期刊
NONLINEAR DYNAMICS
卷 89, 期 3, 页码 2241-2253出版社
SPRINGER
DOI: 10.1007/s11071-017-3582-2
关键词
Nonlinear control; Underactuated mechanical system; Torque-coupled relationship; Passivity; Cascade-connected system
资金
- National Natural Science Foundation of China [61304023, 61374106]
- Applied Mathematics Enhancement Program of Linyi University
An underactuated mechanical system with n (n >= 3) degree of freedoms (DOFs) is a complicated nonlinear system. This paper develops a new strategy to solve the nonlinear stabilizing control problem for this kind of mechanical systems. First, we introduce a coupled relationship between control torques. It changes the n-DOF underactuated system into a cascade-connected system, which has a 2-DOF driven subsystem and a (n-2)-DOF stable driving subsystem. And then, we analyze the passivity of the driven subsystem and discuss how to design an passivity-based controller that stabilizes the driven subsystem at the origin. Finally, the stabilization of the n-DOF underactuated system is achieved by the triangle lemma. Our proposed strategy transforms the stabilization of the n-DOF underactuated system into that of the 2-DOF driven subsystem. This makes the structure of the control system simple and also makes the problem of stabilizing a multi-DOF underactuated system easy to handle. As an application of the strategy, we give detailed statements of using it to achieve the global stabilization of a 3-DOF underactuated mechanical system called spring-coupled horizontal three-link underactuated manipulator. Simulation results demonstrate its validity.
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