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Volume 10
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10.3390/app10051728
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Article

Adaptive Sliding Mode PID Control for Underwater Manipulator Based on Legendre Polynomial Function Approximation and Its Experimental Evaluation

by
Chao Yang
1,2,*,
Feng Yao
1,
Mingjun Zhang
1,
Zhiqiang Zhang
2,
Zhenzhen Wu
3 and
Peijian Dan
2
1
College of Mechanical and Electrical Engineering, Harbin Engineering University, Nangang District, Harbin 150001, China
2
Institute of Materials, China Academy of Engineering Physics, Huafeng Village, Jiangyou, Mianyang 621907, Sichuan, China
3
Finance & Trade, Chongqing Vocational Institute of Engineering, Jiangjin 402260, Chongqing, China
*
Author to whom correspondence should be addressed.
Appl. Sci. 2020, 10(5), 1728; https://doi.org/10.3390/app10051728
Submission received: 4 February 2020 / Revised: 22 February 2020 / Accepted: 27 February 2020 / Published: 3 March 2020
(This article belongs to the Special Issue Applications of Intelligent Control Methods in Mechatronic Systems)
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Abstract

The joint control problem of the underwater manipulator is addressed in this paper, under the influence of uncertainty factors such as model uncertainty, external disturbance, and manipulator joint lag. In general, for the uncertainty factors, it is usually approximated online, but it is difficult to select a reasonable value for the approximation error boundary, too conservative estimated values would cause chattering problem easily. And the influence of joint lag on the manipulator control should be considered in actual work. Unlike most previous control method, in this paper, the function approximation technique (FAT), which uses the Legendre polynomial, is adopted to approximate the uncertainty factors online. Then, based on the proportion integral differential (PID) sliding manifold with the integral and differential of tracking error, a sliding model PID controller is designed to speed up the response and reduce the effects of joint lag. For the error boundary, the adaptive law is proposed, and it will reduce chattering of the control quantity under the steady state of the system. It was proved that the joint error of the control system is uniformly asymptotic convergence through the stability analysis. Finally, the effectiveness of the proposed approach is demonstrated with pool comparison experiments of the underwater manipulator installed in the autonomous underwater vehicles (AUVs).
Keywords: underwater manipulator; sliding mode control; function approximation technique; joint lag; error boundary; uncertainty estimation underwater manipulator; sliding mode control; function approximation technique; joint lag; error boundary; uncertainty estimation

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MDPI and ACS Style

Yang, C.; Yao, F.; Zhang, M.; Zhang, Z.; Wu, Z.; Dan, P. Adaptive Sliding Mode PID Control for Underwater Manipulator Based on Legendre Polynomial Function Approximation and Its Experimental Evaluation. Appl. Sci. 2020, 10, 1728. https://doi.org/10.3390/app10051728

AMA Style

Yang C, Yao F, Zhang M, Zhang Z, Wu Z, Dan P. Adaptive Sliding Mode PID Control for Underwater Manipulator Based on Legendre Polynomial Function Approximation and Its Experimental Evaluation. Applied Sciences. 2020; 10(5):1728. https://doi.org/10.3390/app10051728

Chicago/Turabian Style

Yang, Chao, Feng Yao, Mingjun Zhang, Zhiqiang Zhang, Zhenzhen Wu, and Peijian Dan. 2020. "Adaptive Sliding Mode PID Control for Underwater Manipulator Based on Legendre Polynomial Function Approximation and Its Experimental Evaluation" Applied Sciences 10, no. 5: 1728. https://doi.org/10.3390/app10051728

APA Style

Yang, C., Yao, F., Zhang, M., Zhang, Z., Wu, Z., & Dan, P. (2020). Adaptive Sliding Mode PID Control for Underwater Manipulator Based on Legendre Polynomial Function Approximation and Its Experimental Evaluation. Applied Sciences, 10(5), 1728. https://doi.org/10.3390/app10051728

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