•  
  •  
 

Keywords

Sliding mode controller (SMC), Conventional PID (C-PID), Finite time stability (FTS), 1-Degree of freedom (1-DOF)

Document Type

Research Paper

Abstract

In this paper, the application of Sliding Mode Control (SMC) and its integration with Finite-Time Stability (FTS) for controlling 1-degree of-freedom (DOF) system has been explored. By combining FTS with SMC, the convergence speed is significantly improved, enhancing the system's resistance to external disturbances. This paper demonstrates a detailed comparative study on the application of SMC based on FTS with a SMC, and with conventional-PID (C-PID). The SMC developed in this paper is based on a PID controller to ensure that the system's trajectory converges exponentially to zero. The results show that using SMC with FTS provides faster and more reliable system stability compared to the other two methods. The comparison also includes the utilization of different functions in the developed SMC, such as sign, tan, and saturation functions. The effects of disturbance and uncertainty have been considered as well. The results show that using SMC with FTS significantly outperforms SMC without FTS and the C-PID in all cases; the achieved Settling Time of SMC with FTS is approximately 1.5 seconds, compared to 4 seconds for the Conventional PID (C-PID) controller. This represents a 62.5% improvement in response speed. The reduction in Overshoot for the C-PID controller is around 15%, while using SMC with an FTS controller reduces the overshoot value to just 3%, indicating an 80% improvement in overshoot and demonstrating enhanced stability and performance.

References

Y. Huang, Z. Zhang‏, Neural Adaptive H∞ Sliding-Mode Control for Uncertain Nonlinear Systems with Disturbances Using Adaptive Dynamic Programming, Entropy, 25 (2023) 1-23. https://doi.org/10.3390/e25121570 S. A. Al-Samarraie, S. M. Raafat, M. K. Hamza, Event-Triggered Sliding Mode Control Versus Time-Triggered Sliding Mode Control: A Comparative Study, Iraqi J. Computers, Commn. Control & Syst. Eng., 24 (2024) 17-28. https://doi.org/10.33103/uot.ijccce.24.2.2 L. Wu, J. Liu, S. Vazquez, S.K. Mazumder, Sliding Mode Control in Power Converters and Drives: A Review, IEEE J. Autom. Syst., 22 (2021) 212-222. https://doi.org/10.1109/JAS.2021.1004380 Zinober, A.S. Variable structure and Lyapunov control; In: Lecture notes in control and information sciences, Springer, Berlin,1994. H. S. Zad, A. Ulasyar, A. Zohaib, M. Irfan, S.A. Haider, Z. Yaqoob‏, Adaptive Sliding Mode Control of DC-DC Buck Converter with Load Fluctuations for Renewable Energy Systems, Eng. Proc., 75 (2024) 1-7. https://doi.org/10.3390/engproc2024075010 S. A. Al-Samarraie, Positively Invariant Sets in Sliding Mode Control Theory with Application to Servo Actuator System with Friction, Iraqi J. Computers, Commn. Control & Syst. Eng., 10 (2010) 121-134. A. A. Uppal, M. R. Azam, J. Iqbal, Sliding Mode Control in Dynamic Systems, Electronics, 12 (2023)1-4. https://doi.org/10.3390/electronics12132970 A. Levant, Sliding Order and Sliding Accuracy in Sliding Mode Control, International Journal of Control, 58 (1993)1247-1263.https://doi.org/10.1080/00207179308923053 J.Y. Hung, W. Gao, J.C. Hung‏, Variable structure control: A survey, IEEE Trans. Ind. Electron., 40 (1993) 2–22. https://doi.org/10.1109/41.184817 V.N. Pande, U.M. Mate, S. Kurode‏, Discrete sliding mode control strategy for direct real and reactive power regulation of wind driven DFIG, Electr. Power Syst. Res., 100 (2013) 73–81. https://doi.org/10.1016/j.epsr.2013.03.001 H.N. Iordanou, B.W. Surgenor‏, Experimental evaluation of the robustness of discrete sliding mode control versus linear quadratic control, IEEE Trans. Control Syst. Technol., 5 (1997) 254– 260. https://doi.org/10.1109/87.556029 Sastry, S., Bodson, M. Adaptive control: stability, convergence and robustness; Dover Books on Electrical Engineering Series. Dover Publications, Mineola, 2011. Chen, B.M. Robust and H∞ control communication and control engineering. Springer, London, 2000. Krsti´c, M., Kanellakopoulos, I., Kokotovi´c, P.V. Nonlinear and adaptive control design; In: Communications, and control. Adaptive and learning systems for signal processing. Wiley, New York, 1995. G. Zong, Y. Wu‏, Finite time terminal sliding mode control for a class of time delay systems, in Proc. 5th World Congr. Intell. Control Autom., 2, 2004, 966–969. http://doi.org/10.1109/WCICA.2004.1340753 H. Xiao, D. Zhao, S. Gao, S.K. Spurgeon, Sliding Mode Predictive Control: A Survey, Annu. Rev. Control, 54 (2022) 148-166. http://doi.org/10.1109/JAS.2022.1004380 A. Polyakov, D. Efimov, W. Perruquetti‏,Finite-time and fixed-time stabilization: Implicit Lyapunov function approach, Automatica, 51 (2015), pp. 332–340. http://doi.org/10.1016/j.automatica.2014.10.082 Y. Feng, X. Yu, F. Han‏,On nonsingular terminal sliding-mode control of nonlinear systems, Automatica, 49 (2013) 1715–1722. http://doi.org/10.1016/j.automatica.2013.01.051 W. He, Y. Shang, Finite-time parameter observer-based sliding mode control for a DC/DC boost converter with constant power loads, Electronics, 11 (2022)1-16. http://doi.org/10.3390/electronics11050819 X. Yu, Y. Feng, Z. Man‏, Terminal sliding mode control - An overview, IEEE Open J. Ind. Electron. Soc., 2 (2021) 36-52. http://doi.org/10.1109/OJIES.2020.3040412 Bandyopadhyay, B., Janardhanan, S., Spurgeon, S. K.  Advances in Sliding Mode Control: Concept; Theory and Implementation. Springer, 2013. https://doi.org/10.1007/978-3-642-36986-5 J. A. González-Prieto, Finite Time Adaptive Smooth Non Linear Sliding Mode Control for Second Order Dynamic Systems . 2022. doi: 10.21203/rs.3.rs-1241962/v1. A. Polyakov, Nonlinear feedback design for fixed-time stabilization of linear control systems, IEEE Trans. Autom. Control, 57 (2012) 2106-2110. https://doi.org/10.1109/TAC.2011.2179869 S.P. Bhat, D.S. Bernstein, Finite-time stability of continuous autonomous systems, SIAM J. Control Optim., 38 (2000) 751-766. https://doi.org/10.1137/S0363012997321358 N. Mishra, S.P. Singh, B.C. Nakra‏, Dynamic analysis of a single link flexible manipulator using Lagrangian-assumed modes approach, in 2015 IEEE International Conference on Industrial Instrumentation and Control (IIC), 2015, 1–6. https://doi.org/10.1109/IIC.2015.7150920 M. Hu, H. Ahn, Y. Chung, K You, Speed Regulation for PMSM with Super-Twisting Sliding-Mode Controller via Disturbance Observer, Mathematics , 11 (2023)1-15. https://doi.org/10.3390/math11071618 A.H. Martinez‐Vasquez, R. Castro‐Linares,‏ Flatness-based sliding mode control for stabilizing a spherical pendulum on a quadrotor, Asian J. Control, 26 (2024) 1646-1662 . https://doi.org/10.1002/asjc.3308 Utkin, V. I., Guldner, J., and Shi, J. Sliding mode control in electro-mechanical systems;CRC press, 2009. https://doi.org/10.1201/9781420065619 I. Eker‏, Sliding mode control with PID sliding surface and experimental application to an electromechanical plant, ISA Trans., 45 (2006) 109–118. https://doi.org/10.1016/S0019-0578(07)60070-6

Highlights

A PID-based sliding surface ensures exponential convergence of the system's trajectory to zero. Combines PID precision with SMC robustness for enhanced stability against disturbances. Achieves finite-time stability, improving efficiency and responsiveness to disruptions. Integrates SMC with FTS for faster convergence, reduced errors, and smoother performance. Resists disturbances effectively, enabling rapid stabilization in unstable conditions.

DOI

10.30684/etj.2025.155004.1842

First Page

607

Last Page

630

Download

Share

COinS