Bode plot based stability analysis of a fractional-order PI controller with first-order time-delayed plant

• Autorzy: Sadalla T.

Warianty tytułu

PL

Analiza stabilności układu z regulatorem rzędu ułamkowego i obiektem pierwszego rzędu z opóźnieniem na podstawie charakterystyk Bodego

• Języki publikacji: EN

Abstrakty

EN

The main aim of the paper is to present the stability analysis of a fractional-order PI controller with firstorder, time-delayed plant based on Bode plot. In the paper there is a comparison, presented between the tuning method based on Hermite-Biehler and Pontryagin theorems with, and without taking the gain and phase margins into consideration. The quality performance is based on two quality indices, namely the Integral of Absolute Error and the Integral of a Squared Error.

PL

Głównym celem artykułu jest analiza stabilności obiektu pierwszego rzędu z opóźnieniem oraz regulatora PI rzędu ułamkowego na podstawie charakterystyk Bode'go. W pracy zaprezentowano porównanie metod strojenia opartych na teoriach Hermite-Biehler'a i Pontryagin'a gdy zapas modułu oraz fazy są brane pod uwagę oraz gdy nie są brane pod uwagę. Jakość śledzenia jest oparta na dwóch wskaźnikach jakości całki z wartości bezwzględniej uchybu (IAE) oraz całki z kwadratu uchybu (ISE).

Słowa kluczowe

EN

stability analysis; fractional-order PI controller; time-delay; Bode plot

PL

analiza stabilności; opóźnienie transportowe; wykres Bodego

• Wydawca: Poznańskie Towarzystwo Przyjaciół Nauk
• Czasopismo: Studia z Automatyki i Informatyki
• Rocznik: 2017
• Tom: T. 42
• Strony: 53--60
• Opis fizyczny: Bibliogr. 14 poz., rys.

Twórcy

autor

Sadalla T.

• Poznan University of Technology, Faculty of Electrical Engineering, Institute of Control, Robotics and Information Engineering, Piotrowo 3a Str., 60-965 Poznan, Poland

Bibliografia

• [1] R. Bellman and K. L. Cooke. Differential-Difference Equations. Academic, 1963.
• [2] R. Caponetto, G. Dongola, L. Fortuna, and I. Petras. Fractional Order Systems Modeling and Control Applications. World Scientific Series on Nonlinear Science Series A: Volume 72, 2010.
• [3] H. Fan, Y. Sun, X. Zhang, and H. Fan. Research on fractional order controller in servo press control system. In Mechatronics and Automation, 2007. ICMA 2007. International Conference, pages 2934-2938, Harbin, China, 2007.
• [4] W. Giernacki, T. Sadalla, J. Goslinski, P. Kozierski, J. ao P. Coelho, and S. Sladič. Rotational speed control of multirotor UAV's propulsion unit based on fractional-order PI controller. In In Methods and Models in Automation and Robotics (MMAR), 22th International Conference, pages 993-998, Miedzyzdroje, Poland, 2017.
• [5] S. Hafsi, K. Laabidi, and R. Farkh. Synthesis of a fractional PI controller for a first-order time delay system. Transactions of the Institute of Measurement and Control, 35(8):997-1007, 2013.
• [6] D. Horla. Minimum variance adaptive control of a servo drive with unknown structure and parameters. Asian Journal of Control, 15(1):120-131, 2013.
• [7] Inteco. User’s Manual - Modular Servo System. Inteco, —.
• [8] I. Podlubny. Fractional Differential Equationsl. Academic Press, 1999.
• [9] I. Podlubny. Fractional order systems and PID controller. IEEE Transaction on Automatic Control, 44(2):208-214, 1999.
• [10] K. Rumatowski and D. Horla. Quality analysis of the tracking systems with anti-windup compensators for oscillatory plant models. Pomiary Automatyka Kontrola, 53(10):45-49, 2007.
• [11] T. Sadalla and D. Horla. Initial comparison of experimental vs. simulation results of velocity fractional-order PI controller of a servo drive. In In Automation 2017, International Conference, pages 76-85, Warsaw, Poland, 2017.
• [12] T. Sadalla, D. Horla, W. Giernacki, and P. Kozierski. Stability analysis and tracking performance of fractional-order PI controller for a second-order oscillatory system with time-delay. In In Methods and Models in Automation and Robotics (MMAR), 21th International Conference, pages 322-326, Miedzyzdroje, Poland, 2016.
• [13] T. Sadalla, D. Horla, P. Kozierski, and A. Owczarkowski. Stability analysis of simple anti-windup compensation in approximate pole-placement control of a second order oscillatory system with time delay. In In Methods and Models in Automation and Robotics (MMAR), 21th International Conference, pages 312-315, Miedzyzdroje, Poland, 2016.
• [14] A. Tepljakov, E. Petlenkov, J. Belikov, and J. Finajev. Fractional-order controller design and digital implementation using FOMCON toolbox for MATLAB. In In Methods and Models in Automation and Robotics (MMAR), 21th International Conference, pages 340-345, Hyderabad, India, 2013.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).