Proceedings ArticleDOI
The method of controlled Lagrangians: Energy plus force shaping
Dong Eui Chang
- pp 3329-3334
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Various easily verifiable criteria for stabilizability by this method of controlled Lagrangians are given and they are illustrated with examples.Abstract:
We present our recent results on the method of controlled Lagrangians in order to stabilize mechanical systems by shaping both energy and external forces. Various easily verifiable criteria for stabilizability by this method are given and they are illustrated with examples. Our results incorporate and extend those in the literature.read more
Citations
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Proceedings ArticleDOI
Generalization of the IDA-PBC method for stabilization of mechanical systems
TL;DR: In this paper, the authors generalize and strengthen the method of Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) for the stabilization of mechanical systems, and derive a new set of matching conditions where the new kinetic matching conditions are simpler than those in the literature.
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Control via interconnection and damping assignment of linear time-invariant systems: a tutorial
TL;DR: The purpose of this article is to present the results of interconnection and damping assignment in a tutorial, self-contained form – invoking only basic linear algebra methods.
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Tracking controller design methodology for passive port-controlled Hamiltonians with application to type-2 STATCOM systems
TL;DR: A dynamic extension of the STATCOM system is made to conveniently design a reference output and then put the dynamics into the form of port-controlled Hamiltonian to apply the proposed tracking controller.
Journal ArticleDOI
Pseudo‐energy shaping for the stabilization of a class of second‐order systems
TL;DR: In this article, a pseudo-energy shaping method was proposed for a class of second-order systems that includes mechanical systems and matching conditions were derived for the construction of an energy-like Lyapunov function that shall be called a pseudo energy function.
Proceedings ArticleDOI
Gyroscopic forces for mechanical manipulators
TL;DR: Several ways to parameterize the artificial gyroscopic force with respect to the desired path profile of the end-effector as well as the desired velocity field that is often used as an indirect way to specify the target path are presented.
References
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Book
Nonholonomic mechanics and control
TL;DR: In this paper, the authors propose energy-based methods for stabilizing nonholonomic systems using non-holonomic control theory based on geometric properties of the system's properties. But they do not discuss the energy-independent methods of stabilisation.
Journal ArticleDOI
Controlled Lagrangians and the stabilization of mechanical systems. I. The first matching theorem
TL;DR: In this article, a method for the stabilization of mechanical systems with symmetry based on the technique of controlled Lagrangians was developed, which involves making structured modifications to the Lagrangian for the uncontrolled system, thereby constructing the controlled Lagranian.
Journal ArticleDOI
Controlled Lagrangians and the stabilization of mechanical systems. II. Potential shaping
TL;DR: The method of controlled Lagrangians is extended to include potential shaping, which achieves complete state-space asymptotic stabilization of mechanical systems and extends the method to include a class of mechanical system without symmetry such as the inverted pendulum on a cart that travels along an incline.
Journal ArticleDOI
Stabilization of rigid body dynamics by internal and external torques
TL;DR: It is shown that with external torques, the equations for the rigid body with momentum wheels are Hamiltonian with respect to a Lie-Poisson bracket structure and these equations are shown to generalize the dual-spin equations.
Journal ArticleDOI
The equivalence of controlled lagrangian and controlled hamiltonian systems
TL;DR: In this article, the equivalence of controlled Lagrangians and their Hamiltonian counterpart was shown under general hypotheses, where almost Poisson structures (Poisson brackets that may fail to satisfy the Jacobi identity) on the Hamiltonian side were used.
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