İki Girişli İki Çıkışlı Sistemlerde Ayrık Zamanda PI-PR2 Kontrolör Tasarımı

Öz

Bu çalışmada, iki giriş iki çıkışlı sistemler için ayrık zaman düzleminde oransal-integral oransal-çift gecikmeli (PI-PR2) kontrolör yapısı önerilmiştir. Tasarım yöntemi olarak kontrol sistemlerinde sıkça karşılaşılan baskın kutup atama yaklaşımı kullanılmıştır. İki giriş iki çıkışlı sistem bir ayrıştırıcı ile iki alt sisteme bölünmüş ve her bir alt sistem için PIR2 kontrolör tasarlanmıştır. Baskın kutuplar istenilen kapalı çevrim sistemin performans özelliklerine göre yerleştirilmiş ve kalan kutupların sınırı baskınlık katsayısı yardımıyla bir çember bölgesi olarak belirlenmiştir. Bu sınır bölgesi, parametre düzlemine aktarılmış ve ilgili kontrolör çözüm kümesi elde edilmiştir. Kontrolör sıfırının konumunun belirlenmesi avantajından yararlanmak için elde edilen PIR2 kontrolör PI-PR2 kontrolör yapısına çevrilmiştir. Önerilen tasarım yöntemi, bir benzetim çalışması üzerinden anlatılmış ve literatürdeki bazı kontrol yöntemleriyle karşılaştırılmıştır.

Anahtar Kelimeler

• PI-PR2 kontrolör tasarımı
• PIR kontrolör
• PID kontrolör
• baskın kutup atama
• ayrık zaman düzlemi

Discrete PI-PR2 Controller Design for Two Input Two Output Systems

Öz

In this study, a proportional integral double retarded (PI-PR2) controller structure is proposed for two-inputs two-outputs systems in discrete time domain. The dominant pole assignment approach, which is frequently encountered in control systems, is used as the primary design method. The two input two output system is divided into two subsystems by a decoupler and the PIR2 controller is designed for each subsystem. Dominant poles are placed according to the desired performance characteristics of the closed-loop system and the boundary of the remaining poles is determined as a circle with the help of the dominance coefficient. This boundary is transferred to the parameter plane and the corresponding controller solution set is obtained. In order to take advantage of determining the location of the controller zero, the obtained PIR2 controller is converted to the PI-PR2 controller structure. The proposed design method is explained through a simulation study and compared with some control methods in the literature.

Anahtar Kelimeler

• PI-PR2 controller design
• PIR controller
• PID controller
• dominant pole placement
• discrete time domain

Kaynakça

1. Åström KJ, Murray RM. Feedback systems: An introduction for scientists and engineers. New Jersey, USA, Princeton University, 2010.
2. Ackermann J, Bartlett A, Kaesbauer D, Sienel W, Steinhauser R, Robust control: Systems with uncertain physical parameters. London, Springer, 1993.
3. Halder K, Das S, Gupta A, Time delay handling in dominant pole placement with PID controllers to obtain stability regions using random sampling, International Journal of Control, 2020, 94(12), 3384-3405.
4. Wang H, Han QL, Liu J, He D, Discrete-time filter proportional–integral–derivative controller design for linear time-invariant systems, Automatica, 2020, 116, 1-15.
5. Wang QG, Zhang Z, Åström KJ, Zhang Y, Zhang Y, Guaranteed dominant pole placement with PID controllers, IFAC Proceedings Volumes, 2008, 41(2), 5842–5845.
6. Dincel E, Söylemez MT, Guaranteed dominant pole placement with discrete-PID controllers: a modified Nyquist plot approach, IFAC Proceedings Volumes, 2014, 47(3), 3122–3127.
7. Åström KJ, Hägglund T, The future of PID control, Control Engineering Practice, 2001, 9(11), 1163–1175.
8. Kharitonov VL, Niculescu SI, Moreno J, Michiels W, Static output feedback stabilization: Necessary conditions for multiple delay controllers, IEEE Transactions on Automatic Control, 2005, 50(1), 82-86.

9. Niculescu SI, Michiels W, Stabilizing a chain of integrators using multiple delays, IEEE Transactions on Automatic Control, 2004, 49(5), 802-807.
10. Ramírez A, Mondié S, Garrido R, Sipahi R, Design of proportional-integral-retarded (PIR) controllers for second-order LTI systems, IEEE Transactions on Automatic Control, 2015, 61(6), 1688–1693.
11. López K, Mondié S, Garrido R, A tuning procedure for the Cascade Proportional Integral Retarded Controller, IFAC-PapersOnLine, 2018, 51(14), 61-65.
12. Ramirez A, Sipahi R, Fast Consensus Against Noise in a Large-Scale Multi-Agent System with Distributed Proportional-Retarded (PR) Controllers, 2018 Annual American Control Conference (ACC), 2018, Milwaukee, WI, USA, 3666-3671.
13. Mammadov AD, Dincel E, Söylemez MT, Analytical design of discrete PI–PR controllers via dominant pole assignment, ISA Transactions, 2022, 123, pp. 312–322, 2022.
14. Hu Z, Li D, Wang J, Xue F, Analytical Design of PID Decoupling Control for TITO Processes with Time Delays, Journal of Computers, 2011, 6(6), 1064-1070.
15. Noeding M, Martensen J, Lemke N, Tegethoff W, Koehler J, Selection of decoupling control methods suited for automated design for uncertain TITO processes, 2018 IEEE 14th International Conference on Control and Automation (ICCA), 2018, Anchorage, AK, USA, 498–505.
16. Wutthithanyawat C, Wangnippamto S, Design of Decentralized PID Controller with Coefficient Diagram Method Based on Inverted Decoupling for TITO System, 2018 International Electrical Engineering Congress (iEECON), 2018, Krabi, Thailand, 1–4.
17. Lakshmanaprabu SK, Elhoseny M, Shankar K, Optimal tuning of decentralized fractional order PID controllers for TITO process using equivalent transfer function, Cognitive Systems Research, 2019, 58, 292–303.
18. Mammadov AD, Dincel E, Söylemez MT, Design of decentralized proportional–integral proportional–retarded controllers in discrete-time domain for two-input two-output processes, Transactions of the Institute of Measurement and Control, 2023, 45(3), 427-439.
19. Maghade DK, Patre BM, Decentralized PI/PID controllers based on gain and phase margin specifications for TITO processes, ISA Transactions, 2012, 51(4), 550–558.
20. Chien IL, Huang HP, Yang JC, A simple multiloop tuning method for PID controllers with no proportional kick, Industrial & engineering chemistry research, 1999, 38(4), 1456-1468.
21. Reddy MDL, Padhy PK, Ansari IA, Auto-tuning method for decentralized PID controller of TITO systems using firefly algorithm, 2019 International Conference on Intelligent Computing and Control Systems (ICCS), 2019, Madurai, India, 683–688.
22. Khandelwal S, Aldhandi S, Detroja KP, Decoupling control with etf based gpm tuning for multivariable processes, 2019 Fifth Indian Control Conference (ICC), 2019, New Delhi, India, 63–67.
23. Hajare VD, Patre BM, Khandekar AA, Malwatkar GM, Decentralized PID controller design for TITO processes with experimental validation, International Journal of Dynamics and Control, 2017, 5(3), 583–595.