Discrete-time modeling of Hamiltonian systems

Yaprak YALÇIN; Leyla Gören SÜMER; Salman KURTULAN

Article Details

Discrete-time modeling of Hamiltonian systems

Authors:

Yaprak YALÇIN | Leyla Gören SÜMER | Salman KURTULAN

Publisher:

TUBITAK

Journal:

Turkish Journal of Electrical Engineering and Computer Science 2015 Vol.23 Issue 1, pp.149-170

Document Type:

Article

Publication Date:

3/2015

Document Language:

Turkish

Document ID (Org No.):

2000742745

Frequency:

Bimonthly

eISSN:

1303-6203

pISSN:

1300-0632

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.

 

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.

Article Details

Discrete-time modeling of Hamiltonian systems

Authors: Yaprak YALÇIN | Leyla Gören SÜMER | Salman KURTULAN

Publisher: TUBITAK

Journal: Turkish Journal of Electrical Engineering and Computer Science 2015 Vol.23 Issue 1, pp.149-170

Document Type: Article

Publication Date: 3/2015

Document Language: Turkish

Document ID (Org No.): 2000742745

Frequency: Bimonthly

eISSN: 1303-6203

pISSN: 1300-0632

Issues

Authors:

Yaprak YALÇIN | Leyla Gören SÜMER | Salman KURTULAN

Publisher:

TUBITAK

Journal:

Turkish Journal of Electrical Engineering and Computer Science 2015 Vol.23 Issue 1, pp.149-170

Document Type:

Article

Publication Date:

3/2015

Document Language:

Turkish

Document ID (Org No.):

2000742745

Frequency:

Bimonthly

eISSN:

1303-6203

pISSN:

1300-0632