A Chattering Suppression of Proportional Sliding Mode Control with Composite Nonlinear Feedback Technique using Sigmoid Function for MacPherson Active Suspension System

Muhamad Fahezal Ismail, Yahaya Md.Sam, Shahdan Sudin, Kemao Peng, Mohd Khairi Aripin


The chattering problem phenomenon occurred due to the high-frequency switching of a sliding mode controller exciting unmodelled dynamics in the closed loop. Unmodelled dynamics may be those of sensors and actuators neglected in the principal modelling process since they are generally significantly faster than the main system dynamics. In the MacPherson active suspension system, the phenomenon occurred due to unmodelled dynamics on tire in a quarter car model. The Proportional Integral Sliding Mode Control (PISMC) is combined with Composite Nonlinear Feedback (CNF) technique due to its characteristics on the transient response and fast settling time. The sigmoid function is used in PISMC-CNF control law to reduce chattering problem. The Evolution Strategy is used to find the best boundary layer thickness based on the road profiles applied to the MacPherson active suspension system. The results show the significant of the proposed solution in the mentioned application based on acceleration of spring mass.


Boundary layer solution; Chattering problem; Sigmoid function; Unmodelled dynamics.

Article Metrics

Abstract view : 348 times
PDF - 143 times

Full Text:



M. S. Fallah, R. Bhat and W. F. Xie, H∞ robust control of semi-active Macpherson suspension system: New applied design, Vehicle System Dynamics, 48(3), 339–360, 2010.

K.-S. Hong, D.-S. Jeon, W.-S. Yoo, H. Sunwoo, S.-Y. Shin, C.-M. Kim and B.-S. Park, A new model and an optimal pole-placement control of the Macpherson suspension system, SAE Technical Paper, 1999-01-1331, 1999.

K. Chen and D. G. Beale, Base dynamic parameter estimation of a Macpherson suspension mechanism, Vehicle System Dynamics, 39(3), 227–244, 2003.

Y. M. Goh, J. D. Booker and C. A. McMahon, Uncertainty modeling of a suspension unit, Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 219(6), 755–771, 2005.

J. Hurel, A. Mandow and A. Garcia-Cerezo, Kinematic and dynamic analysis of the McPherson suspension with a planar quarter-car model, Vehicle System Dynamics, 51(9), 1422–1437, 2013.

Y. M. Sam, J. H. S. Osman and M. R. M. Ghani, A class of proportional-integral sliding mode control with application to active suspension system, Systems and Control Letters, 51(3–4), 217–223, 2004.

J. Lin and R.-J. Lian, Hybrid self-organizing fuzzy and radial basis-function neural-network controller for active suspension systems, International Journal of Innovative Computing, Information and Control, 7(6), 3359–3378, 2011.

A. Chamseddine, H. Noura and T. Raharijaona, Control of linear full vehicle active suspension system using sliding mode techniques. IEEE International Conference on Control Applications, Munich, Germany, 2006, pp. 1306–1311.

S. Zhou and S. Zhang, Semi-active control on leaf spring suspension based on SMC, Chinese Control and Decision Conference, Xuzhou, China, 2010, pp. 1462–1466.

B.-C. Chen, Y.-H. Shiu and F.-C. Hsieh, Sliding-mode control for semi-active suspension with actuator dynamics, Vehicle System Dynamics, 49(1-2), 277–290, 2010.

A. Pati, S. Singh and R. Negi, Sliding mode controller design using PID sliding surface for half car suspension system, Students Conference on Engineering and Systems, Allahabad, India, 2014, pp. 1–6.

P. F. Puleston, S. Spurgeon and G. Monsees, Automotive engine speed control: A robust nonlinear control framework, IEE Proceedings - Control Theory and Applications, 148(1), 81–87, 2001.

L. Xiaoqiu and S. Yurkovich, Sliding mode control of delayed systems with application to engine idle speed control, IEEE Transactions on Control Systems Technology, 9(6), 802–810, 2001.

S. Govindaswamy, T. Floquet and S. K. Spurgeon, Discrete time output feedback sliding mode tracking control for systems with uncertainties, International Journal of Robust and Nonlinear Control, 24, 2098–2118, 2013.

H. Alwi and C. Edwards, An adaptive sliding mode differentiator for actuator oscillatory failure case reconstruction, Automatica, 49(2), 642–651, 2013.

B. Zhang and W. Lan, Improving transient performance for output regulation problem of linear systems with input saturation, International Journal of Robust and Nonlinear Control, 23(10), 1087–1098, 2013.

Z. Lin, M. Pachter and S. Banda, Toward improvement of tracking performance nonlinear feedback for linear systems, International Journal of Control, 70(1), 1–11, 1998.

B. M. Chen, T. H. Lee, K. M. Peng and V. Venkataramanan, Composite nonlinear feedback control for linear systems with input saturation: Theory and an application, IEEE Transactions on Automatic Control, 48(3), 427–439, 2003.

V. Utkin, J. Guldner and J. Shi, Sliding mode control in electro-mechanical systems, CRC Press, 2009.

X. Zhao, M. Kremb and C. Schindler, Assessment of wheel loader vibration on the riding comfort according to ISO standards, Vehicle System Dynamics, 51(10), 1548–1567, 2013.

S. Mobayen, V. J. Majd and M. H. Asemani, Selection of nonlinear function in integral sliding mode-based composite nonlinear feedback method for transient improvement of uncertain linear systems, The 2nd International Conference on Control, Instrumentation and Automation, Shiraz, Iran, 2011, pp. 513–518.

S. Mobayen and V. J. Majd, Robust tracking control method based on composite nonlinear feedback technique for linear systems with time-varying uncertain parameters and disturbances, Nonlinear Dynamics, 70(1), 171–180, 2012.

S. Mobayen and V. J. Majd, Tracker design using composite nonlinear feedback with application to a DC servomotor, 3rd Power Electronics and Drive Systems Technology, Tehran, Iran, 2012, pp. 435–440.

S. Mobayen, Robust tracking controller for multivariable delayed systems with input saturation via composite nonlinear feedback, Nonlinear Dynamics, 76(1), 827–838, 2014.

S. Mobayen, Design of CNF-based nonlinear integral sliding surface for matched uncertain linear systems with multiple state-delays, Nonlinear Dynamics, 77(3), 1047–1054, 2014.

B. Bandyopadhyay, D. Fulwani and Y. J. Park, A robust algorithm against actuator saturation using integral sliding mode and composite nonlinear feedback, Proceedings of the 17th World Congress The International Federation of Automatic Control, Seoul, South Korea, 2008, pp.



  • There are currently no refbacks.