Robust Disturbance Attenuation in Hamiltonian Systems Via Direct Digital Control

Yalçın, Yaprak; Goren-Sumer, Leyla; Kurtulan, Salman

doi:10.1002/asjc.1019

Cited by 2 publications

(8 citation statements)

References 33 publications

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“…In this section the main results of our previous studies [20,21] are summarized to exploit them in the sequel while obtaining the new results. In [20,21], it has been shown that a static feedback of the form…”

Section: Previous Resultsmentioning

confidence: 99%

“…In [21] it has been shown that the robust control problem for n-dof mechanical systems can be reduced to a disturbance attenuation problem. The port-controlled Hamiltonian formulation of the considered class of uncertain systems is …”

Section: Robust Disturbance Attenuationmentioning

confidence: 99%

“…In , it has been shown that the robust control problem for n ‐DOF mechanical systems can be reduced to a disturbance attenuation problem. The PCH formulation of the considered class of uncertain systems is

\begin{matrix} aligned \\ right [\begin{matrix} \overset{q}{true} \\ ṗ \end{matrix}] & left = MathClass-open(J - R MathClass-open(q, p MathClass-close) MathClass-close) \nabla \overset{MathClass-op̃}{H} + G_{w} MathClass-open(q MathClass-close) w_{e} MathClass-open(t MathClass-close) + G_{u} MathClass-open(q MathClass-close) u MathClass-open(t MathClass-close), & right \\ right y MathClass-open(t MathClass-close) & left = G_{w}^{T} MathClass-open(q MathClass-close) \nabla \overset{MathClass-op̃}{H}, \end{matrix}

with

G_{w} (q) MathClass-rel= ([], \begin{matrix} falsenonefalsearray \\ arraycenter 0 \\ arraycenter g_{w} MathClass-open(q MathClass-close) \end{matrix}) MathClass-punc, G_{u} (q) MathClass-rel= ([], \begin{matrix} falsenonefalsearray \\ arraycenter 0 \\ arraycenter g_{u} MathClass-open(q MathClass-close) \end{matrix}) MathClass-punc,

where

\overset{H}{true} MathClass-rel= H MathClass-bin- ΔH

\begin{matrix} leftalign \\ rightalign-odd H MathClass-open(q, p MathCl... \end{matrix}

…”

Section: Problem Formulationmentioning

confidence: 99%

“…In this study, some new results on the disturbance attenuation and robust disturbance attenuation problems for Hamiltonian systems are presented in the discrete‐time setting. In our previous publications , the discrete‐time disturbance attenuation problem and robust disturbance attenuation problem for n ‐DOF Hamiltonian systems with energy function uncertainty have been considered. This problem has been formulated for the discrete‐time Hamiltonian model of the system and sufficient conditions for the existence of the solutions of the problems have been given.…”

Section: Introductionmentioning

confidence: 99%

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Some results on disturbance attenuation for Hamiltonian systems via direct discrete‐time design

Yalçın

Goren-Sumer

Astolfi

2014

Intl J Robust & Nonlinear

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SUMMARYThe disturbance attenuation and robust disturbance attenuation problems for Hamiltonian systems in the discrete-time setting are considered and some new results are presented. The new results are derived utilizing the recently presented dissipativity equality obtained by adding the dissipation rate function to the classical dissipativity inequality. A selection of the dissipation rate function yields the new results. These results include a condition on the dissipation structure of the system to achieve the desired disturbance attenuation level and gives direct construction of optimal control laws for any desired disturbance attenuation level. The results remove the need to solve Hamilton-Jacobi-Isaacs inequalities.

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Section: Previous Resultsmentioning

confidence: 99%

Section: Robust Disturbance Attenuationmentioning

confidence: 99%

\begin{matrix} aligned \\ right [\begin{matrix} \overset{q}{true} \\ ṗ \end{matrix}] & left = MathClass-open(J - R MathClass-open(q, p MathClass-close) MathClass-close) \nabla \overset{MathClass-op̃}{H} + G_{w} MathClass-open(q MathClass-close) w_{e} MathClass-open(t MathClass-close) + G_{u} MathClass-open(q MathClass-close) u MathClass-open(t MathClass-close), & right \\ right y MathClass-open(t MathClass-close) & left = G_{w}^{T} MathClass-open(q MathClass-close) \nabla \overset{MathClass-op̃}{H}, \end{matrix}

with

G_{w} (q) MathClass-rel= ([], \begin{matrix} falsenonefalsearray \\ arraycenter 0 \\ arraycenter g_{w} MathClass-open(q MathClass-close) \end{matrix}) MathClass-punc, G_{u} (q) MathClass-rel= ([], \begin{matrix} falsenonefalsearray \\ arraycenter 0 \\ arraycenter g_{u} MathClass-open(q MathClass-close) \end{matrix}) MathClass-punc,

where

\overset{H}{true} MathClass-rel= H MathClass-bin- ΔH

\begin{matrix} leftalign \\ rightalign-odd H MathClass-open(q, p MathCl... \end{matrix}

…”

Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Some results on disturbance attenuation for Hamiltonian systems via direct discrete‐time design

Yalçın

Goren-Sumer

Astolfi

2014

Intl J Robust & Nonlinear

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“…It might be noted that the discrete time models proposed here were used in the sampled-data control of port-Hamiltonian systems in the sense of passivity-based control and disturbance attenuation in [14][15][16][17][18], respectively. It should be emphasized that [17] reported a real application where the proposed model was easily and successfully utilized.…”

Section: Introductionmentioning

confidence: 99%

Discrete-time modeling of Hamiltonian systems

Yalçın¹,

Goren-Sumer²,

Kurtulan³

2015

Turk J Elec Eng & Comp Sci

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Abstract:The problem of discrete-time modeling of the lumped-parameter Hamiltonian systems is considered for engineering applications. Hence, a novel gradient-based method is presented, exploiting the discrete gradient concept and the forward Euler discretization under the assumption of the continuous Hamiltonian model is known. It is proven that the proposed discrete-time model structure defines a symplectic difference system and has the energy-conserving property under some conditions. In order to provide alternate discrete-time models, 3 different discrete-gradient definitions are given. The proposed models are convenient for the design of sampled-data controllers. All of the models are considered for several well-known Hamiltonian systems and the simulation results are demonstrated comparatively.

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Robust Disturbance Attenuation in Hamiltonian Systems Via Direct Digital Control

Cited by 2 publications

References 33 publications

Some results on disturbance attenuation for Hamiltonian systems via direct discrete‐time design

Some results on disturbance attenuation for Hamiltonian systems via direct discrete‐time design

Discrete-time modeling of Hamiltonian systems

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