Adaptive Interconnection and Damping Assignment Passivity Based Control for Underactuated Mechanical Systems
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ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555
Adaptive Interconnection and Damping Assignment Passivity Based Control for Underactuated Mechanical Systems Mutaz Ryalat*, Dina Shona Laila, and Hisham ElMoaqet Abstract: In this paper, we present two adaptive control approaches to handle uncertainties caused by parametric and modeling errors in a class of nonlinear systems with uncertainties. The methods use the Port-controlled Hamiltonian (PCH) modelling framework and the interconnection and damping assignment passivity-based control (IDA-PBC) control design methodology being the most effectively applicable method to such models. The methods explore an extension on the classical IDA-PBC by adopting the state-transformation, yielding a dynamic state-feedback controller that asymptotically stabilizes a class of underactuated mechanical systems and preserves the PCH structure of the augmented closed-loop system. The results are applied to the underactuated mechanical systems that are a class of mechanical systems with broad applications and are more interesting as well as challenging control problems within this context. The results are illustrated with numerical simulations applied to two underactuated robotic systems; the Acrobot and non-prehensile planar rolling robotic (disk-on-disk) systems. Keywords: Adaptive control, Hamiltonian systems, passivity-based control, underactuated mechanical systems.
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INTRODUCTION
An important issue in the field of nonlinear control is the control of systems with uncertainties. The behavior of the control systems can be influenced by some externally acting signals (disturbances, noises, etc.) and model uncertainties which can be clearly noticed in the implementation phase. The control of nonlinear systems with uncertainties is traditionally approached as a robust or an adaptive control problem. Adaptive control has been proved to be a very useful method for controlling uncertain nonlinear systems. Most adaptive methods proposed in literature have adopted Lyapunov functions for the design and analysis of the control systems [1–4]. Recently, new results that adopted the two classical tools of nonlinear regulator theory and geometric nonlinear control (system) immersion and (manifold) invariance (I&I) have been developed in [5, 6]. In [7] passivity-based control (PBC) approaches have been proposed for systems with Lagrangian and Hamiltonian structures. Adaptive control has also attracted the attention of the robotics research communities. Composite learning robot control with guaranteed parameter convergence has been proposed in [8] for serial-link robots. Without considering a stringent condition called persistent excitation, the method achieves fast parameter convergence using a com-
posite adaptation law. As for mobile robots, the work in [9] has proposed an adaptive controller for the stabilization and tracking problem of a nonholonomic mobile robot with input saturation and disturbance. Port-controlled Hamiltonian (PCH) model, together with Euler-Lagrange model
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