Robust Adaptive Control for a Class of Systems with Deadzone Nonlinearity
ABSTRACT
This paper presents a robust adaptive control scheme for a class of continuous-time linear systems with unknown non-smooth asymmetrical deadzone nonlinearity at the input of the plant. The methodology is applied to handle input deadzone as well as unmeasurable disturbances simultaneously in strictly matched systems. The proposed controller robustly cancels any residual distortion caused by the inaccurate deadzone cancellation scheme. The scheme is shown to successfully cancel the deadzone’s deleterious effect as well as eliminate other unmeasurable disturbances within the span of the input. The new controller ensures the global stability of all states and adaptations, and achieves asymptotic tracking. The asymptotic stability of the closed-loop system is proven by Lyapunov arguments, and simulation results confirm the efficacy of the control methodology.
This paper presents a robust adaptive control scheme for a class of continuous-time linear systems with unknown non-smooth asymmetrical deadzone nonlinearity at the input of the plant. The methodology is applied to handle input deadzone as well as unmeasurable disturbances simultaneously in strictly matched systems. The proposed controller robustly cancels any residual distortion caused by the inaccurate deadzone cancellation scheme. The scheme is shown to successfully cancel the deadzone’s deleterious effect as well as eliminate other unmeasurable disturbances within the span of the input. The new controller ensures the global stability of all states and adaptations, and achieves asymptotic tracking. The asymptotic stability of the closed-loop system is proven by Lyapunov arguments, and simulation results confirm the efficacy of the control methodology.
Cite this paper
Ahmad, N. , Alnaser, M. , Sultan, E. and Alhendi, K. (2015) Robust Adaptive Control for a Class of Systems with Deadzone Nonlinearity. Intelligent Control and Automation, 6, 10-19. doi: 10.4236/ica.2015.61002.
Ahmad, N. , Alnaser, M. , Sultan, E. and Alhendi, K. (2015) Robust Adaptive Control for a Class of Systems with Deadzone Nonlinearity. Intelligent Control and Automation, 6, 10-19. doi: 10.4236/ica.2015.61002.
References
[1] 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, 15-17 December 1993, San Antonio, 2647, 2653. [2] Toa, G. and Kokotovic, P. (1994) Adaptive Control of Plants with Unknown Dead-Zones. IEEE Transactions on Automatic Control, 39, 59-68. http://dx.doi.org/10.1109/9.273339 [3] 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 [4] 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 [5] Selmic, R.R. and Lewis, F.L. (2000) Deadzone Compensation in Motion Control Systems Using Neural Networks. IEEE Transaction of Automatic Control, 45, 602-613. [6] Wang, X.-S., Su, C.-Y. and Hong, H. (2004) Robust Adaptive Control of a Class of Nonlinear Systems with Unknown Dead-Zone. Automatica, 40, 407-413. [7] Zhonghua, W., Bo, Y., Lin, C. and Shusheng, Z. (2006) Robust Adaptive Deadzone Compensation of DC Servo System. IEE Proc.-Control Theory Application, 153, 709-713. [8] Sedighi, H.M., Shirazi, K.H. and Zare, J. (2012) Novel Equivelent Function for Deadzone Nonlinearity: Applied to Analytical Solution of Beam Vibration Using He’s Parameter Expanding Method. Latin American Journal of Solids and Structures, 9, 1-10. [9] 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 Engin- eering, 2, 287-292. [10] Ahmad, N.J., Ebraheem, H., Alnaser, M. and Alostath, J. (2011) Adaptive Control of a DC Motor with Uncertain Deadzone Nonlinearity at the Input. Control and Decision Conference (CCDC), 4295-4299. [11] Sedighi, H.M., Shirazi, K.H. and Zare, J. (2012) Novel Equivelent Function for Deadzone Nonlinearit: Appled to Analytical Solution of Beam Vibration Using He’s Parameter Expanding Method. Latin American Journal of Solids and Structures, 9, 443-451.
http://dx.doi.org/10.1590/S1679-78252012000400002 [12] 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, Seatle, 1580-1584. [13] Sankaranarayanan, S., Melkote, H. and Khorrami, F. (1999) Adaptive Variable Structure Control of a Class of Nonlinear Systems with Nonvanishing Perturbations via Backstepping. Proceedings of the American Control Conference, San Diego, 4491-4495. [14] Zhang, T.P. and Feng, C.B. (1997) Adaptive Fuzzy Sliding Mode Control for a Class of Nonlinear Systems. ACTA Automatica Sinica, 23, 361-369.
[1] 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, 15-17 December 1993, San Antonio, 2647, 2653. [2] Toa, G. and Kokotovic, P. (1994) Adaptive Control of Plants with Unknown Dead-Zones. IEEE Transactions on Automatic Control, 39, 59-68. http://dx.doi.org/10.1109/9.273339 [3] 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 [4] 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 [5] Selmic, R.R. and Lewis, F.L. (2000) Deadzone Compensation in Motion Control Systems Using Neural Networks. IEEE Transaction of Automatic Control, 45, 602-613. [6] Wang, X.-S., Su, C.-Y. and Hong, H. (2004) Robust Adaptive Control of a Class of Nonlinear Systems with Unknown Dead-Zone. Automatica, 40, 407-413. [7] Zhonghua, W., Bo, Y., Lin, C. and Shusheng, Z. (2006) Robust Adaptive Deadzone Compensation of DC Servo System. IEE Proc.-Control Theory Application, 153, 709-713. [8] Sedighi, H.M., Shirazi, K.H. and Zare, J. (2012) Novel Equivelent Function for Deadzone Nonlinearity: Applied to Analytical Solution of Beam Vibration Using He’s Parameter Expanding Method. Latin American Journal of Solids and Structures, 9, 1-10. [9] 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 Engin- eering, 2, 287-292. [10] Ahmad, N.J., Ebraheem, H., Alnaser, M. and Alostath, J. (2011) Adaptive Control of a DC Motor with Uncertain Deadzone Nonlinearity at the Input. Control and Decision Conference (CCDC), 4295-4299. [11] Sedighi, H.M., Shirazi, K.H. and Zare, J. (2012) Novel Equivelent Function for Deadzone Nonlinearit: Appled to Analytical Solution of Beam Vibration Using He’s Parameter Expanding Method. Latin American Journal of Solids and Structures, 9, 443-451.
http://dx.doi.org/10.1590/S1679-78252012000400002 [12] 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, Seatle, 1580-1584. [13] Sankaranarayanan, S., Melkote, H. and Khorrami, F. (1999) Adaptive Variable Structure Control of a Class of Nonlinear Systems with Nonvanishing Perturbations via Backstepping. Proceedings of the American Control Conference, San Diego, 4491-4495. [14] Zhang, T.P. and Feng, C.B. (1997) Adaptive Fuzzy Sliding Mode Control for a Class of Nonlinear Systems. ACTA Automatica Sinica, 23, 361-369.