Local linear dynamics assignment in IDA-PBC

Kotyczka, Paul

doi:10.1016/j.automatica.2013.01.028

Cited by 31 publications

(24 citation statements)

References 14 publications

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“…First, to prove P2.1, we take the state transformation (20), and we differentiate it with respect to time to obtain…”

Section: Proofmentioning

confidence: 99%

“…Clearly, it is also possible to use the more systematic and classical technique of evaluation of the eigenvalues of the linearized closed-loop system, but this turned out to be unnecessary. It should be mentioned that there are some advanced techniques to carry out the IDA-PBC design ensuring that the linearisation of the closed-loop dynamics has, indeed, the desired eigenvalues [20].…”

Section: Simulations Of the Perturbed System With Interconnection Andmentioning

confidence: 99%

See 1 more Smart Citation

Robust IDA-PBC for underactuated mechanical systems subject to matched disturbances

Donaire

Romero

Ortega

et al. 2016

Int. J. Robust. Nonlinear Control

110

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The problem of robustification of interconnection and damping assignment passivity-based control for underactuated mechanical system vis-à-vis matched, constant, and unknown disturbances is addressed in the paper. This is achieved adding an outer-loop controller to the interconnection and damping assignment passivity-based control. Three designs are proposed, with the first one being a simple nonlinear PI, while the second and the third ones are nonlinear PIDs. While all controllers ensure stability of the desired equilibrium in spite of the presence of the disturbances, the inclusion of the derivative term allows us to inject further damping enlarging the class of systems for which asymptotic stability is ensured. Numerical simulations of the Acrobot system and experimental results on the disk-on-disk system illustrate the performance of the proposed controller.

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“…First, to prove P2.1, we take the state transformation (20), and we differentiate it with respect to time to obtain…”

Section: Proofmentioning

confidence: 99%

Section: Simulations Of the Perturbed System With Interconnection Andmentioning

confidence: 99%

Robust IDA-PBC for underactuated mechanical systems subject to matched disturbances

Donaire

Romero

Ortega

et al. 2016

Int. J. Robust. Nonlinear Control

110

View full text Add to dashboard Cite

show abstract

“…-Compare their transient performances, for instance, investigating the flexibility to locate the eigenvalues of their tangent approximations-as done in [14] for IDA-PBC.…”

Section: Conclusion and Future Researchmentioning

confidence: 99%

Global Stabilisation of Underactuated Mechanical Systems via PID Passivity-Based Control

et al. 2017

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In this note we identify a class of underactuated mechanical systems whose desired constant equilibrium position can be globally stabilised with the ubiquitous PID controller. The class is characterised via some easily verifiable conditions on the systems inertia matrix and potential energy function, which are satisfied by many benchmark examples. The design proceeds in two main steps, first, the definition of two new passive outputs whose weighted sum defines the signal around which the PID is added. Second, the observation that it is possible to construct a Lyapunov function for the desired equilibrium via a suitable choice of the aforementioned weights and the PID gains and initial conditions. The results reported here follow the same research line as [7] and [20]-bridging the gap between the Hamiltonian and the Lagrangian formulations used, correspondingly, in these papers. Two additional improvements to our previous works are the removal of a non-robust cancellation of a potential energy term and the establishment of equilibrium attractivity under weaker assumptions.

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“…We design a passivitybased controller for the stabilization of an equilibrium ξ * ∈ Q. The controller is thereafter parametrized applying local linear dynamics assignment (LLDA), a method used to fix design parameters in nonlinear passivity based control by making use of the linearized model (Kotyczka [2013]). Using this approach, prescribed local dynamics (in terms of the closed-loop eigenvalues) can be achieved.…”

Section: Existing Workmentioning

confidence: 99%

Energy shaping for the robust stabilization of a wheeled inverted pendulum

Delgado

Kotyczka

2015

IFAC-PapersOnLine

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The paper deals with the robust energy-based stabilization of a wheeled inverted pendulum, which is an underactuated, unstable mechanical system subject to nonholonomic constraints. The equilibrium to be stabilized is characterized by the length of the driven path, the orientation, and the pitch angle. We use the method of Controlled Lagrangians which is applied in a systematic way, and is very intuitive, for it is physically motivated. After a detailed presentation of the model under nonholonomic constraints, we provide an elegant solution of the matching equations for kinetic and potential energy shaping for the considered systems. Simulations show the applicability and robustness of the method.

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Local linear dynamics assignment in IDA-PBC

Cited by 31 publications

References 14 publications

Robust IDA-PBC for underactuated mechanical systems subject to matched disturbances

Robust IDA-PBC for underactuated mechanical systems subject to matched disturbances

Global Stabilisation of Underactuated Mechanical Systems via PID Passivity-Based Control

Energy shaping for the robust stabilization of a wheeled inverted pendulum

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