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A unified symplectic pseudospectral method for motion planning and tracking control of 3D underactuated overhead cranes
Author(s) -
Wang Xinwei,
Liu Jie,
Zhang Yong,
Shi Boyang,
Jiang Dianheng,
Peng Haijun
Publication year - 2019
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4488
Subject(s) - pseudospectral optimal control , control theory (sociology) , trajectory , overhead crane , controller (irrigation) , underactuation , computer science , overhead (engineering) , optimal control , symplectic geometry , pseudo spectral method , mathematical optimization , mathematics , control (management) , engineering , artificial intelligence , mathematical analysis , fourier analysis , agronomy , physics , structural engineering , fourier transform , astronomy , pure mathematics , biology , operating system
Summary In this paper, a unified symplectic pseudospectral method for motion planning and tracking control of 3D underactuated overhead cranes is proposed. A feasible reference trajectory taking constraints into consideration is first generated offline by the symplectic pseudospectral optimal control method. Then, a trajectory tracking model predictive controller also based on the symplectic pseudospectral method is developed to track the reference trajectory. At each sampling instant, the trajectory tracking controller works by solving an open‐loop optimal control problem where linearized system dynamics is used instead to improve the computational efficiency. Since the symplectic pseudospectral optimal control method is the core algorithm for both offline trajectory planning and online trajectory tracking, constraints on state variables and control inputs can be easily imposed and hence theoretically guaranteed in solutions. By selecting proper weighted matrices on tracking error and control, the developed controller could achieve control objectives in both accurate trolley positioning and fast suppressing of residual swing angles. Simulations for 3D overhead crane systems in the presence of perturbations in initial conditions, an abrupt variation of system parameter, and various external disturbances demonstrate that the developed controller is robust and of excellent control performance.