Interconnection and damping assignment passivity-based control of mechanical systems with underactuation degree one

Interconnection and damping assignment passivity-based control is a new controller design methodology developed for (asymptotic) stabilization of nonlinear systems that does not rely on, sometimes unnatural and technique-driven, linearization or decoupling procedures but instead endows the closed-lo...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2005-12, Vol.50 (12), p.1936-1955
Main Authors: Acosta, J.A., Ortega, R., Astolfi, A., Mahindrakar, A.D.
Format: Article
Language:English
Subjects:
Aircraft
Applied sciences
Asymptotic properties
Carts
Computer science
control theory
systems
Control system synthesis
Control systems
Control theory. Systems
Damping
Design methodology
Energy shaping
Exact sciences and technology
Hamiltonian systems
Interconnection
Lyapunov method
Mechanical systems
Modelling and identification
nonlinear control
Nonlinear control systems
Nonlinear systems
Partial differential equations
passivity
Pendulums
Robustness
Studies
underactuated mechanical systems
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Summary:Interconnection and damping assignment passivity-based control is a new controller design methodology developed for (asymptotic) stabilization of nonlinear systems that does not rely on, sometimes unnatural and technique-driven, linearization or decoupling procedures but instead endows the closed-loop system with a Hamiltonian structure with a desired energy function-that qualifies as Lyapunov function for the desired equilibrium. The assignable energy functions are characterized by a set of partial differential equations that must be solved to determine the control law. We prove in this paper that for a class of mechanical systems with underactuation degree one the partial differential equations can be explicitly solved. Furthermore, we introduce a suitable parametrization of assignable energy functions that provides the designer with a handle to address transient performance and robustness issues. Finally, we develop a speed estimator that allows the implementation of position-feedback controllers. The new result is applied to obtain an (almost) globally stabilizing scheme for the vertical takeoff and landing aircraft with strong input coupling, and a controller for the pendulum in a cart that can swing-up the pendulum from any position in the upper half plane and stop the cart at any desired location. In both cases we obtain very simple and intuitive position-feedback solutions.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2005.860292