Linearization of a class of non-linear systems modelled by multibond graphs

González-A, Gilberto; Ayala, Gerardo; Gallegos, Noe Barrera; Jose, Aaron Padilla

doi:10.1080/13873954.2019.1621905

Cited by 5 publications

(4 citation statements)

References 14 publications

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“…Recently, some developments with multibond graphs have been published, and the representation of electrical circuits of phasors containing real and imaginary parts with two-dimensional multibond and steady state was proposed in [22]. The linearization of a class of nonlinear systems that can be modeled with multibond graphs was presented in [23]. The direct determination of the steady-state response for LTI systems modeled with multibond graphs with a derivative causality assignment to the storage elements was proposed in [24].…”

Section: Introductionmentioning

confidence: 99%

Modeling and Simulation in Multibond Graphs Applied to Three-Phase Electrical Systems

et al. 2023

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The modeling of three-phase electrical systems in the coordinates d,q,0 in a simple and direct way in a multibond graph approach is presented. From the graphical model obtained, a mathematical model in state space can be determined. Thus, studies of the electromagnetic transients of electrical systems can be analyzed. Likewise, this modeling in the physical domain can be applied to balanced or unbalanced systems and the storage elements (inductances and capacitances) can be connected to be linearly independent or dependent. Structural properties such as stability, controllability, observability or controller design can be analyzed in multibond graphs. The proposed methodology is applied to two examples and the simulation results are shown using 20-Sim software.

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Section: Introductionmentioning

confidence: 99%

Modeling and Simulation in Multibond Graphs Applied to Three-Phase Electrical Systems

et al. 2023

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“…A bond graph methodology to linearize a class of nonlinear systems is proposed in [27][28][29]. Additionally, the linearization of nonlinear systems modeled by multibond graphs is presented in [30].…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, the linearized models by bond graph determine a degree of symmetry with respect to their origin in nonlinear models. Some of the main advantages of this paper with respect to previously published works are: (1) The classical approach of linearization with piecewise [8], recursive [17] or other schemes [13][14][15][16] are based on algebraic analysis of the equations; if the configuration of these schemes changes, it is not easy to adapt these modifications, while in bond graph linearization the adaptation process is simple; (2) the papers [8,[13][14][15][16][17] are dedicated to specific models and the bond graph has a multi-domain energy characteristic; (3) the linearization papers [18,27,30] solved the problem using bond graphs in an operation point and this paper determines a trajectory of operation points that can be used for tracking systems.…”

Section: Introductionmentioning

confidence: 99%

Approximation of Linearized Systems to a Class of Nonlinear Systems Based on Dynamic Linearization

et al. 2021

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An alternative method to analyze a class of nonlinear systems in a bond graph approach is proposed. It is well known that the analysis and synthesis of nonlinear systems is not a simple task. Hence, a first step can be to linearize this nonlinear system on an operation point. A methodology to obtain linearization for consecutive points along a trajectory in the physical domain is proposed. This type of linearization determines a group of linearized systems, which is an approximation close enough to original nonlinear dynamic and in this paper is called dynamic linearization. Dynamic linearization through a lemma and a procedure is established. Therefore, linearized bond graph models can be considered symmetric with respect to nonlinear system models. The proposed methodology is applied to a DC motor as a case study. In order to show the effectiveness of the dynamic linearization, simulation results are shown.

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“…Nonlinear science is widely used in natural and social sciences, and it has been booming in the field of nonlinear biochemical reactions [10,11]. To better analyse the process of biochemical reactions, it is essential to establish a nonlinear system model based on chemical reactions.…”

Section: Introductionmentioning

confidence: 99%

Modelling and analysis of haemoglobin catalytic reaction kinetic system

Liu

Wang

et al. 2020

Mathematical and Computer Modelling of Dynamical Systems

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In order to study whether haemoglobin (Hb) can replace peroxidase and has good catalytic properties. The key to exploring the characteristics of Hb peroxidase is to establish a suitable kinetic model, which is studied in this paper. First, according to the Hb catalytic reaction, a nonlinear system is established and improved. It is proved that the established system is in line with the practical significance. The stability of the original system is judged by analysing the stability of the simplified system. Then, considering the effect of time delay on Hb catalytic reaction, a nonlinear timedelay catalytic reaction system is obtained. For convenient application, the system is linearized using Taylor's formula, and the dynamic characteristics of Hopf bifurcation are analysed. The response diagrams of three system are plotted by setting perturbation parameters, and their variations are observed to analyse the differences among them. The results show that the nonlinear timedelay system can better describe the characteristics of the catalytic reaction.

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Linearization of a class of non-linear systems modelled by multibond graphs

Cited by 5 publications

References 14 publications

Modeling and Simulation in Multibond Graphs Applied to Three-Phase Electrical Systems

Modeling and Simulation in Multibond Graphs Applied to Three-Phase Electrical Systems

Approximation of Linearized Systems to a Class of Nonlinear Systems Based on Dynamic Linearization

Modelling and analysis of haemoglobin catalytic reaction kinetic system

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