A bond graph model of a singularly perturbed LTI MIMO system with a slow state estimated feedback

González-A, Gilberto

doi:10.1177/0959651816655038

Cited by 6 publications

(7 citation statements)

References 23 publications

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“…Hence, the reduced models for the different dynamics of three timescale systems can be obtained. A direct and interesting result to get the quasi-steady-state model in a bond graph approach is proposed in [24,26,27]. However, these published results have been extended for three timescale systems in this paper.…”

Section: Reduced Models In the Physical Domainmentioning

confidence: 99%

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Quasi‐Steady‐State Models of Three Timescale Systems: A Bond Graph Approach

Gonzalez

Barrera

Ayala

et al. 2019

Mathematical Problems in Engineering

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Modelling in bond graph to obtain reduced models of systems with singular perturbations is applied. This singularly perturbed system is characterized by having three timescales, i.e., slow, medium, and fast dynamics. From a bond graph whose storage elements have an integral causality assignment (BGI), the mathematical model of the complete system can be determined. By assigning a derivative causality assignment to the storage elements for the fast dynamics and maintaining an integral causality assignment for the slow and medium dynamics on the bond graph, reduced models for the slow and medium dynamics are obtained. When a derivative causality to the storage elements for the fast and medium dynamics is assigned and an integral causality assignment to the slow dynamics is applied, the most reduced model is determined. Finally, the proposed methodology to the Ward Leonard system is applied.

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Section: Reduced Models In the Physical Domainmentioning

confidence: 99%

“…Approximate bond graph models for two timescale systems are proposed in [26]. e analysis of a singular perturbed system with a feedback and observer in the physical domain is presented in [27].…”

Section: Introductionmentioning

confidence: 99%

Quasi‐Steady‐State Models of Three Timescale Systems: A Bond Graph Approach

Gonzalez

Barrera

Ayala

et al. 2019

Mathematical Problems in Engineering

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“…where the fast dynamics associated to x 2 (t) must be stable, and the as it will be shown in section 4 the quasi-steady state can be gotten setting = 0 or in a bond graph approach using the result of Gonzalez-A (2016). Moreover, the proposed augmented bond graph ensures that all the storage elements accept a predefined integral causality assignment as shown in Fig.…”

Section: Background and Problem Statementmentioning

confidence: 99%

“…The present article does not focus on an specific physical system as in the work of Sharon, Hogan & Hardt (1991). It focus on an a dynamic feedback rather than on an observer-control design as in the works of Gawthrop (1995) or Gonzalez-A (2016), and it is a closed loop methodology while the work of Yeh (2002) is based on an open-loop design.…”

Section: Introductionmentioning

confidence: 99%

Passivity-based control of linear time-invariant systems modelled by bond graph

Galindo

Ngwompo

2017

International Journal of Control

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Closed loop control systems are designed for Linear Time-Invariant (LTI) controllable and observable systems modelled by bond graph. Cascade and feedback interconnections of bond graph models are considered and are realized through active (signal) bonds with no loading effect. The use of active bonds may lead to non-conservation of energy and the overall system is modelled by proposed pseudojunction structures. These structures are build by adding parasitic elements to the bond graph models which assure that each storage element is connected to a dissipative element and the overall system may become singularly perturbed. The structures for these interconnections can be seen as consisting of inner structures that satisfy energy conservation properties and outer structures including multiportcoupled dissipative fields. These structures are called pseudo due to the structural properties of power conservation not being satisfied in the outer structures. The multiport-coupled dissipative fields highlight energy properties like passivity. These properties are useful for control design. In both interconnections, junction structures and multiport-coupled dissipative fields for the controllers are proposed and passivity is guaranteed for the closed loop systems assuring robust stability. The pseudo-junction structure for the cascade interconnection is applied to the structural representation of the closed loop transfer functions, in a one-degree of freedom feedback configuration, when a controller from the parametrisation of all stabilizing controllers is applied to a given nominal plant. Applications are given when the plant and the controller are described by state-space realizations, in this case parasitic elements are not added. Moreover, the feedback interconnection is used and the controller is tuned getting necessary and sufficient stability conditions based on the characteristic polynomial of the closed loop transfer function, solving a pole-placement problem and achieving zero-stationary state error.

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“…The different dynamics of a system through causal loops were identified in [18,21]. State feedback using an observer for LTI systems in the physical domain was proposed in [22]. Furthermore, the modeling of a class of nonlinear systems with two time scales was presented in [23].…”

Section: Introductionmentioning

confidence: 99%

Direct Determination of Reduced Models of a Class of Singularly Perturbed Nonlinear Systems on Three Time Scales in a Bond Graph Approach

Ayala-Jaimes

González-A²,

Gallegos³

et al. 2022

Symmetry

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One of the most important features in the analysis of the singular perturbation methods is the reduction of models. Likewise, the bond graph methodology in dynamic system modeling has been widely used. In this paper, the bond graph modeling of nonlinear systems with singular perturbations is presented. The class of nonlinear systems is the product of state variables on three time scales (fast, medium, and slow). Through this paper, the symmetry of mathematical modeling and graphical modeling can be established. A main characteristic of the bond graph is the application of causality to its elements. When an integral causality is assigned to the storage elements that determine the state variables, the dynamic model is obtained. If the storage elements of the fast dynamics have a derivative causality and the storage elements of the medium and slow dynamics an integral causality is assigned, a reduced model is obtained, which consists of a dynamic model for the medium and slow time scales and a stationary model of the fast time scale. By applying derivative causality to the storage elements of the fast and medium dynamics and an integral causality to the storage elements of the slow dynamics, the quasi-steady-state model for the slow dynamics is obtained and stationary models for the fast and medium dynamics are defined. The exact and reduced models of singularly perturbed systems can be interpreted as another symmetry in the development of this paper. Finally, the proposed methodology was applied to a system with three time scales in a bond graph approach, and simulation results are shown in order to indicate the effectiveness of the proposed methodology.

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A bond graph model of a singularly perturbed LTI MIMO system with a slow state estimated feedback

Cited by 6 publications

References 23 publications

Quasi‐Steady‐State Models of Three Timescale Systems: A Bond Graph Approach

Quasi‐Steady‐State Models of Three Timescale Systems: A Bond Graph Approach

Passivity-based control of linear time-invariant systems modelled by bond graph

Direct Determination of Reduced Models of a Class of Singularly Perturbed Nonlinear Systems on Three Time Scales in a Bond Graph Approach

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