Effects of objective function in PID controller design for an AVR system

Abstract

Regulation capability of an automatic voltage regulator (AVR) system still needs to be improved to keep the output voltage of the generator within the AVR system at the desired level. Researchers have been developing new control structures and designing controllers to improve the performance of the AVR system. Designing of PID controller, which is commonly preferred controller due to its simple structure and robustness against to system parameter changes, has an important place among these studies. Especially with the development of metaheuristic algorithms, more successful PID controller designs are emerging by using these algorithms than traditional design methods. Undoubtedly, the objective function utilized also has a significant effect on this success. Therefore, effects of the objective function in PID controller design process for an AVR system are examined in this study. Two different PID controllers are designed using two different metaheuristic algorithms, namely, crow search algorithm (CSA) and ant colony optimization (ACO) algorithm. The parameters of the PID controllers are optimally tuned by using five different objective functions in both algorithms. These objective functions are: Integral of absolute error (IAE), integral of squared error (ISE), integral of time-weighted absolute error (ITAE), integral of time-weighted squared error (ITSE), and a commonly used user-defined objective function. The performance of the designed PID controllers are compared in terms of transient response characteristics and performance metrics. In addition, in order to evaluate the stability of the AVR system with the designed controllers, bode analysis, pole-zero map analysis and robustness analysis are performed.

Keywords

• Ant colony optimization
• Automatic voltage regulator
• Crow search algorithm
• PID Controller

References

1. H. Saadat, Power system analysis, New York, NY, USA: McGraw-Hill, 1999.
2. S. Chatterjee and V. Mukherjee, “PID controller for automatic voltage regulator using teaching-learning based optimization technique,” International Journal of Electrical Power and Energy Systems, vol. 77, pp. 418-429, May 2016, doi: 10.1016/j.ijepes.2015.11.010.
3. S. Ekinci and B. Hekimoglu, “Improved Kidney-Inspired Algorithm Approach for Tuning of PID Controller in AVR System,” IEEE Access, vol. 7, pp. 39935-39947, March 2019, doi: 10.1109/ACCESS.2019.2906980.
4. Z. L. Gaing, “A particle swarm optimization approach for optimum design of PID controller in AVR system,” IEEE Transactions on Energy Conversion, vol. 19-2, pp. 384-391, May 2004, doi: 10.1109/TEC.2003.821821.
5. J. G. Ziegler and N. B. Nichols, “Optimum settings for automatic controllers,” InTech, 1995.
6. G. H. Cohen and G. A. Coon, “Theoretical Consideration of Retarded Control,” Trans. ASME, vol. 75, pp. 384-391, 1953.
7. B. Hekimoğlu, “Sine-cosine algorithm-based optimization for automatic voltage regulator system,” Transactions of the Institute of Measurement and Control, vol. 41-6, pp. 1761-1771, November 2019, doi: 10.1177/0142331218811453.
8. M. Dorigo, V. Maniezzo, and A. Colorni, “Ant system: Optimization by a colony of cooperating agents,” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 26-1, pp. 29-41, February 1996, doi: 10.1109/3477.484436.

9. M. Dorigo, M. Birattari, and T. Stützle, “Ant colony optimization artificial ants as a computational intelligence technique,” IEEE Computational Intelligence Magazine, vol. 1-4, pp. 28-39, November 2006, doi: 10.1109/CI-M.2006.248054.
10. R. Ruchita, R. Kumar, R. Kumar and K. Sharma, "Comparative Analysis of Optimization Techniques for Controlling an AVR System," 2019 International Conference on Recent Advances in Energy-efficient Computing and Communication (ICRAECC), 2019, doi: 10.1109/ICRAECC43874.2019.8995130.
11. A. G. S. Babu and B. T. Chiranjeevi, “Implementation of fractional order PID controller for an AVR system using GA and ACO optimization techniques,” IFAC-PapersOnLine, 2016, doi: 10.1016/j.ifacol.2016.03.096.
12. M. J. Blondin, J. Sanchis, P. Sicard, and J. M. Herrero, “New optimal controller tuning method for an AVR system using a simplified Ant Colony Optimization with a new constrained Nelder–Mead algorithm,” Applied Soft Computing Journal, vol. 62, pp. 216-229, January 2018, doi: 10.1016/j.asoc.2017.10.007.
13. H. Anantwar and A. S. Ramachandran, “PID controller tuning using ACO algorithm for AVR systems,” International Journal of Engineering and Advanced Technology, vol. 9-3, pp. 560-563, February 2020, doi: 10.35940/ijeat.F8747.029320.
14. A. Askarzadeh, “A novel metaheuristic method for solving constrained engineering optimization problems: Crow search algorithm,” Computers and Structures, vol. 169, pp. 1-12, June 2016, doi: 10.1016/j.compstruc.2016.03.001.
15. R. Ramjug-Ballgobin and R. Fowdar, “Application of metaheuristic control strategies to voltage regulation,” SN Applied Sciences, vol. 1-12, pp. 1731, November 2019, doi: 10.1007/s42452-019-1802-8.
16. A. K. Bhullar, R. Kaur, and S. Sondhi, “Enhanced crow search algorithm for AVR optimization,” Soft Computing, vol. 24, pp. 11957–11987, January 2020, doi: 10.1007/s00500-019-04640-w.
17. W. C. Schultz and V. C. Rideout, “Control system performance measures: Past, present, and future,” IRE Transactions on Automatic Control, vol. 1, pp. 22-35, February 1961, doi: 10.1109/tac.1961.6429306.
18. M. S. Ayas, “Design of an optimized fractional high-order differential feedback controller for an AVR system,” Electrical Engineering, vol. 101, pp. 1221–1233, November 2019, doi: 10.1007/s00202-019-00842-5.