno fuzzy observer for a switching bioprocess: Sector nonlinearity approach, In: New Developments in Robotics Automation and Control. Ed. Alex Lazinica, Intech, Shangai, China, (2008) 155-180.
• [33] E. Chavero-Navarrete, M. Trejo-Perea, J. Jáuregui-Correa, R. Carrillo-Serrano, and G. Ríos-Moreno: Expert control systems implemented in a pitch control of wind turbine: A review. IEEE Access, 7 (2019), 13241-13259. DOI: 10.1109/ACCESS.2019.2892728.
• [34] Z. Lendek, T. Guerra, R. Babuška and B. De-Shutter: Stability Analysis and Nonlinear Observer Design Using Takagi-Sugeno Fuzzy Models. Studies in Fuzziness and Soft Computing, 262 Springer, India, 2010.
• [35] M. Chadli, H. Karimi and P. Shi: On stability and stabilization of singular uncertain Takagi-Sugeno fuzzy systems. Journal of the Franklin Institute, 351 (2014), 1453-1463. DOI: 10.1016/j.jfranklin.2013.11.008.
• [36] Purtojo and Wahyudi: Integral anti-windup scheme of full-state feedback control for point-to-point (PTP) positioning system. In: International Conf. on Electronic Design, Ed. IEEE, Penang, Malaysia, (2008), 1-6. DOI: 10.1109/ICED.2008.4786777.
• [37] W. Liu, Y. Zheng, Q. Chen and D. Geng: An adaptive CGPC based anti-windup PI controller with stability constraints for the intermittent power penetrated system. International Journal of Electrical Power & Energy Systems, 130 (2021), 106922. DOI: 10.1016/j.ijepes.2021.106922.
• [38] P. Bui, S. You, H. Kim and S. Lee: Dynamics modelling and motion control for high-speed underwater vehicles using H-infinity synthesis with anti-windup compensator. Journal of Ocean Engineering and Science, 2021, Preprint. DOI: 10.1016/j.joes.2021.07.002.
• [39] K. Ogata: Modern Control Engineering. 5th edition, Pearson Education, Inc., Upper Saddle River, New Jersey, 2010.
• [40] M. Grant and S. Boyd: CVX: Matlab software for disciplined convex programming. Version 2.0 beta, 2013, Available from: http://cvxr.com/cvx/ download/.
• [41] R. Sree and M. Chidambaram: Simple method of tuning PI controllers for stable inverse response systems. Journal of the Indian Institute of Science, 83 (2003), 73-85.
• [42] J. Jeng and S. Lin: Robust proportional-integral-derivative controller design for stable/integrating processes with inverse response and time delay. Industrial & Engineering Chemistry Research, 51 (2012), 2652-2665. DOI: 10.1021/ie201449m.
• [43] A. Ma’Arif, A. Cahyadi, S. Herdjunanto and O. Wahyunggoro: Tracking control of high order input reference using integrals state feedback and coefficient diagram method tuning. IEEE Access, 8 (2020), 182731-182741. DOI: 10.1109/ACCESS.2020.3029115.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)