State and Parameter Estimation of a Nonlinear Servo System Handling Noises and Varying Payloads
Payload estimators have many parameters, which are trained using the recorded position, velocity and known payload information. To use these payload estimators in the real-time applications, accurate position and velocity information of the system are required. In this paper, first recently proposed sliding-mode observers (SMOs) are designed and compared for velocity estimation of a nonlinear servo system. Second, a parameter estimation based on sliding-mode super-twisting approach is designed to estimate unknown and varying parameter for a class of nonlinear systems. The convergence property of observers is considered using Lyapunov stability method. In the applications, the constant and varying payloads of the servo system have been estimated using the designed method and compared with Extended-Kalman Filter (EKF). In the final section, artificial noises with different SNR are applied to the measurement signal. When the less amplitude of noise signal is applied, second order SMO estimated the states and the payload better than EKF. However, EKF provides much better estimation results than second order SMO for large amplitude of noise signals. For the sake of generalization, second order SMO is a fast and robust observer for small noise cases. In addition, the filtering property of EKF has still importance for large noise cases.
Keywords:
Extended-Kalman filter, Noise, Sliding mode control State and parameter estimation, Varying payload,
___
- D. Luenberger, “Observers for multivariable systems”, IEEE Transactions on Automatic Control, 11(2):190–197, 1966.
- E. E. Thau, “Observing the state of nonlinear dynamic systems”, International Journal of Control, 17:471–479, 1973.
- M. Zeitz. “The extended luenberger observer for nonlinear systems”, Syst. Control Lett., 9(2):149–156, 1987.
- J.P. Gauthier, H. Hammouri, and S. Othman, “A simple observer for nonlinear systems applications to bioreactors”, IEEE Transactions on Automatic Control, 37(6):875 –880, 1992.
- S. V. Drakunov, “An adaptive quasioptimal filter with discontinuous parameters”, Automatic Remote Control, 44(9):1167–1175, 1983.
- J.J.E. Slotine, J.K. Hedrick, and E.A. Misawa, “On sliding observers for nonlinear systems”, ASME Journal of Dynamic Systems and Control, 109:24–252, 1987.
- H. Cox, “On the estimation of state variables and parameters for noisy dynamic systems”, IEEE Transactions on Automatic Control, 9(1):5–12, 1964.
- D. Simon, “Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches” Wiley-Interscience, 2006.
- K. Tanaka and H.O. Wang, “Fuzzy regulators and fuzzy observers: a linear matrix inequality approach”, In Proceedings of the 36th IEEE Conference on Decision and Control, volume 2, pages 1315 –1320, San Diego, California USA, 1997.
- J.H. Park, P.S. Yoon, and G.T. Park, “Robust adaptive observer using fuzzy systems for uncertain nonlinear systems”, In The 10th IEEE International Conference on Fuzzy Systems, volume 3, pages 749–752, The University of Melbourne, Australia, 2001.
- S. Beyhan, “Adaptive dynamic neural-network observer design of velocity feedbacks”, In International Symposium on Innovations in Intelligent Systems and Applications, pages 1 –5, Trabzon, Turkey, July 2012.
- V. I. Utkin, “Variable structure systems with sliding modes”, IEEE Transactions on Automatic Control, 22(2):212–222, 1977.
- F. Chen and M.W. Dunnigan, “Comparative study of a sliding-mode observer and Kalman filters for full state estimation in an induction machine”,IEEE Proceedings Electric Power Applications, 149(1):53–64, 2002.
- S. K. Spurgeon, “Sliding-mode observers: a survey”, International Journal of Systems Science, 39(8):751–764, 2008.
- Y. Zhang, Z. Zhao, T. Lu, L. Yuan, W. Xu, and J. Zhu, “A comparative study of luenberger observer, sliding mode observer and extended Kalman filter for sensorless vector control of induction motor drives”, In Energy Conversion Congress and Exposition, pages 2466 –2473, 2009.
- M. Leahy, M. Johnson, and S. Rogers, “Neural network payload estimation for adaptive robot control”, IEEE Transactions on Neural Networks, 2(1):93–100, 1991.
- H. C. Nho and P. Meckl, “Intelligent feedforward control and payload estimation for a two-link robotic manipulator”, IEEE/ASME Transactions on Mechatronics, 8(2):277–283, 2003.
- S. Abiko and K. Yoshida, “On-line parameter identification of a payload handled by flexible based manipulator”, In Proceedings of the International Conference on Intelligent Robots and Systems, volume 3, pages 2930–2935, Sendai, Japan, 2004.
- M. Savia and H. N. Koivo, “Neural-network-based payload determination of a moving loader”, Control Engineering Practice, 12(5):555–561, 2004.
- J. Davila, L. Fridman, and A. Levant, “Second-order sliding-mode observer for mechanical systems”, IEEE Transactions on Automatic Control, 50(11):1785 – 1789, nov. 2005.
- N. K. M. Sirdi, A. Rabhi, I. Fridman, J. Davila, and Y. Delanne, “Second order sliding-mode observer for estimation of vehicle dynamic parameters”, International Journal of Vehicle Design, 48(3):190–207, 2008.
- R. Sharma and M. Aldeen, “Design of integral sliding mode observers with application to fault and unknown input reconstruction”, In Proceedings of the 48th IEEE Conference on Decision and Control, pages 6958 –6963, December 2009.
- C. P. Tan, X. Yu, and Z. Man, “Terminal sliding mode observers for a class of nonlinear systems”, Automatica, 46(8):1401 – 1404, 2010.
- R. E. Kalman, “A new approach to linear filtering and prediction problems”, Transactions of the ASME–Journal of Basic Engineering, 82(Series D):35–45, 1960.
- V. Aidala, “Parameter estimation via the Kalman filter”, IEEE Transactions on Automatic Control, 22(3):471 – 472, 1977.
- Li Xin Wang. “A course in fuzzy systems and control”. Prentice-Hall Inc., London, 1997.
- ISSN: 2147-8228
- Yayın Aralığı: Yılda 4 Sayı
- Başlangıç: 2013
- Yayıncı: Selçuk Üniversitesi