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

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.

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 ]