Artículos regulares

 

Two-Degrees-of-Freedom Robust PID Controllers Tuning Via a Multiobjective Genetic Algorithm

 

Sintonización de controladores PID robustos de dos grados de libertad mediante un algoritmo genético multiobjetivo

 

José Rubén Lagunas-Jiménez¹, Víctor Moo-Yam¹, and Benjamín Ortíz-Moctezuma²

 

¹ Universidad Autónoma de Campeche, Campeche, Mexico jrlaguna@uacam.mx, victmmoo@uacam.mx

² Universidad Politécnica de Victoria, Tamaulipas, Mexico mortizm@upv.edul.mx

 

Abstract

In this paper, a design methodology for a proportional integral derivative (PID) control design is presented by means of the statement of a multiobjective optimization problem (MOP). Two-degrees-of-freedom controller (PID-ISA) is used. The objective functions are deployed considering a set point response, load disturbances and robustness to model uncertainty as its components. The time constant of measurement noise filter is a component of the vector of decision variables. The optimization problem is solved by means of a genetic algorithm.

Keywords: Multiobjective optimization, two-degrees-of-freedom PID controller, robustness, uncertainty, genetic algorithm.

 

Resumen

En este artículos e presenta una metodología de diseño de controladores PID (Proporcional, Integral y Derivativo), de dos grados de libertad mediante el planteamiento de un problema de optimización multiobjetivo. Las funciones objetivo propuestas consideran entre otros: respuesta de referencia al escalón, perturbación de carga y robustez ante incertidumbre en el modelado. También se incluye un filtro para minimizar el ruido de medición y la constante de tiempo se incluye en el vector de variables de decisión. El problema de optimización se resuelve con un algoritmo genético.

Palabras clave: Optimización multiobjetivo, controlador PID de dos grados de libertad, robustez, incertidumbre, algoritmo genético.

 

DESCARGAR ARTÍCULO EN FORMATO PDF

 

References

1. Ackermann, J., Blue, P., Bünte, T., Güvenc, L., Kaesbauer, D., Kordt, M., Muhler, M., & Odenthal, D. (2002). Robust Control: The Parameter Space Approach. London: Springer.         [ Links ]

2. Äström, K.J., Panagopoulos, H., & Hägglund, T. (1998). Design of PI Controllers based on Non-Convex Optimization. Automatica, 34(5), 585-601.         [ Links ]

3. Äström, K.J. & Hägglund, T. (1995). PID Controllers: Theory, Design, and Tuning (2^nd Ed.). Research Triangle Park, N.C.: International Society for Measurement and Control.         [ Links ]

4. Bechikh, S., Belgasmi, N., Said, L.B., & Ghedira, K. (2008). PHC-NSGA-II: A Novel Multi-objective Memetic Algorithm for Continuous Optimization. 20^th IEEE International Conference on Tools with Artificial Intelligence (ICTAI 08), Dayton, OH, 1, 180-189.         [ Links ]

5. Campos-Delgado, D.U. & Zhou, K. (2003). Mixed £₁/H₂/H_∞ control design: numerical optimization approaches. International Journal of Control, 76(7), 687-697.         [ Links ]

6. Chakraborty, J., Konar, A., Nagar, A., Das, S. (2009). Rotation and translation selective Pareto optimal solution to the box-pushing problem by mobile robots using NSGA-II. IEEE Congress on Evolutionary Computation (CEC 09), Trondheim, Norway, 2120-2126.         [ Links ]

7. Coello, C.A., Veldhuizen, D.A., & Lamont, G.B. (2002). Evolutionary Algorithms for Solving Multi- Objective Problems. New York: Kluwer Academic Publishers.         [ Links ]

8. Coello, C.A. (1999). An Update Survey of Evolutionary-Based Multiobjective Optimization Techniques: State of the Art and Future Trends. 1999 Congress on Evolutionary Computation. Washington, D.C., 3-13.         [ Links ]

9. Coello, C.A. & Becerra, R.L. (2003). Evolutionary Multiobjective optimization using a Cultural Algorithm. 2003 IEEE Swarm Intelligence Symposium, Indianapolis, In., USA, 6-13.         [ Links ]

10. Coello, C.A., Lamont, G.B., & Veldhuizen, D.A. (2007). Evolutionary Algorithms for Solving Multi-Objective Problems (2^nd ed.). New York: Springer.         [ Links ]

11. Doyle, J.C., Francis, B.A., & Tannenbaum, A.R. (1992). Feedback Control Theory. New York: Macmillan Pub. Co.         [ Links ]

12. Fonseca, C.M. & Fleming, P.J. (1998). Multiobjective Optimization and Multiple Constraint Handling with Evolutionary Algorithms-Part I: A unified Formulation. IEEE Transactions on Systems, Man, Cybernetics, 28(1), 26-37.         [ Links ]

13. Gambier, A. (2011). Control of a Reverse Osmosis plant by using a robust PID design based on multi-objective optimization. 50^th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), Orlando, FL, 7045-7050.         [ Links ]

14. Hang, C.C., Äström, K.J., & Wang, Q.G. (2002). Relay feedback auto-tuning of process controllers -a tutorial review. Journal of Process Control, 12(1), 143-162.         [ Links ]

15. Herreros, A. (2000). Diseño de controladores Robustos Multiobjetivo por medio de Algoritmos Genéticos. Tesis Doctoral, Universidad de Valladolid, España.         [ Links ]

16. Jamshidi, M., Krohling, R.A., Coelho, L.D.S., & Fleming, P.J. (2003). Robust Control Systems with Genetic Algorithms. Boca Raton, Fla.: CRC Press.         [ Links ]

17. Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. (2002). A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2), 182-197.         [ Links ]

18. Kasat, R.B., Kunzru, D., Saraf, D.N., & Gupta, S.K. (2002). Multiobjective Optimization of Industrial FCC Units using Elitist Nondominated Sorting Genetic Algorithm. Industrial & Engineering Chemistry Research, 41(19), 4765-4776.         [ Links ]

19. Kristiansson, B. & Lennartson, B. (2006). Robust tuning of PI and PID Controllers: using derivative action despite sensor noise. IEEE Control Systems, 26(1), 55-69.         [ Links ]

20. Lennartson, B. & Kristiansson, B. (1997). Pass Band and High frequency Robustness for PID Control. 36^th Conference on Decision and Control, San Diego California, USA, 3, 2666-2671.         [ Links ]

21. Ming-Tzo, H. & Chia-Yi, L. (2002). PID Controller Design for Robust Performance. 41^st IEEE Conference on Decision and Control, Las Vegas, Nevada USA, 1, 1062-1067.         [ Links ]

22. Panagopoulos, H., Äström, K.J., & Hägglund, T. (1999). Design of PID Controllers based on Constrained Optimization. 1999 American Control Conference, San Diego California, USA, 6, 38583862.         [ Links ]

23. Sánchez, G., Villasana, M., & Strefezza, M. (2008). Solving Multi-Objective Linear Control Design Problems Using Genetic Algorithms. 17^th World Congress, the International Federation of Automatic Control, Seoul, Korea, 12324-12329.         [ Links ]

24. Zhou, K. & Doyle, J.C. (1998). Essentials of Robust Control. Upper Saddle River, N.J.: Prentice Hall.         [ Links ]

25. Wuhua, H., Gaoxi, X., & Wen-Jian, C. (2011). PID controller design based on two-degrees-of-freedom direct synthesis. 2011 Chinese Control and Decision Conference (CCDC), Mianyang, China, 629-634.         [ Links ]

26. Xiang-Zhong, G. (2009). Multi-objective PID Controller Based on NSGA-II Algorithm with Application to Main Steam Temperature Control. 2009 International Conference on Artificial Intelligence and Computational Intelligence (AICI '09). Shanghai, China 21-25.         [ Links ]

27. Yamamoto, S., Hirahara, H., Tanaka, A., & Ara, T. (2012). Simple robust design of Two-Degree-of-Freedom PID controller for tracking drives of Linear Servo Motors. 15^th International Conference on Electrical Machines and Systems (ICEMS), Sapporo, Japan, 1-6.         [ Links ]

28. Ziegler, J.G. & Nichols, N.B. (1942). Optimum Settings for Automatic Controllers. Transactions ASME, 64(11), 759-768.         [ Links ]