A Software Realization of Disturbance Rejection Optimal FOPID Controller Design Methodology by Using Soft Computing Techniques

Abstract

This study presents a soft computing tool for the computer-aided design of disturbance rejection FOPID controllers based on the maximization of Reference to Disturbance Ratio (RDR) index. The study illustrates the utilization of software routines to implement a soft computing scheme in order to solve a closed loop disturbance rejection FOPID control system design problem for a target gain margin specification. Authors demonstrate that the complex design efforts, which involve a high level of mathematical knowledge, can be easily performed by using basic software routines when soft computing techniques are employed effectively in the computation processes. Illustrative design examples are shown to show effectiveness of the proposed design method.

Keywords

• Disturbance rejection control
• FOPID controller
• genetic algorithm
• phase margin
• RDR

References

1. K.B. Oldham, J. Spanier, “Fractional Calculus.” Academic Press Inc., 1974.
2. R. Hilfer, “Application of Fractional Calculus in Physics.” World Scientific, 2000.
3. Y.Q. Chen, T. Bhaskaran, and D. Xue, “Practical tuning rule development for fractional order proportional and integral controllers.” J. Comput. Nonlinear Dyn., vol. 3, 2, 2008,pp. 214031–214038.
4. W. Jifeng, L. Yuankai, “Frequency domain Analysis and Applications for Fractional Order Control System.” IOP, Journal of Physics: Conf. 13, 2005, pp. 268- 273.
5. D. Xue, Y.Q. Chen, “A Comparative Introduction of Four Fractional Order Controllers.” Proceedings of the 4th World Congress on Intelligent Control and Automation, Shanghai, P.R. China, 2002, pp. 3228-3235.
6. G.F. Franklin, J.D. Powell, A.E. and Baeini, “Feedback Control of Dynamic Systems.” Addison-Wesley, Reading, MA, 1986.
7. K. Ogata, “Modern Control Engineering.” 2nd edn. Prentice-Hall, Englewcod Cliffs, NJ, 1990.
8. J.L. Chang, “Robust output feedback disturbance rejection control by simultaneously estimating state and disturbance.” J Control Sci Eng, 2011, pp. 1–13.

9. Z. Vukic, O. Kuljaca, “Lect PID Controllers.”, Vol. 23, 2002.
10. D. Vrancic, S. Strmčnik, J. Kocijan, P.B. de Moura Oliveirac, “Improving disturbance rejection of PID controllers by means of the magnitude optimum method.” ISA Trans, Vol. 49, 1, 2010, pp. 47–56.
11. J.M.E. Vandeursen, J.A. Peperstraete, “Model-based and PID controllers for disturbance rejection in processes with time delay: a comparison.” ISA Trans, Vol. 35, 3, 1996, pp. 225–236.
12. F.N., Deniz, C., Keles, B.B., Alagoz, and N. Tan, “Design of fractional-order PI controllers for disturbance rejection using RDR measure.” In International Conference on Fractional Differentiation and Its Applications 2014 (ICFDA 2014), 2014.
13. B.B. Alagoz, F.N. Deniz, C. Keles, and N. Tan, “Disturbance rejection performance analyses of closed loop control systems by reference to disturbance ratio.” ISA Transactions, Vol. 55, 2015, pp. 63–71. doi:10.1016/j.isatra.2014.09.013.
14. A. Biswas, S. Das, and A. Abraham, and S. Dasgupta, “Design of fractional-order PIλDμ controllers with an improved differential evolution.” Engineering Applications of Artificial Intelligence, Vol. 22, 2009,pp. 343-350.
15. M. Zamani, M. Karimi-Ghartemani, N. Sadati, M. Parniani, “Design of a fractional order PID controller for an AVR using particle swarm optimization.” Control Engineering Practice, Vol. 17, 2009, pp.1380-1387.
16. G. Zhe, X. Liao, “Rational approximation for fractionalorder system by particle swarm optimization,” Nonlinear Dynamics, Vol. 67, 2, 2012, pp. 1387-1395.
17. A. Richards, “Fast Model Predictive Control with Soft Constraints.” European Control Conference (ECC) Julay, Zürich, Switzerland, pp. 17-19.
18. J.C. Regin, “Using hard constratints for representing soft constraints, International Conference on AI and OR Techniques in Constriant Programming for Combinational Optimization Problems.” Springer, Berlin, Heideberg, 2011, pp. 176-189.
19. P. Meseguer, F. Rossi, and T. Schiex, “Soft Constraints, Foundation of Artificial Intelligence.” Elsevier, 2006, pp. 281-328 (Soft global constraining page 312).
20. M. Chandrasekaran, M. Muralidhar, C.M. Krishna, U.S. Dixit, “Application of soft computing techniques in machining performance prediction and optimization: a literature review.” The international journal of Advanced manufacturing Technology, Vol. 46, 5, 2010, pp. 445-464.
21. S. Rahnamayan, H.R. Tizhoosh, M.M.A. Salama, “Oposition versus randomness in soft computing techniques,” Applied Soft Computing, Vol. 8, 2008, pp. 906-918.
22. B.B. Alagoz, N. Tan, F.N. Deniz, C. Keles, “Implicit disturbance rejection performance analysis of closed loop control systems according to communication channel limitations.” IET Control Theory & Applications, Vol. 9, 17, 2015, pp. 2522-2531.
23. A. Ates, B.B. Alagoz, C. Yeroglu, et al., “Disturbance rejection FOPID control of rotor by multi-objective bb-bc optimization algorithm.” In: ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 13th ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications Cleveland, Ohio, USA, Vol. 9, 6–9 (August 2017).
24. S. Tufenkci, B. Senol, B.B. Alagoz, & R. Matušů, “Disturbance rejection FOPID controller design in v-domain.” Journal of Advanced Research, Vol. 25, 2020, pp. 171-180.
25. N. Ozbey, C. Yeroglu, B.B. Alagoz, N. Herencsar, A. Kartci, & R. Sotner, “2DOF multi-objective optimal tuning of disturbance reject fractional order PIDA controllers according to improved consensus oriented random search method.” Journal of Advanced Research., Vol. 25, 2020, pp. 159-170.
26. Q. Jin, Y. Shi, Q. Liu, M. Chu, & Y. Zhang, “Graphical robust PID tuning for disturbance rejection satisfying multiple objectives.” Chemical Engineering Communications, Vol. 205, 12, 2018, pp. 1701-1711.
27. D. Goldberg, J. Holland, “Genetic Algorithms and Machine Learning.” Mach. Learn., Vol. 3, 2-3, 1988, pp. 95–99.
28. K.F. Man, K.S. Tang, ve S. Kwong, “Genetic Algorithms.” Springer Publishing, 1999.
29. D.E. Goldberg, “Genetic Algorithms in Search, Optimization and Machine Learning.” Addison-Wesley Publishing Company, 1989.
30. A.R. Tavakolpour, I.Z. Mat Darus, O. Tokhi, M. Mailah, “Genetic Algorithm-Based Identification of Transfer Function Parameters for a Rectangular Flexible Plate System.” Eng. Appl. Artif. Intel., Vol. 23, 8, 2010, pp. 1388–1397.
31. C. Zhao, D. Xue, & Y. Chen, “A fractional order PID tuning algorithm for a class of fractional order plants.” In IEEE International Conference Mechatronics and Automation, Vol. 1, 2005, pp. 216-221.
32. X. Dingyu, “Fractional-Order Control Systems: Fundamentals and Numerical Implementations,” Walter de Gruyter, Berlin, Germany, Boston, MA, USA, 2017.
33. M. Tabatabaei, R. Salehi, “Fractional order PID controller design based on Laguerre orthogonal functions.” International Journal of Dynamics and Control, Vol. 5, 3, 2017, pp. 542-550.