Tham khảo tài liệu 'advanced strategies for robot manipulators part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 12 On Nonlinear Control Perspectives of a Challenging Benchmark Guangyu Liu and Yanxin Zhang The University of Auckland New Zealand 1. Introduction Dynamical systems are often nonlinear in nature. It motives people to explore various theoretical nonlinear analysis and control design tools of which constructive nonlinear design methods are the most celebrated ones. However applying a constructive tool faces up a big hurdle that the tool deals only with a certain dynamical structure often not possessed by the natural dynamics. Nonlinear constructive control designs heavily relies on the identification of a particular structure via coordinate transformation and control transformation. To be realistic these theoretical tools are not general to all of the nonlinear systems. Here a challenging benchmark example-a four degrees of freedom inverted pendulum under the influence of a planar force-is considered that is nonlinear multiple input and multiple output underactuated and unstable. The benchmark is also of practical interests because it is an abstract of several applications. Three challenging control objectives are envisaged for the first time in the literature in order to how to apply various cuttingedge theoretical nonlinear control tools. In fact the key step of all of the nonlinear designs is to identify spectral structures- certain normal forms. From this aspect a sequence of preliminary designs will accompany the existing tools to construct nonlinear controllers which is quite different from the linear control designs. 2. The benchmark problem Modeling The spherical inverted pendulum is subject to a holonomic constraint on the vertical direction and its self-spin about the principal axis along the pole is neglected from the context. As a result the benchmark has only four degrees of freedom described by a set of generalized coordinates q e ỈÀ that include two translational ones also called external variables and two angular ones also called shape variables
