Partially saturated coupled-dissipation control for underactuated overhead cranes

• Published in: Mechanical systems and signal processing Vol. 136; p. 106449
• Main Authors: Zhang, Shengzeng, He, Xiongxiong, Zhu, Haiyue, Chen, Qiang, Feng, Yuanjing
• Format: Journal Article
• Language: English
• Published: Berlin Elsevier Ltd 01.02.2020; Elsevier BV
• Subjects: Control stability; Controllers; Cranes; Damping; Energy dissipation; Energy shaping; Energy storage; Mathematical analysis; Matrix methods; Nonlinear control; Overhead cranes; Partial saturation; Passivity; Stability analysis; Underactuated mechanical systems; Overhead cranes; Energy shaping; Passivity; Partial saturation; Underactuated mechanical systems; Nonlinear control
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2019.106449

•Different from most energy shaping methods modifying only the inertia matrix and the potential energy function, the assignable storage function in this work is especially quadratic in a new error vector.•A new coupled-dissipation signal is introduced to guarantee enhanced performance. Furthermore, owing to the elaborate structure of the coupled-dissipation term, the proposed controller can be always active in case of different cable lengths.•The proposed controller is extended by a smooth saturated function so that the initial control effort ensures an upper bound when given zero initial conditions, thus leading to a soft trolley start. This paper proposes a partially saturated nonlinear controller for underactuated overhead cranes based on passivity. The main contribution is that the total energy shaping method yields an assignable storage function which is characterized by a desired damping matrix and especially quadratic in a new error vector of the coupling form. Consequently, a partially saturated nonlinear controller enforcing the coupled-dissipation inequality is derived to introduce additional damping terms to the sway angle, thus guaranteeing favorable transit performance. Owing to the elaborate structure of the coupled-dissipation term, the control system can achieve significant oscillation reduction over a wide range of cable lengths and transportation distances without readjusting the control gains. Besides the Lyapunov theory, LaSalle’s invariance principle is carried illustrating the corresponding stability. The proposed controller is evaluated through both simulation and experimental results that demonstrate the improved performance and robustness.