Analysis and Control of Underactuated Systems

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Author Index
A B C D E F G H I
J K L M N O P Q R
S T U V W X Y Z

Semi-Global Practical Stabilization and Disturbance Adaptation for an Underactuated Ship

Authors:

Kristin Y. Pettersen, Henk Nijmeijer,

Volume: 1, Page 2144 Paper number 1872

Abstract:

We consider the problem of stabilizing the position and orientation of a ship to constant desired values, when the ship has only two independent controls and also the ship is subject to an environmental force of unknown magnitude. We propose a time-varying feedback control law and a disturbance adaptation law, and show that this provides semi-global practical asymptotic stability. The control and adaptation laws are derived using a combined integrator backstepping and averaging approach. Simulation results are presented.

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Tracking and Regulation Control of an Underactuated Surface Vessel with Nonintegrable Dynamics

Authors:

Aman Behal, Darren M. Dawson, Warren E. Dixon, Yongchun Fang,

Volume: 1, Page 2150 Paper number 1128

Abstract:

In this paper, a continuous, time-varying tracking controller is designed that globally exponentially forces the position/orientation tracking error of an underactuated surface vessel to a neighborhood about zero that can be made arbitrarily small (i.e., global uniformly ultimately bounded). The result is facilitated by fusing a filtered tracking error transformation with the design of a dynamic oscillator. We also illustrate that the proposed tracking controller yields a GUUB result for the regulation problem. In addition, an extension is provided that illustrates that the proposed unified tracking/regulation controller can be applied to a twin rotor helicopter model.

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Robust Global Stabilization Of An Underactuated Marine Vehicle On A Linear Course By Smooth Time-Invariant Feedback

Authors:

Giovanni Indiveri, Michele Aicardi, Giuseppe Casalino,

Volume: 1, Page 2156 Paper number 1071

Abstract:

Robust global stabilization of an underactuated marine vehicle on a linear course by smooth time-invariant feedback Robust global stabilization of an underactuated marine vehicle on a linear course by smooth time-invariant feedback The stabilization of an underactuated marine vehicle on a linear course is considered. In spite of being controllable, standard tools of nonlinear control as feedback linearization cannot be applied. A smooth, time invariant, globally converging control solution is designed on the basis of a simple and novel idea to derive motion control laws for underactuated systems. Robustness with respect to model parameter uncertainty and state measurement errors is discussed both analytically and through simulations.

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Cascade Normal Forms For Underactuated Mechanical Systems

Authors:

Reza Olfati-Saber,

Volume: 1, Page 2162 Paper number 1098

Abstract:

In this paper, we introduce cascade normal forms for underactuated mechanical systems that are convenient for control design. These normal forms are partially linear which results from a well-known fact that underactuated systems can be partially linearized using a change of control (due to Spong 1996). The difficulty arises when the new control appears both in the linear and nonlinear subsystems. We introduce a method for decoupling these two subsystems by applying a change of coordinates that transforms the dynamics of the system into a cascade normal form with the property that control of the overall system reduces to control of its nonlinear subsystem. Under a symmetry condition on the inertia matrix of the system, this transformation can be obtained explicitly from the Lagrangian. This eventually leads to classification of underactuated systems. We provide several applications and two detailed examples of complex underactuated systems, namely, the Acrobot and the Rotating Pendulum.

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Stabilization of a Class of Underactuated Systems

Authors:

José Alfredo Rosas Flores, Jaime Alvarez-Gallegos, Rafael Castro Linares,

Volume: 1, Page 2168 Paper number 60

Abstract:

In this paper the problem of stabilization of a class of underactuated systems by using backstepping is considered. To use the backstepping technique a suitable change of coordinates is constructed. Using backstepping a simple control law is proposed; this control law ensures the origin to be asymptotically stable. The acrobot system is used to illustrate the application of the results obtained.

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On Passivity Based Control for Partial Stabilization of Underactuated Systems

Authors:

Anton S. Shiriaev, Olga Kolesnichenko,

Volume: 1, Page 2174 Paper number 1932

Abstract:

The stabilization problem for a class of an underactuated Lagrangian systems with respect to part of state variables is considered. It is assumed that this part of the state variables is directly affected by control. Moreover, on the rest of variables we impose additional constraints, based on the form of the total energy of the system, which should be valid after the transition time. Intuitively this can be interpreted as a decoupling, by suggested control strategy, the state variables into parts. To motivate this investigation, the problem of swinging the Pendubot is considered.

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