Kalman State Estimation and LQR Assisted Adaptive Control Of a Variable Loaded Servo System

O. Aydogdu, M. L. Levent


This study actualized a new hybrid adaptive controller design to increase the control performance of a variable loaded time-varying system. A structure in which LQR and adaptive control work together is proposed. At first, a Kalman filter was designed to estimate the states of the system and used with the LQR control method which is one of the optimal control servo system techniques in constant initial load. Then, for the variable loaded servo (VLS) system, the Lyapunov based adaptive control was added to the LQR control method which was inadequate due to the constant gain parameters. Thus, it was aimed to eliminate the variable load effects and increase the stability of the system. In order to show the effectiveness of the proposed method, a Quanser servo module was used in Matlab-Simulink environment. It is seen from the experimental results and performance measurements that the proposed method increases the system performance and stability by minimizing noise, variable load effect and steady-state error.


adaptive control; Lyapunov method; LQR; Kalman filter; VLS system

Full Text:



G. Bishop, G. Welch, An Introduction to the Kalman Filter, ACM, 2001

B. O. Teixeira, M. A. Santillo, R. S. Erwin, D. S. Bernstein, “Spacecraft tracking using sampled-data Kalman filter”, IEEE Control Systems Magazine, Vol. 28, No. 4, pp. 78-94, 2008

M. E. Hough, “Precise orbit determination using satellite radar ranging”, Journal of Guidance, Control, and Dynamics, Vol. 35, No. 4, pp. 1048-1058, 2012

J. R. Vetter, “Fifty years of orbit determination”, Johns Hopkins APL Technical Digest, Vol. 27, No. 3, pp. 239-252, 2007

H. Chen, G. Chen, E. Blasch, K. Pham, “Comparison of several space target tracking filters”, in: Sensors and Systems for Space Applications III, Vol. 7330, pp. 73300I-1 - 73300I-12, SPIE, 2009

H. H. Bilgic, M. A. Sen, A. Yapici, M. Kalyoncu, “Dofrusal Ters Sarkacin Denge Kontrolu Icin Yapay Sinir Agi Tabanli Bulanik Mantik & LQR Kontrolcu Tasarimi”, Otomatik Kontrol Ulusal Toplantisi Bildiriler Kitabi, Kocaeli, Turkey, July 11-13, 2014 (in Turkish)

J. Arslan, G. Muhurcu, “Speed Control of Direct Current Motor with Linear Quadratic Gaussian Control”, Elektrik – Elektronik – Bilgisayar ve Biyomedikal Muhendisligi Sempozyumu–(ELECO 2014), Bursa, Turkey, November 27-29, 2014

D. Grewal, “Kalman Filtering”, in: International Encyclopedia of Statistical Science, Springer, 2011

S. Tunyasrirut, V. Kinnares, J. Ngamwiwit, “Performance improvement of a slip energy recovery drive system by a voltage-controlled technique”, Renewable Energy, Vol. 35, No. 10, pp. 2235-2242, 2010

Y. Zhi, G. Li, Q. Song, K. Yu, J. Zhang, “Flight control law of unmanned aerial vehicles based on robust servo linear quadratic regulator and Kalman filtering”, International Journal of Advanced Robotic Systems, Vol. 14, No. 1, 2017

S. Pankaj, J. S. Kumar, R. K. Nema, “Comparative analysis of MIT rule and Lyapunov rule in model reference adaptive control scheme”, Innovative Systems Design and Engineering, Vol. 2, No. 4, pp. 154-162, 2011

F. J. Lin, S. G. Chen, I. F. Sun, “Adaptive backstepping control of six‐phase PMSM using functional link radial basis function network uncertainty observer”, Asian Journal of Control, Vol. 19, No. 6, pp. 2255-2269, 2017

H. Wang, X. Zhao, Y. Tian, “Trajectory tracking control of XY table using sliding mode adaptive control based on fast double power reaching law”, Asian Journal of Control, Vol. 18, No. 6, pp. 2263-2271, 2016

W. L. Mao, C. W. Hung, S. Suprapto, “Adaptive fuzzy trajectory control for biaxial motion stage system”, Advances in Mechanical Engineering, Vol. 8, No. 4, 2016

B. Rashidi, M. Esmaeilpour, M. R. Homaeinezhad, “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, Vol. 28, pp. 79-95, 2015

O. Aydogdu, O. Alkan, “Adaptive control of a time-varying rotary servo system using a fuzzy model reference learning controller with variable adaptation gain”, Turkish Journal of Electrical Engineering & Computer Sciences, Vol. 21, No. 2, pp. 2168-2180, 2013

C. Kasnakoglu, “Modeling and control of flow problems by adaptation-based linear parameter varying models”, Turkish Journal of Electrical Engineering & Computer Sciences, Vol. 18, No. 5, pp. 819-852, 2010

F. L. Lewis, L. Xie, D. Popa, Optimal and Robust Estimation, CRC Press, 2007

E. Flores, R. E. Castro, L. F. Chaves, “Conventional compensators design using Newton's method”, 11th World Congress on Intelligent Control and Automation, Shenyang, China, June 29-July 4, 2014

M. Pal, G. Sarkar, R. K. Barai, T. Roy, “Design of different reference model based model reference adaptive controller for inversed model non-minimum phase system”, Mathematical Modelling of Engineering Problems, Vol. 4, No. 2, pp. 75-79, 2017

P. Swarnkar, S. Jain, R. K. Nema, “Effect of Adaptation Gain in Model Reference Adaptive Controlled Second Order System”, Engineering, Technology & Applied Science Research, Vol. 1, No. 3, pp. 70-75, 2011

S. B. Roland, Advanced Control Engineering, Burterworth-Heinemann, 2001

eISSN: 1792-8036     pISSN: 2241-4487