Journal ArticleDOI
On the matching equations of energy shaping controllers for mechanical systems
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This paper proves that the claim that considering a more general form for the target dynamic forces that relax the skew-symmetry condition further reduces the number of KE PDEs is wrong.Abstract:
Total energy shaping is a controller design methodology that achieves (asymptotic) stabilisation of mechanical systems endowing the closed-loop system with a Lagrangian or Hamiltonian structure with a desired energy function. The success of the method relies on the possibility of solving two partial differential equations (PDEs) which identify the kinetic and potential energy functions that can be assigned to the closed loop. Particularly troublesome is the PDE associated to the kinetic energy (KE) which is quasi-linear and non-homogeneous, and the solution that defines the desired inertia matrix must be positive definite. This task is simplified by the inclusion of gyroscopic forces in the target dynamics, which translates into the presence of a free skew-symmetric matrix in the KE matching equation that reduces the number of PDEs to be solved. Recently, it has been claimed that considering a more general form for the target dynamic forces that relax the skew-symmetry condition further reduces the number...read more
Citations
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L2 Gain And Passivity Techniques In Nonlinear Control
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Journal ArticleDOI
Simultaneous interconnection and damping assignment passivity-based control of mechanical systems using dissipative forces
TL;DR: Two modifications to the standard IDA-PBC method are presented, it is proposed to avoid the splitting of the control action into energy-shaping and damping injection terms, but instead to carry them out simultaneously and to consider the inclusion of dissipative forces.
Book ChapterDOI
Passivity-Based Control of Mechanical Systems
TL;DR: In this article, the authors briefly recall the history of PBC of mechanical systems and summarize its main recent developments, including an explicit formula for one of the free tuning gains that simplifies the computations, addition of PID controllers to robustify and make constructive the PBC design and to track ramp references.
Journal ArticleDOI
IDA-PBC with adaptive friction compensation for underactuated mechanical systems
TL;DR: A new interconnection-and-damping-assignment passivity-based-control (IDA-PBC) design is presented, which includes the adaptive estimation of the friction forces and the introduction of a nonlinear dissipative term in the closed-loop system dynamics.
References
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Book
L2-Gain and Passivity Techniques in Nonlinear Control
TL;DR: In this article, a small gain and passivity of input-output maps are discussed. But the authors focus on the Hamiltonian system as passive systems and do not consider the Hamilton-Jacobi Inequalities.
Journal ArticleDOI
A new feedback method for dynamic control of manipulators
Morikazu Takegaki,Suguru Arimoto +1 more
TL;DR: A new approach to the dynamic control of manipulators is developed from the viewpoint of mechanics and it is shown that a linear feedback of generalized coordinates and their derivatives are effective for motion control in the large.
Journal ArticleDOI
Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment
TL;DR: This work describes a class of systems for which IDA-PBC yields a smooth asymptotically stabilizing controller with a guaranteed domain of attraction, given in terms of solvability of certain partial differential equations.
L2 Gain And Passivity Techniques In Nonlinear Control
TL;DR: L2 gain and passivity techniques in nonlinear control is downloaded for free to help people who are facing with some harmful virus inside their desktop computer.
Book
Nonlinear and adaptive control with applications
TL;DR: In this article, the authors provide a detailed treatment of the design of robust adaptive controllers for nonlinear systems with uncertainties, based on the ideas of system immersion and manifold invariance.