Optimized Adaptive Combined Hierarchical Sliding Mode Controller Design for a Class of Uncertain Under-actuated Time-Varying Systems

Document Type : Original Article

Authors

Department of Electrical and Computer Engineering, University of Kashan, Kashan, Iran.

Abstract

This paper proposes an optimized adaptive combined hierarchical sliding mode controller (ACHSMC) for a class of under-actuated time-varying systems in presence of uncertainties and noise. For this purpose, the un-modeled dynamics and friction force are modeled as additive and multiplicative uncertainties, respectively. A combined hierarchical sliding mode controller (CHSMC) is designed using two layers of sliding manifolds. Then, the controller is adapted by considering a time-varying coefficient of the second layer sliding manifold of CHSMC system. The stability of this controller is approved by Lyapunov theorem. Finally, this method is performed on an under-actuated crane model that has two subsystems: trolley and payload can be controlled by a single input signal and the first layer sliding manifold parameter of ACHSMC is optimized by genetic algorithm (GA) to save energy of input signal. The simulation results show the stability and robust performance of the proposed controller against input noise and additive and multiplicative uncertainties and time varying parameters of the system compared to CHSMC method.

Keywords

References

[1] N. Sun, Y. Fang, H. Chen, B. Lu, "Amplitude-saturated nonlinear output feedback anti-swing control for under-actuated cranes with double-pendulum cargo dynamics", IEEE transactions on Industrial Electronics, vol. 64, pp. 2135-2146, 2017.
[2] C. Yang, Z. Li, R. Cui, B. Xu, "Neural network-based motion control of under-actuated wheeled inverted pendulum models", IEEE Trasactions on Neural Networks and Learning Systems, vol. 25, pp. 2004-2016, 2014.
[3] Z. Wang, Y. Guo, "Unified control for pendubot at four equilibrium points", IET Control Theory and Applications, vol. 5, no. 1, pp. 155-163, 2011.
[4] C. Yang, Z. Li, J. Li, "Trajectory planning and optimized adaptive for a class of wheeled inverted pendulum vehicle models", IEEE Transactions on Cybernetics, vol. 43, pp. 24-36, 2013.
[5] X. Lai, P. Zhang, Y. Wang, M. Wu, "Position-posture control of a planar four-link under-actuated manipular based on genetic algorithm", IEEE Transactions on Industrial Electronics, vol. 64, pp. 4781-4791, 2017.
[6] X. Huang, A.L. Ralescu, H. Gao, H. Huang, "A survey on the application of fuzzy systems for under-actuated systems", Journal of Systems and Control Engineering, 2018. 
[7] Y. Zhao, H. Gao, "Fuzzy-Model-Based Control of an Overhead Crane With Input Delay and Actuator Saturation", IEEE Transactions on Fuzzy Systems, vol. 20, no. 1, p. 181-186, 2012.
[8] C.Y. Chang, T.C. Chiang, "Overhead cranes fuzzy control design with dead-zone compensation", Neural Computing and Applications, vol. 18, no. 7, pp. 749-757, 2009.
[9] M.I. Solihin, Wahyudi, A. Legowo, "Fuzzy-tuned PID anti-swing control of automatic gantry crane", Journal of Vibration and Control, vol. 16, no. 1, pp. 127-145, 2010.
[10] J.J.E. Slotin and W. Li, "Applied Nonlinear Control", New Jercy, 1991.
[11]V. Utkin, J. Guldner and J. Shi, "Sliding Mode Control in Electromechanical Systems", 1991.
[12] R. Xu, Ü. Özgüner, "Sliding mode control of a class of under-actuated systems," Automatica, vol. 44, no. 1, pp. 233-241, 2009.
[13] Y. Shtessel, Ch. Edwards, L. Fridman, A. Levant, "Sliding Mode Control and Observation", New York, 2014.
[14] C. Vázquez, L. Fridman, J. Collado, I. Castillo, "Second-Order Sliding Mode Control of a Perturbed-Crane", Journal of Dynamic Systems, Measurement, and Control, vol. 137(8), 2015.
[15] M. Shahravi, M. Azimi, "A Hybrid Scheme of Synthesized Sliding Mode/Strain Rate Feedback Control Design for Flexible Spacecraft Attitude Maneuver Using Time Scale Decomposition", Int. J. Structural Stability and Dynamics, vol. 16, p. 1450101, 2016.
[16] J. Fei, H. Wang, "Recurrent Neural Network Fractional-order Sliding Mode Control of Dynamic Systems", J. the Franklin Institute, pp. 1-20, 2020.
[17] B. Hashtarkhani, M.J. Khosrowjerdi, "Adaptive actuator failure compensation for uncertain nonlinear fractional order strict feedback form systems", Trans. of the Institute of Measurement and Control, vol. 41, no. 4, pp. 1032-1044, 2019.
[18] J. Fei, C. Lu, "Adaptive Fractional Order Sliding Mode Controller with Neural Estimator", Journal of the Franklin Institute-engineering and Applied Mathematics, vol. 355, no. 5, pp. 2369-2391, 2019.
[19] T.Y. Lee, P.C. Chen, D.S. Juang, "Sliding mode control on isolated bridges with columns of irregular heights using pole assignment and PSO-SA hybrid algorithm", Int. J. Structural Stability and Dynamics, vol. 12, no. 3, pp. 1250014, 2012.
[20] A. Barou, Z. Rahmani, S. Minagar, " Designing an Adaptive Continuous Terminal Sliding Mode Controller for a class of nonlinear systems in presence of perturbation", Tabriz Journal of Electrical Engineering, vol. 50, no. 1, pp. 9-17, spring 2020.
[21] D. Qian, J. Yi, "Hierarchical Sliding Mode Control for Under-actuated Cranes", 2016.
[22] S.Y. Shin, J.J. Lee, "Fuzzy sliding mode control for an under-actuated system with mismatched uncertainties", Artificial Life and Robotics, vol. 15, no. 3, pp. 355–358, 2010.
[23] H. Mazinan, A.H. Ebrahimi Mollabashi, "Incremental SMC-based CNF control strategy considering magnetic ball suspension and inverted pendulum systems through cuckoo search-genetic optimization algorithm", Complex & Intelligent Systems, vol. 5, pp. 353–362, 2019.
[24] S. Choi, D. Park, S. Jayasuriy, "A time-varying sliding surface for fast and robust tracking control of second-order uncertain systems", Automatica, vol. 30, no. 5, pp. 899–904, 1994.
[25] M. Khashei Varnamkhasti, Kh. Shojaei Arani, "Tracking control of quadrotor by using Adaptive Sliding Mode Control based on Chebyshev Neural Networks", Tabriz Journal of Electrical Engineering, vol. 49, no. 4, pp. 1591-1601, winter 2019.
[26] C.C. Chiang and Y.C. Chen, "Adaptive Model Reference Hierarchical Sliding Mode Control of Uncertain Underactuated System with Time Delay and Dead-Zone Input", Int. J. Control Science and Eng., vol. 9, no. 1, pp. 15-25, 2019.
[27] D. Qian, X. Liu, J. Yi, "Adaptive Control Based on Incremental Hierarchical Sliding Mode for Overhead Crane Systems", Applied Mathematics & Information Sciences, vol. 7, no. 4, pp. 1359-1364, 2013.
[28] Y. Zou, "Nonlinear robust adaptive hierarchical sliding mode control approach for quadrotor", Int. J. of Robust Nonlinear Control, 2016.

Files

Share

How to cite

Statistics