PI-PD Controller Design Based on Weighted Geometric Center Method for Time Delay Active Suspension Systems

Öz

In this study, a PI-PD controller was designed via weighted geometric center method (WGC) for a quarter vehicle model to suppress the vertical vibrations. The proposed design is based on finding the weighted geometric center of the area formed by the control parameters that make the system stable. The WGC method has two main stages. First, an area formed by the parameters of the PD controller (kf, kd) in the inner loop is obtained and the weighted geometric center of this area is calculated. Then, using these obtained parameters, the inner loop is reduced to a single block, and the parameters of the PI controller in the external loop (kp, ki) are calculated using the stability boundary curve as in the first step, and the weighted geometric center is calculated. The simulation results show that the PI-PD controller designed with the weighted geometric center method offers successful responses for the time delay quarter vehicle system.

Anahtar Kelimeler

• Quarter vehicle model
• PI-PD controller
• Weighted geometrical center method
• Stability

Kaynakça

1. Ahmad I, Shahzad M, Palensky P. 2014. Optimal PID control of magnetic levitation system using genetic algorithm. IEEE International Energy Conference and Exhibition (EnergyCon), May 13-16, Dubrovnik, Croatia, pp: 1-5.
2. Åström KJ, Hägglund T. 1995. Pid controllers: theory, design, and tuning. The international society of measurement and control. URL: https://aiecp.files.wordpress.com/2012/07/1-0-1-k-j-astrom-pid-controllers-theory-design-and-tuning-2ed.pdf (accessed date: March 21, 2023).
3. Åström KJ, Hägglund T, Hang CC, Ho WK. 1993. Automatic tuning and adaptation for PID controllers-a survey. Control Eng Pract, 1(4): 699–714.
4. Atic S, Cokmez E, Peker F, Kaya I. 2018. PID controller design for controlling integrating processes with dead time using generalized stability boundary locus. IFAC, 51: 924–929.
5. Chidambaram M, Sree RP. 2003. A simple method of tuning PID controllers for integrator/dead-time processes. Comp Chem Engin, 27(2): 211–215.
6. Ho MT, Datta A, Bhattacharyya SP. 1996. A new approach to feedback stabilization. Proceedings of 35th IEEE Conference on Decision and Control, December 15-17, Kobe, Japan, pp: 4643–4648.
7. Ho MT, Datta A, Bhattacharyya, SP. 1997. A linear programming characterization of all stabilizing PID controllers. Proceedings of the American Control Conference, June 15-17, New Mexico, Mexico, 6: 3922–3928.
8. Ho WK, Hang CC, Cao, LS. 1995. Tuning of PID controllers based on gain and phase margin specifications. Automatica, 31(3): 497–502.

9. Ho WK, Lim KW, Xu W. 1998. Optimal gain and phase margin tuning for PID controllers. Automatica, 34(8): 1009–1014.
10. Kararsiz G, Paksoy M, Metin M, Basturk, HI. 2021. An adaptive control approach for semi-active suspension systems under unknown road disturbance input using hardware-in-the-loop simulation. Tran Inst Meas Control, 43(5): 995–1008.
11. Kaya I. 2003. A PI-PD controller design for control of unstable and integrating processes. ISA Trans, 42(1): 111–121.
12. Kaya I. 2016. PI-PD controllers for controlling stable processes with inverse response and dead time. Electr Eng, 98(1): 55–65.
13. Kumar EV, Jerome J. 2013. LQR based optimal tuning of PID controller for trajectory tracking of magnetic levitation system. Prodecia Eng, 64: 254–264.
14. Luyben WL. 2003. Identification and tuning of integrating processes with deadtime and inverse response. Ind Eng Chem Res, 42(13): 3030–3035.
15. Maslen EH, Schweitzer G. 2009. Magnetic bearings: theory, design, and application to rotating machinery. In Magnetic Bearings. Springer, New York, USA, pp: 521.
16. Nema S, Padhy PK. 2015. Identification and cuckoo PI-PD controller design for stable and unstable processes. Trans Inst Meas Control, 37(6): 708–720.
17. Onat C, Daskin M, Turan A, Özgüven ÖF. 2021. Manyetik levitasyon sistemleri için ağırlıklı geometrik merkez yöntemi ile PI-PD kontrolcü tasarımı. Müh Makina, 62: 556–579.
18. Onat C. 2018. A new design method for PI–PD control of unstable processes with dead time. ISA Trans, 84: 69–81.
19. Onat C, Sahin M, Yaman Y. 2013. Optimal control of a smart beam by using a luenberger observer. 3rd International Conference of Engineering Against Failure (ICEAF III), 26-28 June, Kos, Greece, pp: 804–811.
20. Onat C, Turan A, Daskin, M. 2017. WGC based PID tuning method for integrating processes with dead-time and inverse response. International Conference on Mathematics and Engineering, 10 - 12 May, İstanbul, Türkiye, pp: 274-279.
21. Onat C. 2013. A new concept on PI design for time delay systems: weighted geometrical center. Int Innov Comp Inf Control, 9(4): 1539–1556.
22. Onat C, Hamamci SE, Obuz S. 2012. A practical PI tuning approach for time delay systems. IFAC Proceed, 45(14): 102–107.
23. Özbek NS, Eker I. 2016. Gain-scheduled PI-PD based modified Smith predictor for control of air heating system: experimental application. International Mediterranean Science and Engineering Congress, 26-28 October, Adana, Türkiye, pp: 706–715.
24. Ozyetkin MM, Onat C, Tan N. 2018. PID tuning method for integrating processes having time delay and inverse response. IFAC-PapersOnLine, 51(4): 274–279.
25. Ozyetkin MM, Onat C, Tan, N. 2019. PI‐PD controller design for time delay systems via the weighted geometrical center method. Asian J Control, 22(5): 1811–1826.
26. Ozyetkin MM, Onat C, Tan, N. 2020. PI-PD controller design for time delay systems via the weighted geometrical center method. Asian J Control, 22(5): 1811–1826.
27. Padhy PK, Majhi S. 2006. Relay based PI–PD design for stable and unstable FOPDT processes. Comp Chem Eng, 30(5): 790–796.
28. Pai NS, Chang SC, Huang CT. 2010. Tuning PI/PID controllers for integrating processes with deadtime and inverse response by simple calculations. J Process Control, 6: 726-733.
29. Paksoy M, Metin M. 2019. Nonlinear semi-active adaptive vibration control of a half vehicle model under unmeasured road input. J Vib Control, 25(18): 2453–2472.
30. Paksoy M, Metin M. 2020. Nonlinear adaptive semiactive control of a half-vehicle model via hardware in the loop simulation. Turk J Electr Eng Comput Sci, 28(3): 1612–1630.
31. Park JH, Sung SW, Lee IB. 1998. An enhanced PID control strategy for unstable processes. Automatica, 34(6): 751–756.
32. Sain D, Swain SK, Mishra SK. 2018. Real Time Implementation of Optimized I-PD Controller for the Magnetic Levitation System using Jaya Algorithm. IFAC-PapersOnLine, 51(1): 106–111.
33. Tan N. 2009. Computation of stabilizing PI-PD controllers. Int J Control Autom Syst, 7(2): 175–184.
34. Turan A, Aggumus A. 2021. Implementation of Advanced PID Control Algorithm for SDOF System. J Soft Comp Artif Intell, 2(2): 43–52.
35. Turan A, Onat C, Şahin M. 2019. Active vibration suppression of a smart beam via PID controller designed through weighted geometric center method. 10th Ankara International Aerospace Conference, AJAC-2019, 13-15 September, Ankara, Türkiye, pp: 79.
36. Turan A. 2021. Improved optimum PID controller tuning by minimizing settling time and overshoot. in advances in machinery and digitization. URL: https://assets.researchsquare.com/files/rs-844641/v1_covered.pdf?c=1631877580 (accessed date: March 15, 2022).
37. Yeroglu C, Onat C, Tan N. 2009. A new tuning method for PIλDμ controller. International Conference on Eectrical and Electronics Egineering-ELECO 2009, 5-8 November, Bursa, Türkiye, pp: 12–316.
38. Zhuang M, Atherton DP. 1993. Automatic tuning of optimum PID controllers. IET Control Theory Appl, 140(3): 216–224.
39. Ziegler JG, Nichols NB. 1942. Optimum settings for automatic controllers. Transact Amer Soc Mechan Engin, 69(8): 759–765.