Abstract
In this paper, an adaptive backstepping-based sliding mode controller is proposed for a magnetic levitation (maglev) platform. A novel non-singular finite-time sliding surface is proposed to reduce the steady-state error. The proposed controller is tested using numerical simulation in MATLAB/Simulink, and the results are compared with an adaptive backstepping-based sliding mode controller having a conventional non-singular terminal sliding surface. Backstepping is used to derive the sliding surface, and two adaptively tuned gains are included in the controller. The control law is obtained at the final step of backstepping where a power rate reaching law is used to obtain a faster convergence. Detailed stability analysis of the entire controller, including the smaller subsystems obtained via backstepping is also presented, and conditions based on the stability criteria are derived which can be used to design the controller parameters.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
It was observed that for the same parameters of the system, increasing the value of Wc beyond 3500 results in unstable operation of the closed-loop system.
References
Adhikary, N., Mahanta, C.: Sliding mode control of position commanded robot manipulators. Control. Eng. Pract. 81, 183–198 (2018)
Blažič, S., Matko, D., Škrjanc, I.: A new leakage term in the adaptive law. IFAC Proc. Vol. 41(2), 8913–8918 (2008)
Chien, Y.H., Wang, W.Y., Leu, Y.G., Lee, T.T.: Robust adaptive controller design for a class of uncertain nonlinear systems using online t–s fuzzy-neural modeling approach. IEEE Trans. Syst. Man Cybern. Part B (Cybernetics) 41(2), 542–552 (2010)
Jin, M., Lee, J., Chang, P.H., Choi, C.: Practical nonsingular terminal sliding-mode control of robot manipulators for high-accuracy tracking control. IEEE Trans. Industr. Electron. 56(9), 3593–3601 (2009)
Krstic, M., Kokotovic, P.V., Kanellakopoulos, I.: Nonlinear and Adaptive Control Design. Wiley, New York (1995)
Lee, H.W., Kim, K.C., Lee, J.: Review of Maglev train technologies. IEEE Trans. Magn. 42(7), 1917–1925 (2006)
Ma, H., Li, Y., Xiong, Z.: Discrete-time sliding-mode control with enhanced power reaching law. IEEE Trans. Industr. Electron. 66(6), 4629–4638 (2018)
Sira-Ramírez, H., Aguilar-Orduña, M., Zurita-Bustamante, E.: On the sliding mode control of mimo nonlinear systems: an input-output approach. Int. J. Robust Nonlinear Control 29(3), 715–735 (2019)
Wai, R., Chuang, K.: Design of backstepping particle-swarm-optimisation control for maglev transportation system. IET Control Theory Appl. 4(4), 625–645 (2010)
Wai, R.J., Lee, J.D., Chuang, K.L.: Real-time pid control strategy for maglev transportation system via particle swarm optimization. IEEE Trans. Industr. Electron. 58(2), 629–646 (2010)
Zehden, A.: Electric traction apparatus. uS Patent 782,312 (1905)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Adhikary, N., Mathew, J. (2022). Adaptive Backstepping-Based Non-singular Finite-Time Sliding Mode Controller for Suspension of Maglev Platforms. In: Gu, J., Dey, R., Adhikary, N. (eds) Communication and Control for Robotic Systems. Smart Innovation, Systems and Technologies, vol 229. Springer, Singapore. https://doi.org/10.1007/978-981-16-1777-5_5
Download citation
DOI: https://doi.org/10.1007/978-981-16-1777-5_5
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-16-1776-8
Online ISBN: 978-981-16-1777-5
eBook Packages: EngineeringEngineering (R0)