Adaptive and Robust Second Order Sliding Mode Controller Dedicated to Nonlinear Uncertain Pendulum Application System


  •   Hedi Dhouibi

  •   Jalel Ghabi

  •   Tarek Selmi


The research work presented within this paper deals with an innovative second-order sliding mode control (SOSMC) allocated to adaptive gain and associated with nonlinear systems subject to unknown but bounded uncertainties. The derived controller   guarantees the control gain dynamical adaptation for the sake of counteracting the system’s uncertainties and to mitigate the chattering phenomenon. The Lyapunov method is also used to analyses the stability of any closed loop system (CLS) within a finite-time under bounded uncertainties assumptions. To assess how effective is the approach considered within this paper, the adaptive controller has been carefully studied on a benchmark of nonlinear systems on a damped overturned pendulum.

Keywords: Control, Gain, Finite-Time, Sliding-Mode, Stability, Adaptive, Nonlinear System, Uncertainty


Rachit Mehra, Sumeet G.Satpute, FarukKazi and N.M.Singh, " Control of a class of underactuated mechanical systems obviating matching conditions", Automatica, Vol. 86, pp. 98-103, December 2017.

Xinrong Zhang, Jie Ma, Lian Lin and Lele Wang, "Study on Swing-up Control of Rotary Inverted Pendulum Based on Energy Feedback", IEEE 5th International Conference on Information Science and Control Engineering (ICISCE), Zhengzhou, China, 20-22 July 2018,

Xuebo Yang and Xiaolong Zheng, " Swing-Up and Stabilization Control Design for an Underactuated Rotary Inverted Pendulum System: Theory and Experiments", IEEE Transactions on Industrial Electronics, Vol. No.9, pp. 7229-7238, Sept. 2018.

D Zhai, L An, J Dong and Q Zhang, " Robust adaptive fuzzy control of a class of uncertain nonlinear systems with unstable dynamics and mismatched disturbances", IEEE Transactions on Cybernetics, Vol. 48, No.11, pp. 3105-3115, Nov. 2018.

Yong Feng, Fengling Han and Xinghuo Yu, " Chattering free full-order sliding-mode control", Automatica, Vol. 50, No. 4, pp. 1310-1314, April 2014.

Jun Yang, Shihua Li, Jinya Su and Xinghuo Yu, " Continuous nonsingular terminal sliding mode control for systems with mismatched disturbances", Automatica, Vol. 49, No.7, pp. 2287-2291, July 2013.

Hongyi Li, Peng Shi, Deyin Yao and Ligang Wu, " Observer-based adaptive sliding mode control for nonlinear Markovian jump systems", Automatica, Vol. 64, pp. 133-142, Feb. 2016.

Sanjoy Mondal and Chitralekha Mahanta, " Chattering free adaptive multivariable sliding mode controller for systems with matched and mismatched uncertainty", ISA Transactions, Vol. 52, No. 3, pp. 335-341, May 2013.

Amini M., Shahbakhti M. and Hedrick J., "Easily Verifiable Adaptive Sliding Mode Controller Design with Application to Automotive Engines", SAE Technical Paper 2016-01-0629, 2016.

Xiaohui Yuan, Zhihuan Chen, Yanbin Yuan, Yuehua Huang, Xianshan Li and Wenwu Li, " Sliding mode controller of hydraulic generator regulating system based on the input/output feedback linearization method", Mathematics and Computers in Simulation, Vol. 119, pp. 18-34, January 2016.

Mohammad Reza Amini, Mahdi Shahbakhti and Selina Pan, " Adaptive Discrete Second-Order Sliding Mode Control with Application to Nonlinear Automotive Systems", Journal of Dynamic Systems, Measurements and Control, Vol. 140, No.12, pp. 1-13, 2018.

Fatma Lajmi, Achraf Jabeur Talmoudi and Hedi Dhouibi, Fault Diagnosis of Uncertain Systems Based on Interval Fuzzy PETRI Net, Studies in Informatics and Control, ISSN 1220-1766, vol. 26(2), pp. 239-248, 2017.

Boubellouta A. and Boulkroune A., "Synchronization of Incommensurate Fractional-Order Chaotic Systems with Input Nonlinearities Using a Fuzzy Variable-Structure Control", Advanced Control Engineering Methods in Electrical Engineering Systems, ICEECA 2017, Lecture Notes in Electrical Engineering, Vol 522. Springer, Cham 2019.

Amit K. Sanyal and Jan Bohm, " Finite-time stabilisation of simple mechanical systems using continuous feedback", International Journal of Control, Vol. 88, No.4, pp. 783-791, 2015.

F. Lopez-Ramirez, D. Efimov, A. Polyakov and W. Perruquetti, " On Necessary and Sufficient Conditions for Fixed-Time Stability of Continuous Autonomous Systems", IEEE European Control Conference (ECC), Limassol, Cyprus, 12-15 June 2018.

Juan Diego Sánchez-Torres, Edgar N. Sanchez and Alexander G. Loukianov, " Predefined-time stability of dynamical systems with sliding modes", IEEE American Control Conference (ACC), Chicago, IL, USA, 1-3 July 2015.

Abdalla Swikir and Vadim Utkin, " Chattering analysis of conventional and super twisting sliding mode control algorithm", IEEE 14th International Workshop on Variable Structure Systems (VSS), Nanjing, China, 1-4 June 2016.

A. Rosales, Y. Shtessel, L. Fridman and C. B. Panathula, " Chattering Analysis of HOSM Controlled Systems: Frequency Domain Approach", IEEE Transactions on Automatic Control, Vol. 62, No.8, pp. 4109 - 4115, Aug. 2017.

Salah Mobayen, Fairouz Tchier and Lakhdar Ragoub, " Design of an adaptive tracker for n-link rigid robotic manipulators based on super-twisting global nonlinear sliding mode control", International Journal of Systems Science, Vol. 48, No.9, pp. 1990-2002, 2017.

Vadim Utkin, " Discussion Aspects of High-Order Sliding Mode Control", IEEE Transactions on Automatic Control, Vol. 61, No. 3, pp. 829 – 833, March 2016.

A.Benamor, M.T.Benchouia, K. Srairi and M.E.H.Benbouzid, " A novel rooted tree optimization apply in the high order sliding mode control using super-twisting algorithm based on DTC scheme for DFIG", International Journal of Electrical Power & Energy Systems, Vol. 108, pp. 293-302, June 2019.

Shihong Ding, Jiadian Wang and Wei Xing Zheng, " Second-Order Sliding Mode Control for Nonlinear Uncertain Systems Bounded by Positive Functions", IEEE Transactions on Industrial Electronics, Vol. 62, No. 9, pp. 5899 – 5909, Sept. 2015.

Shihong Ding and Shihua Li, " Second-order sliding mode controller design subject to mismatched term", Automatica, Vol. 77, pp. 388-392, March 2017.

Shihong Ding, Wei Xing Zheng, Jinlin Sun and Jiadian Wang, " Second-Order Sliding-Mode Controller Design and Its Implementation for Buck Converters", IEEE Transactions on Industrial Informatics, Vol. 14, No. 5, pp. 1990-200, May 2018.

Antonella Ferrara and Gian Paolo Incremona, " Design of an Integral Suboptimal Second-Order Sliding Mode Controller for the Robust Motion Control of Robot Manipulators", IEEE Transactions on Control Systems Technology, Vol. 23, No. 6, pp. 2316-2325, Nov. 2015.

Alessandro Pisano, Mara Tanelli and Antonella Ferrara", witched/time-based adaptation for second-order sliding mode control", Automatica, Vol. 64, pp. 126-132, February 2016.

Herman Castañeda, Oscar S.Salas-Peña and Jesús deLeón-Morales, " Extended observer based on adaptive second order sliding mode control for a fixed wing UAV", ISA Transactions, Vol. 66, pp. 226-232, January 2017.

Al-Jodah A. and Khames L., “Second Order Sliding Mode Controller Design for Pneumatic Artificial Muscle”, Journal of Engineering, Vol. 24, No. 1, pp. 159-172. 2018.

Herman Castañeda, Franck Plestan, Abdelhamid Chriette and Jesús de León-Morales, " Continuous Differentiator Based on Adaptive Second-Order Sliding-Mode Control for a 3-DOF Helicopter", IEEE Transactions on Industrial Electronics, Vol. 63, No. 9, pp. 5786-5793, Sept. 2016.

Filiberto Muñoz, Moises Bonilla, Eduardo S. Espinoza, Iván González, Sergio Salazar and Rogelio Lozano, " Robust trajectory tracking for unmanned aircraft systems using high order sliding mode controllers-observers", IEEE International Conference on Unmanned Aircraft Systems (ICUAS), Miami, FL, USA, USA, 13-16 June 2017.

Saleh Mobayen, "Design of LMI‐based global sliding mode controller for uncertain nonlinear systems with application to Genesio's chaotic system", Complexity, Vol. 21, No. 1, pp. 94-98, Sep./Oct. 2015.

Kai Liao and Yan Xu, " A Robust Load Frequency Control Scheme for Power Systems Based on Second-Order Sliding Mode and Extended Disturbance Observer", IEEE Transactions on Industrial Informatics, Vol. 14, No. 7, pp. 3076-3086, July 2018.

Imad Matraji. Ahmed Al-Durra, Andri Haryono, Khaled Al-Wahedi and MohamedAbou-Khousa, "Trajectory tracking control of Skid-Steered Mobile Robot based on adaptive Second Order Sliding Mode Control", Control Engineering Practice, Vol. 72, pp. 167-176, March 2018.

Ananda Rao Gopisetti, B. Amarendra Reddy, K. Anusha and R. Pavon Kumar, " Performance Evaluation of Second Order Sliding Mode Control Strategies for a Coupled Tank System", IEEE International Conference on Current Trends towards Converging Technologies (ICCTCT), Coimbatore, India, 1-3 March 2018.

Pyare MohanTiwari, S.Janardhanan and Mashuqun Nabi, " Attitude control using higher order sliding mode", Aerospace Science and Technology, Vol. 54, pp.108-113, July 2016.

Madhulika Das and Chitralekha Mahanta, " Disturbance observer based optimal second order sliding mode controller for nonlinear systems with mismatched uncertainty", IEEE First International Conference on Control, Measurement and Instrumentation (CMI), Kolkata, India, 8-10 Jan. 2016.

Shihong Ding, Keqi Mei and Shihua Li, " A New Second-Order Sliding Mode and Its Application to Nonlinear Constrained Systems", IEEE Transactions on Automatic Control, Vol. 64, No. 6, pp. 2545 – 2552, June 2019.

Hongyi Li, Peng Shi and Deyin Yao, " Adaptive Sliding-Mode Control of Markov Jump Nonlinear Systems With Actuator Faults", IEEE Transactions on Automatic Control, Vol. 62, No. 4, pp. 1933-1939, April 2017.


Download data is not yet available.


How to Cite
Dhouibi, H., Ghabi, J. and Selmi, T. 2019. Adaptive and Robust Second Order Sliding Mode Controller Dedicated to Nonlinear Uncertain Pendulum Application System. European Journal of Engineering and Technology Research. 4, 12 (Dec. 2019), 20-26. DOI: