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

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.

Dynamic Thresholds for a Reliable Diagnosis of Switched Systems

Safety, availability and reliability are the main concern of many industries. Thus, fault detection and isolation of industrial machines, which are in most cases switched systems, is a primary task in many companies. The presented paper proposes a new diagnostic approach for switched systems using two powerful tools: bond graph and observer. A diagnostic layer detects model errors using bond graph, and a smart algorithm identifies and locates faults using observer. Although observers serve as fault detectors, they also have their own errors caused by convergence delay of calculations; even in the case of no sensor defect, the residue does not converge to zero. In this paper, we propose a new method to solve this problem by integrating dynamic thresholds in the detection procedure, which helped to avoid false alarms and ensure a highly reliable diagnosis.

Model of the Floating Bearing Bushing Movement in an External Gear Pump and the Relation to Its Parameterization

This article presents the modeling, simulation and experimental validation of the movement of the floating bearing bushing in an external gear pump. As a starting point, a complete pump parameterization was carried out through standard tests, and these parameters were used in a first bond graph model in order to simulate the gear pump behavior. This model was experimentally validated under working conditions in field tests. Then, a sophisticated bond graph model of the movement of the floating bushing was developed from the equations that define its lubrication. Finally, as a result, both models were merged by integrating the dynamics of the floating bushing bearing with the variation of the characteristic parameters (loss coefficients). Finally, the final model was experimentally validated both in laboratory and field tests by assembling the pump in a drilling machine to drive the auxiliary movements. The novelty of this article is the conception and construction of a simple and experimentally validated tool for the study of a gear pump, which relates its macroscopic behavior as a black box (defined by the loss coefficients) to the internal changes of the unit (defined by its internal lubrication).

Contribution to the systemic modeling of a photovoltaic devices

The modelling of systems using systemic tools has been for a few years, a subject which has attracted the attention of scientists and especially researchers to allow designers to acquire a rigorous approach to problem solving using the capabilities of already existing methods and tools. This document presents a contribution in the field of modelling, where a methodology based on two methods has been proposed. The first concerns the functional analysis to extract the use functions and the constraint parameters from the system. In this methodology, the static functional study is carried out using the SADT method. On the other hand, the dynamic behavioral analysis is carried out by the SA-RT method. Then, we used a behavioral and parametric analysis, the Bond Graph method, to observe the evolution of representative quantities of a photovoltaic system.

Asymmetric circular graph with Hosoya index and negative continued fractions

It has been known that the Hosoya index of caterpillar graph can be calculated as the numerator of the simple continued fraction. Recently in [MATCH Commun. Math. Comput. Chem. 2020, 84 (2), 399-428], the author introduces a more general graph called caterpillar-bond graph and shows that its Hosoya index can be calculated as the numerator of the general continued fraction. In this paper, we show how the Hosoya index of the graph with non-uniform ring structure can be calculated from the negative continued fraction. We also give the relation between some radial graphs and multidimensional continued fractions in the sense of the Hosoya index.

Dynamic Modeling and Simulation of Double-Planetary Gearbox Based on Bond Graph

New generations of powertrains are using gearboxes with multiple speed-shift designs to improve fuel efficiency. However, transmission controls and calibration are substantially time consuming, specifically during shift processes. To study the dynamic characteristics of a gearbox with a double-planetary gear train and analyze the influence of external excitation and internal parameters on the dynamic response of a system, dynamic modeling and simulation of the transmission system are conducted. Some physical processes are complex and difficult to express via lumped mass modeling. The dynamic model of a double-planetary gearbox is obtained by adopting the bond graph method based on the working principle analysis of the transmission, as well as the kinematic characteristics of the double-planetary gear train. Subsequently, state equations are deduced from the dynamic model of the power transmission system for simplified calculations, which can effectively facilitate the shift process simulation. The basic case of different shift plans and times is originally analyzed, followed by an analysis of the influence of damping, stiffness, and moment of inertia on transmission systems. The analysis results provide references for the structural design, control strategy optimization, and failure diagnostics of this gearbox type.

A novel fault-tolerant control strategy based on inverse bicausal bond graph model in linear fractional transformation

This article presents the development of a novel fault-tolerant control strategy. For this task, a bicausal bond graph model-based scheme is designed to generate online information to the inverse controller about the faults estimation. Secondly, a new approach is proposed for the fault-tolerant control based on the inverse bicausal bond graph in linear fractional transformation form. However, because of the time delay for fault estimation, the PI controller is used to reduce the error before the fault is estimated. Hence, the required input that compensates the fault is the sum of the control signal delivered by the PI controller and the control signal resulting from the inverse bicausal bond graph for fast fault compensation and for maintaining the control objectives. The novelties of the proposed approach are: (1) to exploit the power concept of the bond graph by feeding the power generated by the fault in the inverse model (2) to suitably combining the inverse bicausal bond graph with the PI feedback controller so that the proposed strategy can compensate for the fault with a very short time delay and stabilize the desired output. Finally, the experimental results illustrate the efficiency of the proposed strategy.

Research on the dynamic characteristics of the acquisition mechanism of the oscillating flapping wing wave energy power generation device based on the bond graph

Taking the acquisition mechanism of the oscillating flapping-wing wave energy power generation device as the research object, the design of the acquisition mechanism, the bond graph model of the acquisition mechanism and the dynamic characteristics are studied. According to the working principle of the acquisition mechanism of the oscillating flapping wing wave energy power generation device, the bond graph model and the state space equation of the acquisition mechanism are established. Based on the bond graph theory, the AMESim software is used for simulation analysis to verify the correctness of the bond graph model of the acquisition mechanism. The research results show that the designed oscillating flapping wing wave energy generation device acquisition mechanism responds quickly and stably, and the bond graph model basically matches the real system. The research process provides an effective reference for the development of the acquisition mechanism of the oscillating flapping wing wave energy power generation device.