Augmented Hamiltonian Formulation and Energy-Based Control Design of Uncertain Mechanical Systems

• Published in: IEEE transactions on control systems technology 2008-03, Vol.16 (2), p.202-213
• Main Authors: YUZHEN WANG, GE, Shuzhi Sam
• Format: Article
• Language: English
• Subjects: Adaptative systems; Adaptive control; Applied sciences; Attenuation; Augmented Hamiltonian formulation; Computer science; control theory; systems; Control design; Control system synthesis; Control systems; Control theory. Systems; Derivatives; Differential algebraic equations; Disturbances; energy-based robust adaptive control; Exact sciences and technology; Formulations; Fundamental areas of phenomenology (including applications); Materials handling; Mathematical analysis; Mechanical systems; Operators; Partial differential equations; Physics; Potential energy; potential energy shaping; pre-feedback; Programmable control; Robust control; Solid dynamics (ballistics, collision, multibody system, stabilization...); Solid mechanics; Studies; uncertain mechanical system; unified partial derivative operator (UPDO)
• ISSN: 1063-6536; 1558-0865
• DOI: 10.1109/TCST.2007.903367

This paper mainly investigates augmented Hamiltonian formulation for both fully actuated and underactuated uncertain mechanical systems. First, a high-order partial derivative operator, called the unified partial derivative operator (UPDO), is given, and its properties are investigated, which plays a very important role in presenting the main results of this paper. Secondly, using the tool UPDO, the idea of shaping potential energy, and the pre-feedback technique, an augmented Hamiltonian structure with dissipation is provided for both fully actuated and underactuated uncertain mechanical systems. It is shown that the augmented Hamiltonian formulation has some nice properties for further analysis and control, and at the same time, its matching condition in the underactuated case becomes a set of algebraic equations, which are much easier to solve in comparison with solving a set of partial differential equations. Finally, as an application, the energy-based robust adaptive control is studied by using the augmented Hamiltonian formulation, and a new energy-based adaptive L 2 disturbance attenuation controller is designed for the uncertain mechanical systems. Study of an illustrative example with simulations shows that the controller obtained in this paper works very well in handling disturbances and uncertainties in the systems.