An Adaptive Controller Based on Interconnection and Damping Assignment Passivity-Based Control for Underactuated Mechanical Systems: Application to the Ball and Beam System
Xiaoping Liu,
Huaizhi Shao,
Cungen Liu,
Ning Li,
Xinpeng Guo,
Fei Zheng,
Lijun Sun
Affiliations
Xiaoping Liu
Faculty of Engineering, Lakehead University, Thunder Bay, ON P7B 5E1, Canada
Huaizhi Shao
School of Information and Electrical Engineering, Shandong Jianzhu University, Jinan 250101, China
Cungen Liu
School of Information and Electrical Engineering, Shandong Jianzhu University, Jinan 250101, China
Ning Li
School of Information and Electrical Engineering, Shandong Jianzhu University, Jinan 250101, China
Xinpeng Guo
Shandong Telian Information Technology Co., Ltd., Jinan 250101, China
Fei Zheng
Shandong Marvelous Intelligent Technology Co., Ltd., Jinan 250000, China
Lijun Sun
College of Information Science and Engineering, Henan University of Technology, Zhengzhou 450001, China
In this paper, an adaptive technology and the interconnection and damping assignment passivity-based control method are combined to solve the stabilization problem for underactuated mechanical systems with uncertainties (including matched and unmatched). These uncertainties include unknown friction coefficients and unknown terms in kinetic energy and potential energy. A novel adaptive interconnection and damping assignment passivity-based control scheme is proposed and an adaptive stabilization controller is designed to make the closed-loop system locally stable. Verification is conducted on the ball and beam system. The locally asymptotic stability is demonstrated using the LaSalle’s invariance principle and approximate linearization. The effectiveness of the proposed control law is verified through numerical simulations.
