Adaptive PID-fractional-order nonsingular terminal sliding mode control for cable-driven manipulators using time-delay estimation

Abstract

This paper presents an adaptive proportional-integral-derivative fractional-order nonsingular terminal sliding mode (PID-FONTSM) control for the cable-driven manipulators using time-delay estimation (TDE). The proposed control uses TDE technique to obtain the lumped system dynamics and brings in an effective model-free structure. Then, a PID-FONTSM surface is designed to further enhance the control performance. The proposed PID-FONTSM surface uses the FONTSM error dynamic as its inner loop and utilises a PID-type surface with FONTSM variable as its outer loop. Benefitting from this structure, the proposed PID-FONTSM surface enjoys the advantages from both PID and FONTSM simultaneously. Afterwards, an adaptive algorithm is developed, to timely and precisely regulate the control gain for the robust term. The proposed control method is model-free, highly accurate and essentially continuous thanks to the TDE technique and developed PID-FONTSM surface and adaptive algorithm. The stability of the closed-loop control system under TDE and PID-FONTSM dynamics is proved using Lyapunov stability theory. Finally, comparative simulations were conducted to verify the effectiveness and superiorities of our proposed control method over the existing methods.

KEYWORDS:

• Adaptive control
• PID
• fractional-order nonsingular terminal sliding mode
• FONTSM
• PID-FONTSM
• cable-driven manipulators

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported in part by the National Key R&D Program of China under Grant 2018YFB1309202, Natural Science Foundation of Jiangsu Province (BK20170789), National Natural Science Foundation of China (51705243) and the Open Foundation of the State Key Laboratory of Fluid Power and Mechatronic Systems (GZKF-201915).

Notes on contributors

Yaoyao Wang

Yaoyao Wang (M'17) received the B.S. degree in mechanical engineering from Southeast University, Nanjing, China in 2011 and the Ph.D. degree in mechanical engineering from Zhejiang University, Hangzhou, China in 2016. He is currently an associate professor in the College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China. His current research interests include robust control and adaptive control of mechatronic systems; design and control of cable-driven systems, such as cable-driven underwater manipulators and cable-driven flying manipulators.

Jiawei Peng

Jiawei Peng received his B.S. degree in mechanical engineering from College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2019. He is currently working toward the Master degree in the College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China. His current research interests include design and control of cable-driven flying manipulators.

Kangwu Zhu

Kangwu Zhu received his B.S. degree from Harbin Institute of Technology, Harbin, China, in 2005, M.S. degree from China Ship Scientific Research Center, Wuxi, China, in 2008, and Ph.D. from Zhejiang University, Hangzhou, China, in 2012. He is currently an Associate Researcher with Shanghai Institute of Spaceflight Control Technology, Shanghai, China. His research interests include sliding mode control and nonlinear system control.

Bai Chen

Bai Chen received his B.S. and Ph.D. degrees in mechanical engineering from Zhejiang University, Hangzhou, China, in 2000 and 2005, respectively. He is currently a Professor and Ph.D. candidate supervisor at the College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China. His current research interests include design and control of surgical robots, cable-driven robots and sperm-like swimming micro robots.

Hongtao Wu

Hongtao Wu received his B.S. degree in mechanical engineering from Northeast Heavy Machinery Institute (the name was changed toYanshan University in 1997), Tsitsihar, China in 1982, M.S., and Ph.D. degrees in mechanical engineering from Tianjin University, Tianjin, China, in 1985 and 1992, respectively. He has been a Professor in Nanjing University of Aeronautics and Astronautics (NUAA) since 1998. He has presided over numbers of the national research project of China. He teaches courses of “Introduction to robotics” and “Computational multibody system dynamics” in NUAA. His research interests include multibody system dynamics, robotics, parallel mechanisms and punching machines.