Adaptive Control for a Class of Systems with Output Deadzone Nonlinearity
Author(s)
Nizar J. Ahmad1,
Ebraheem K. Sultan1,
Mohammed Q. Qasem1,
Hameed K. Ebraheem1,
Jasem M. Alostad2
Affiliation(s)
1 Faculty of Electronic Engineering Technology, College of Technological Studies, The Public Authority for Applied Education and Training (PAAET), Kuwait City, Kuwait. 2 Faculty of Computer Science, College of Basic Education, The Public Authority for Applied Education and Training (PAAET), Kuwait City, Kuwait.
1 Faculty of Electronic Engineering Technology, College of Technological Studies, The Public Authority for Applied Education and Training (PAAET), Kuwait City, Kuwait. 2 Faculty of Computer Science, College of Basic Education, The Public Authority for Applied Education and Training (PAAET), Kuwait City, Kuwait.
ABSTRACT
This paper presents a continuous-time adaptive control scheme for systems with uncertain non-symmetrical deadzone nonlinearity located at the output of a plant. An adaptive inverse function is developed and used in conjunction with a robust adaptive controller to reduce the effect of deadzone nonlinearity. The deadzone inverse function is also implemented in continuous time, and an adaptive update law is designed to estimate the deadzone parameters. The adaptive output deadzone inverse controller is smoothly differentiable and is combined with a robust adaptive nonlinear controller to ensure robustness and boundedness of all the states of the system as well as the output signal. The mismatch between the ideal deadzone inverse function and our proposed implantation is treated as a disturbance that can be upper bounded by a polynomial in the system states. The overall stability of the closed-loop system is proven by using Lyapunov method, and simulations confirm the efficacy of the control methodology.
This paper presents a continuous-time adaptive control scheme for systems with uncertain non-symmetrical deadzone nonlinearity located at the output of a plant. An adaptive inverse function is developed and used in conjunction with a robust adaptive controller to reduce the effect of deadzone nonlinearity. The deadzone inverse function is also implemented in continuous time, and an adaptive update law is designed to estimate the deadzone parameters. The adaptive output deadzone inverse controller is smoothly differentiable and is combined with a robust adaptive nonlinear controller to ensure robustness and boundedness of all the states of the system as well as the output signal. The mismatch between the ideal deadzone inverse function and our proposed implantation is treated as a disturbance that can be upper bounded by a polynomial in the system states. The overall stability of the closed-loop system is proven by using Lyapunov method, and simulations confirm the efficacy of the control methodology.
Cite this paper
Ahmad, N. , Sultan, E. , Qasem, M. , Ebraheem, H. and Alostad, J. (2015) Adaptive Control for a Class of Systems with Output Deadzone Nonlinearity. Intelligent Control and Automation, 6, 215-228. doi: 10.4236/ica.2015.64021.
Ahmad, N. , Sultan, E. , Qasem, M. , Ebraheem, H. and Alostad, J. (2015) Adaptive Control for a Class of Systems with Output Deadzone Nonlinearity. Intelligent Control and Automation, 6, 215-228. doi: 10.4236/ica.2015.64021.
References
[1] Ahmad, N.J., Alnaser, M.J. and Alsharhan, W.E. (2013) Asymptotic Tracking of Systems with Non-Symmetrical Input Deadzone Nonlinearity. International Journal of Automation and Power Engineering, 2, 287-292. [2] Tao, G. and Kokotovic, P. (1995) Discrete-Time Adaptive Control of Systems with Unknown Dead-Zones. International Journal of Control, 61, 1-17. http://dx.doi.org/10.1080/00207179508921889 [3] Ahmad, N.J., Ebraheem, H.K., Alnaser, M.J. and Alostath, J.M. (2011) Adaptive Control of a DC Motor with Uncertain Deadzone Nonlinearity at the Input. 2011 Chinese Control and Decision Conference (CCDC), Mianyang, 23-25 May 2011, 4295-4299. http://dx.doi.org/10.1109/CCDC.2011.5968982 [4] Toa, G. and Kokotovic, P. (1996) Adaptive Control of Systems with Actuator and Sensor Nonlinearities. John Wiley & Sons, Inc., New York. [5] Arcak, M. and Kokotovic, P.V. (2000) Robust Output Feedback Design Using a New Class of Nonlinear Observer. Proceedings of the 39th Conference on Decision and Control, Sydney, December 2000, 778-783. [6] Ibrir, S., Xie, W.F. and Su, C.-Y. (2007) Adaptive Tracking of Nonlinear Systems with Non-Symmetric Dead-Zone Input. Automatica, 43, 522-530. http://dx.doi.org/10.1016/j.automatica.2006.09.022 [7] Zhang, T.-P., Zhou, C.-Y. and Zhu, Q. (2009) Adaptive Variable Structure Control of MIMO Nonlinear Systems with Time-Varying Delays and Unknown. International Journal of Automation and Computing, 6, 124-136. http://dx.doi.org/10.1007/s11633-009-0124-5 [8] Andrighetto, P.L. and Bavaresco, D. (2008) Dead Zone Compensation in Pneumatic Servo Systems. ABCM Symposium Series in Mechatronics, 3, 501-509. [9] Recker, D.A. and Kokotovic, P.V. (1993) Indirect Adaptive Nonlinear Control of Discrete-Time Systems Containing a Deadzone. Proceedings of the 32nd Conference on Decision and Control, San Antonio, 15-17 December 1993, 2647-2653. http://dx.doi.org/10.1109/CDC.1993.325676 [10] Zhou, J., Er, M.J. and Wen, C.Y. (2005) Adaptive Control of Nonlinear Systems with Uncertain Dead-Zone Nonlinearity. 44th IEEE Conference on Decision and Control, and the European Control Conference, Seville, 12-15 December 2005, 797-801. [11] Betancor-Martin, C.S., Montiel-Nelson, J.A. and Vega-Martinez, A. (2014) Deadzone Compensation in Motion Control Systems Using Model Reference Direct Inverse Control. 2014 IEEE 57th International Midwest Symposium on Circuits and Systems (MWSCAS), College Station, 3-6 August 2014, 165-168. http://dx.doi.org/10.1109/MWSCAS.2014.6908378 [12] Jang, J.O., Chung, H.T. and Jeon, G.J. (2005) Saturation and Deadzone Compensation of Systems Using Neural Network and Fuzzy Logic. Proceedings of the 2005 American Control Conference, 3, 1715-1720. http://dx.doi.org/10.1109/ACC.2005.1470215 [13] Chang, C.-Y., Hsu, K.-C., Chiang, K.-H. and Huang, G.-E. (2006) An Enhanced Adaptive Sliding Mode Fuzzy Control for Positioning and Anti-Swing Control of the Overhead Crane System. IEEE International Conference on Systems, Man and Cybernetics, 2, 992-997. [14] Kong, X.Z. and Zang, F.Y. (2009) Study on the Intelligent Hybrid Control for Secondary Regulation Transmission System. IEEE International Conference on Automation and Logistics, Shenyang, 5-7 August 2009, 726-729. http://dx.doi.org/10.1109/ICAL.2009.5262830 [15] Bessa, W.M. and Barrêto, R.S.S. (2010) Adaptive Fuzzy Sliding Mode Control of Uncertain Nonlinear Systems. Revista Controle & Automacao, 21, 117-126. [16] Lewis, F.L., Tim, W.K., Wang, L.-Z. and Li, Z.X. (1999) Deadzone Compensation in Motion Control System Using Adaptive Fuzzy Logic Control. IEEE Transactions on Control Systems Technology, 7, 731-742. http://dx.doi.org/10.1109/87.799674 [17] Jain, S. and Khorrami, F. (1995) Robust Adaptive Control of a Class of Nonlinear Systems: State and Output Feedback. Proceeding of the 1995 American Control Conference, Seattle, June 1995, 1580-1584. http://dx.doi.org/10.1109/acc.1995.529773
[1] Ahmad, N.J., Alnaser, M.J. and Alsharhan, W.E. (2013) Asymptotic Tracking of Systems with Non-Symmetrical Input Deadzone Nonlinearity. International Journal of Automation and Power Engineering, 2, 287-292. [2] Tao, G. and Kokotovic, P. (1995) Discrete-Time Adaptive Control of Systems with Unknown Dead-Zones. International Journal of Control, 61, 1-17. http://dx.doi.org/10.1080/00207179508921889 [3] Ahmad, N.J., Ebraheem, H.K., Alnaser, M.J. and Alostath, J.M. (2011) Adaptive Control of a DC Motor with Uncertain Deadzone Nonlinearity at the Input. 2011 Chinese Control and Decision Conference (CCDC), Mianyang, 23-25 May 2011, 4295-4299. http://dx.doi.org/10.1109/CCDC.2011.5968982 [4] Toa, G. and Kokotovic, P. (1996) Adaptive Control of Systems with Actuator and Sensor Nonlinearities. John Wiley & Sons, Inc., New York. [5] Arcak, M. and Kokotovic, P.V. (2000) Robust Output Feedback Design Using a New Class of Nonlinear Observer. Proceedings of the 39th Conference on Decision and Control, Sydney, December 2000, 778-783. [6] Ibrir, S., Xie, W.F. and Su, C.-Y. (2007) Adaptive Tracking of Nonlinear Systems with Non-Symmetric Dead-Zone Input. Automatica, 43, 522-530. http://dx.doi.org/10.1016/j.automatica.2006.09.022 [7] Zhang, T.-P., Zhou, C.-Y. and Zhu, Q. (2009) Adaptive Variable Structure Control of MIMO Nonlinear Systems with Time-Varying Delays and Unknown. International Journal of Automation and Computing, 6, 124-136. http://dx.doi.org/10.1007/s11633-009-0124-5 [8] Andrighetto, P.L. and Bavaresco, D. (2008) Dead Zone Compensation in Pneumatic Servo Systems. ABCM Symposium Series in Mechatronics, 3, 501-509. [9] Recker, D.A. and Kokotovic, P.V. (1993) Indirect Adaptive Nonlinear Control of Discrete-Time Systems Containing a Deadzone. Proceedings of the 32nd Conference on Decision and Control, San Antonio, 15-17 December 1993, 2647-2653. http://dx.doi.org/10.1109/CDC.1993.325676 [10] Zhou, J., Er, M.J. and Wen, C.Y. (2005) Adaptive Control of Nonlinear Systems with Uncertain Dead-Zone Nonlinearity. 44th IEEE Conference on Decision and Control, and the European Control Conference, Seville, 12-15 December 2005, 797-801. [11] Betancor-Martin, C.S., Montiel-Nelson, J.A. and Vega-Martinez, A. (2014) Deadzone Compensation in Motion Control Systems Using Model Reference Direct Inverse Control. 2014 IEEE 57th International Midwest Symposium on Circuits and Systems (MWSCAS), College Station, 3-6 August 2014, 165-168. http://dx.doi.org/10.1109/MWSCAS.2014.6908378 [12] Jang, J.O., Chung, H.T. and Jeon, G.J. (2005) Saturation and Deadzone Compensation of Systems Using Neural Network and Fuzzy Logic. Proceedings of the 2005 American Control Conference, 3, 1715-1720. http://dx.doi.org/10.1109/ACC.2005.1470215 [13] Chang, C.-Y., Hsu, K.-C., Chiang, K.-H. and Huang, G.-E. (2006) An Enhanced Adaptive Sliding Mode Fuzzy Control for Positioning and Anti-Swing Control of the Overhead Crane System. IEEE International Conference on Systems, Man and Cybernetics, 2, 992-997. [14] Kong, X.Z. and Zang, F.Y. (2009) Study on the Intelligent Hybrid Control for Secondary Regulation Transmission System. IEEE International Conference on Automation and Logistics, Shenyang, 5-7 August 2009, 726-729. http://dx.doi.org/10.1109/ICAL.2009.5262830 [15] Bessa, W.M. and Barrêto, R.S.S. (2010) Adaptive Fuzzy Sliding Mode Control of Uncertain Nonlinear Systems. Revista Controle & Automacao, 21, 117-126. [16] Lewis, F.L., Tim, W.K., Wang, L.-Z. and Li, Z.X. (1999) Deadzone Compensation in Motion Control System Using Adaptive Fuzzy Logic Control. IEEE Transactions on Control Systems Technology, 7, 731-742. http://dx.doi.org/10.1109/87.799674 [17] Jain, S. and Khorrami, F. (1995) Robust Adaptive Control of a Class of Nonlinear Systems: State and Output Feedback. Proceeding of the 1995 American Control Conference, Seattle, June 1995, 1580-1584. http://dx.doi.org/10.1109/acc.1995.529773