Kalman Filtresi ile Ayrık Zamanlı Durum Tahmini ve Zamanla Değişen Doğrusal Bir Sistemin Adaptif LQR Kontrolü

Year 2020, Ejosat Special Issue 2020 (ICCEES), 322 - 331, 05.10.2020

Mehmet Latif Levent , Ömer Aydoğdu , Cüneyt Yücelbaş

https://doi.org/10.31590/ejosat.804741

Abstract

Bu çalışmada, değişken yük etkilerini kompanze eden ve yüksek kontrol performansını sağlayan yeni bir adaptif denetleyici tasarımı gerçekleştirilmiştir. Öne sürülen kontrol metodunda, sistem çıkış durumlarını tahmin eden ayrık zamanlı kalman filtresi (Discrete Time Kalman Filter, DKF) ve optimum kontrol yöntemlerinden biri olan Ayrık Zamanlı Doğrusal Kuadratik Regülator (Discrete Time Linear Quadratic Regulator, DLQR) metodlarından yararlanılmıştır. DLQR kontrol metodu zamanla yükü değişmeyen sistemlere tüm periyotlarda uygulandığında iyi sonuçlar üretmesine rağmen, adaptasyon mekanizması bulunmadığından, zamanla değişen sistemlerde istenilen cevabı verememektedir. Bu problemi çözmek için, farklı çevre ortamlarına uyum sağlayan, yeni bir durum geri besleme kazanç matrix değerini (Knew) ve pozisyon (position, x1) kontrol, hız (speed, x2) kontrol ve akım (current, x3) kontrol gibi sistem kontrol blokları için kullanılan optimum lyapunov adaptasyon kazanç değerlerini ( theta1, theta2, theta3, theta4, theta5 ve theta6) sürekli güncelleyen bir lyapunov tabanlı adaptasyon mekanizması yöntemi geliştirilmiştir. Bu mekanizmada lyapunov adaptasyon kazancın başlangıç değerleri, tasarımda yeni bir yaklaşım olarak Yapay Sinir Ağı (Artificial Neural Network, ANN) metodu ile hesaplanmıştır. Böylece değişken yük etkilerinin minimize edilmesi ve sistem kararlılığının artırılması amaçlanmıştır. Önerilen yöntemin etkinliğini pratik uygulama ve simülasyonda göstermek için, zamanla değişen doğrusal bir sistem olan değişken yüklü bir Sanal Simülasyon laboratuvarları (Virtual Simulation Laboratories, VsimLabs) servo sistemi modellenmiş ve Matlab Simulink ortamında kullanılmıştır. Deneysel sonuçlara ve İntegral Karesel Hata (Integral Square Error, ISE), İntegral Mutlak Hata (Integral Absolute Error, IAE), İntegral Zamanlı Mutlak Hata (Integral time absolute error, ITAE) gibi performans ölçümlerine göre, önerilen yöntemin değişken yük etkisini ve sürekli durum hatasını minimize ederek sistem performans ve kararlılığını artırdığı görülmüştür.

Keywords

Adaptasyon Mekanizması, Yapay Sinir Ağı, Lyapunov Yöntemi, Zamanla Değişen Doğrusal Sistem

Supporting Institution

hakkari BAP tarafından desteklenmektedir. (proje numarası FM20BAP11)

Project Number

FM20BAP11

Discrete Time State Estimation with Kalman Filter and Adaptive LQR Control of a Time Varying Linear System

Abstract

In this study, a new adaptive controller design was created that compensates for variable load effects and provides high control performance. In the proposed control method, Discrete Time Kalman Filter method (DKF), which estimates system output states, and Discrete Time Linear Quadratic Regulator (DLQR) method, one of the optimal control methods, were used. Although the DLQR control method produces good results when applied to unvarying systems, it cannot provide the desired response in time varying systems because it has no adaptation mechanism. In order to solve this problem, an adaptation mechanism based lyapunov method which has been developed that adapts to different environmental conditions, constantly updating a new state feedback gain matrix value (Knew) and optimal lyapunov adaptation gain values ( theta1, theta2, theta3, theta4, theta5 and theta6) used for system control block such as position (x1) control, speed (x2) control and current (x3) control. In this mechanism, lyapunov adaptation gain initial values were calculated using the Artificial Neural Network (ANN) method as a new control approach. Thus, it was aimed to minmize the effects of variable load and to increase the control system stability. In order to show the proposed method effectiveness, a variable loaded VsimLabs (Virtual Simulation laboratories) servo system was modelled as a time varying linear system and applied in practical implementation and simulation in environment of Matlab Simulink. Taking reference the results of experimental platform and measurement of performance index such as Integral Square Error (ISE), Integral Absolute Error (IAE) and Integral time absolute error (ITAE), it was observed that the proposed control method increases the system stability and performance by eliminating variable load effect and steady state error.

Keywords

Adaptation mechanism, Artificial neural network, Lyapunov method, Time varying linear system

Project Number

FM20BAP11

References

• Roy, T. K., Pervej, M. F., Tumpa, F. K., & Paul, L. C. (2016, December). Nonlinear adaptive controller design for velocity control of a DC motor driven by a DC-DC buck converter using backstepping approach. In 2016 2nd International Conference on Electrical, Computer & Telecommunication Engineering (ICECTE) (pp. 1-4). IEEE.
• Afjei, E., Ghomsheh, A. N., & Karami, A. (2007, September). Sensorless speed/position control of brushed DC motor. In 2007 International Aegean Conference on Electrical Machines and Power Electronics (pp. 730-732). IEEE.
• Bishop G, Welch G. An introduction to the kalman filter. Chapel Hill, NC, USA: Proc of SIGGRAPH, 2001.J. Breckling, Ed., The Analysis of Directional Time Series: Applications to Wind Speed and Direction, ser. Lecture Notes in Statistics. Berlin, Germany: Springer, 1989, vol. 61.
• Teixeira BO, Santillo MA, Erwin RS, Bernstein DS. Spacecraft tracking using sampled-data Kalman filters. IEEE Control Systems Magazine 2008; 28 (4): 78-94.
• Haixia Q, Banhazi TM, Zhigang Z, Low T, Brookshaw IJ. Preliminary laboratory test on navigation accuracy of an autonomous robot for measuring air quality in livestock buildings. International Journal of Agricultural and Biological Engineering 2016; 9 (2): 29-39.
• Artemciukas E, Sakalauskas L, Zulkas E. Kalman filter for hybrid tracking technique in augmented reality. Elektronika ir Elektrotechnika 2016; 22 (6): 73-79 .
• Kluga A, Kluga J. Dynamic Data Processing with Kalman Filter. Elektronika ir Elektrotechnika 2011; 111 (5): 33-36.
• Bistrovs V, Kluga A. The analysis of the UKF-based navigation algorithm during GPS outage. Elektronika ir Elektrotechnika 2013; 19 (10): 13-16.
• Ziacik P, Wieser V. Mobile radio link adaptation by radio channel state prediction. Elektronika ir Elektrotechnika 2011; 114 (8): 27-30
• Castaneda C, Loukianov A, Sanchez E, Castillo-Toledo B. Real-time torque control using discrete-time recurrent high-order neural networks. Neural Computing and Applications 2013; 22 (6): 1223-1232.
• Castaneda CE, Loukianov AG, Sanchez EN, Castillo-Toledo B. Discrete-time neural sliding-mode block control for a DC motor with controlled flux. IEEE Transactions on Industrial Electronics 2011; 59 (2): 1194-1207.
• Akhlaghi, S., Zhou, N., & Huang, Z. (2017, July). Adaptive adjustment of noise covariance in Kalman filter for dynamic state estimation. In 2017 IEEE power & energy society general meeting (pp. 1-5). IEEE.
• Ali, D., Asim, M., Wallam, F., Abbas, A., & Naudhani, Y. (2019, January). Experimental testing of observers comprising discrete Kalman filter and high-gain observers. In 2019 2nd International Conference on Computing, Mathematics and Engineering Technologies (iCoMET) (pp. 1-5). IEEE.
• Abut, T. (2016). Modeling and Optimal Control of a DC Motor. Int. J. Eng. Trends Technol, 32(3), 146-150.
• Aravind, M. A., Saikumar, N., & Dinesh, N. S. (2017, May). Optimal position control of a DC motor using LQG with EKF. In 2017 international conference on mechanical, system and control engineering (ICMSC) (pp. 149-154). IEEE.
• Lin FJ, Sun IF, Yang KJ, Chang JK. Recurrent fuzzy neural cerebellar model articulation network fault-tolerant control of six-phase permanent magnet synchronous motor position servo drive. IEEE Transactions on Fuzzy Systems 2015; 24 (1): 153-167.
• Wang H, Zhao X, Tian Y. Trajectory tracking control of XY table using sliding mode adaptive control based on fast double power reaching law. Asian Journal of Control 2016; 18 (6): 2263-2271.
• Mao WL, Hung CW, Suprapto. Adaptive fuzzy trajectory control for biaxial motion stage system. Advances in Mechanical Engineering 2016; 8 (4) 1-16.
• Rashidi B, Esmaeilpour M, Homaeinezhad MR. Precise angular speed control of permanent magnet DC motors in presence of high modeling uncertainties via sliding mode observer-based model reference adaptive algorithm Mechatronics 2015; 28: 79-95.
• Talian P, Perdukova D, Fedor P. Stable and Robust Tension Controller for Middle Section of Continuous Line. Elektronika ir Elektrotechnika 2018; 24 (1): 3-10.
• Aydogdu, O., & Levent, M. L. (2019). Kalman state estimation and LQR assisted adaptive control of a variable loaded servo system. Engineering, Technology & Applied Science Research, 9(3), 4125-4130.
• Aydogdu, O., & Levent, M. L. (2020). State Estimation with Reduced-Order Observer and Adaptive-LQR Control of Time Varying Linear System. Elektronika ir Elektrotechnika, 26(2), 24-31.