Journal of Convergence for Information Technology (융합정보논문지)

Convergence Society for SMB (중소기업융합학회)
권호 표지
DOI QR코드

DOI QR Code

A Study on Optimal PID Controller Design Ensure the Absolute Stability

절대안정도를 보장하는 최적 PID 제어기 설계에 관한 연구

  • Cho, Joon-Ho (Electrical Convergence Engineering, Wonkwang University)
  • 조준호 (원광대학교 전자융합공학과)
  • Received : 2021.01.03
  • Accepted : 2021.02.20
  • Published : 2021.02.28
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, an optimal controller design that guarantees absolute stability is proposed. The order of application of the thesis determines whether the delay time is included, and if the delay time is included, the delay time is approximated through the Pade approximation method. Then, the open loop transfer function for the process model and the controller transfer function is obtained, and the absolute stability interval is calculated by the Routh-Hurwitz discrimination method. In the last step, the optimal Proportional and Integral and Derivative(PID) control parameter value is calculated using a genetic algorithm using the interval obtained in the previous step. As a result, it was confirmed that the proposed method guarantees stability and is superior to the existing method in performance index by designing an optimal controller. If we study the compensation method for the delay time in the future, it is judged that better performance indicators will be obtained.

본 논문에서는 절대 안정도를 보장하는 최적의 제어기 설계에 대해 제안하였다. 논문의 적용 순서는 지연시간의 포함여부를 판단하고, 지연시간이 포함되었을 경우 Pade 근사법을 통해서 지연시간을 근사화 한다. 그 다음 공정모델과 제어기 전달함수에 대한 개루프 전달함수를 구하며, Routh-Hurwitz 판별법에 의해서 절대 안정도 구간을 계산한다. 마지막 단계에서는 앞 단계에서 구한 구간을 활용하여 유전자 알고리즘으로 최적의 PID 제어파라미터 값을 구한다. 그 결과 제안 된 방법은 안정성이 보장되며, 최적의 제어기를 설계하여 기존의 방법보다 성능 지표에서 우월함을 확인하였다. 향후 지연시간에 대한 보상방법이 연구된다면 더욱 좋은 성능지표를 얻을 것으로 판단된다.

Keywords

References

  1. J. G. Ziegler & N. B. Nichols. (1942). Optimum settings for automatic controllers. Transactions of the A.S.M.E. 64, 759-768. DOI : 10.1115/1.2899060
  2. K. J. Astrom & T. Hagglund. (1984). Automatic tuning of simple regulators with specifications on phase and amplitude margins. Automatica. 20(5), 645-651. DOI : 10.1016/0005-1098(84)90014-1
  3. W. K. Ho, C. C. Hang, W. Wojsznis & Q. H. Tao. (1996). Frequency domain approach to self-tuning PID control. Control Engineering Practice. 4(6), 807-813. DOI : 10.1016/0967-0661(96)00071-8
  4. M. Zhuang, D.P. Atherton. (1993), Automatic tuning of optimum PID controllers. IEE Proceedings D. 140(3), 216-224. DOI : 10.1049/ip-d.1993.0030
  5. Q. J. Wang, T. H. Lee, H. W. Fung, Q. Bi & Y. Zhang,(1999). PID tuning for Improved performance. IEEE Transactions on Control Systems Technology. 7(4), 457-465. DOI : 10.1109/87.772161
  6. W. K Ho, O. P. Gan, E. B. Tay & E. L. Ang. (1996). Performance and gain and phase margins of well-known PID tuning formulas. IEEE Transactions on Control Systems Technology. 4(4), 473-477. DOI : 10.1109/87.508897
  7. W. K Ho, C. C. Hang & L. S. Cao. (1995). Tuning of PID controllers based on gain and phase margin specifications. Automatica. 31(3), 497-502. DOI : 10.1016/0005-1098(94)00130-B
  8. J. J. Grefenstette. (1986), Optimizaion of control parameters for genetic algorithms. IEEE Transactions on Systems, Man, and Cybernetics. 16(1), 122-128. DOI : 10.1109/TSMC.1986.289288
  9. B. Verma & P. K. Padhy. (2020). Robust Fine Tuning of Optimal PID Controller With Guaranteed Robustness. IEEE Transactions on Industrial Electronics. 67(6), 4911-4920. DOI : 10.1109/TIE.2019.2924603
  10. J. Fu, J. M. M. Faust, B. Chachuat & A. Mitsos. (2015). Local optimization of dynamic programs with guaranteed satisfaction of path constraints, Automatica, 62(1), 184-192. DOI : 10.1016/j.automatica.2015.09.013
  11. B. Verma & P. K. Padhy. (2018). PID controller design with hyperbolic tangent weighted error function using GA, Proc. 5th Int. Conf. Signal Process. Integr. Netw., 792-795. DOI : 10.1109/SPIN.2018.8474095
  12. N. Sun, T. Yang, Y. Fang, Y. Wu & H. Chen. (2019). Transportation control of double-pendulum cranes with a nonlinear quasi-PID scheme: Design and experiments, IEEE Trans. Syst. Man Cybern. Syst., 49(7), 1408-1418. DOI : 10.1109/TSMC.2018.2871627
  13. M. S. Kwon, U. J. Gim, J. J. Lee & O. Jo. (2018). IoT-based Water Tank Management System for Real-time Monitoring and controling. Journal of Convergence for Information Technology, 8(6), 217-223. DOI : 10.22156/CS4SMB.2018.8.6.217
  14. O. S. Lee & C. S. Leem. (2019). A Study on the Influence of Automatic Control System on the Production of Chemical Propylene. Journal of Convergence for Information Technology, 9(2), 34-42. DOI : 10.22156/CS4SMB.2018.8.6.217