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.

A Study of The Design Method and Similitude for A Small-Scale Test Drilling Rig (Part 1): An Application of The Geometrically Distorted Scaled Modeling Method

Drillstrings often vibrate severely and tend to twist off during hard rock drilling. Therefore, dynamic testing is crucial in the design of drilling systems. Designers tend to employ the most powerful analytical tools, using the most elaborate electronic computers, however, actual testing is required to the designed system function optimally. In cases of enormous drilling systems, complex dynamic tests are often performed on a smaller-scale replica of the system, referred to as the model, which is more convenient, cost-effective, and time-effective. This study, therefore, describes the establishment of similar conditions among structural systems, with the main objective of studying the similitude theory’s applicability in establishing the necessary similar conditions for designing scaled-down models to predict the drillstring’s vibration behavior. The scaling laws for all the relevant parameters regarding the scaled drillstring model, as well as the full-size drillstring system, were derived from the respective equations of motion. The scaling factors for all relevant parameters are determined using the theory of dimensional analysis. In addition, the geometry distorted similitude theory is revisited and employed to overcome the physical limitation and develop the necessary similar conditions for dynamic testing of the scaled drillstring. Meanwhile, the similitude relationship between the prototype and the model was validated with a case study using lumped segments bond graph modeling and simulation software.

Bioinspired Feathered Flapping Wing UAV Design for Operation in Gusty Environment

The flight of unmanned aerial vehicles (UAVs) has numerous associated challenges. Small size is the major reason of their sensitivity towards turbulence restraining them from stable flight. Turbulence alleviation strategies of birds have been explored in recent past in detail to sort out this issue. Besides using primary and secondary feathers, birds also utilize covert feathers deflection to mitigate turbulence. Motivated from covert feathers of birds, this paper presents biologically inspired gust mitigation system (GMS) for a flapping wing UAV (FUAV). GMS consists of electromechanical (EM) covert feathers that sense the incoming gust and mitigate it through deflection of these feathers. A multibody model of gust-mitigating FUAV is developed appending models of the subsystems including rigid body, propulsion system, flapping mechanism, and GMS-installed wings using bond graph modeling approach. FUAV without GMS and FUAV with the proposed GMS integrated in it are simulated in the presence of vertical gust, and results’ comparison proves the efficacy of the proposed design. Furthermore, agreement between experimental results and present results validates the accuracy of the proposed design and developed model.

Connecting Qualitative and Quantitative Analysis Through Bond Graph Modeling and System Dynamics

Access to resources can contribute to social progress in extremely impoverished communities. The introduction of cyber-physical systems for electricity, water, and irrigation facilitates greater fulfillment of needs. Yet, the availability of resources may be inconsistent or lacking. The social dynamics of the community can provide insight into how the available resources support well-being. Thus, the cyber-physical system requires the addition of a social consideration to become cyber-physical-social systems. However, the social considerations typically include qualitative parameters. This prompts the need for integrating qualitative and quantitative information. In this paper, we present a method for mathematically representing qualitative and quantitative relationships. This is achieved by connecting Bond Graph Modeling and System Dynamics. The Bond Graph model is used to mathematically represent relationships between qualitative and quantitative elements. These relationships are used in the System Dynamics analysis. The method is anchored in expanding cyber-physical to cyber-physical-social systems through incorporating both qualitative and quantitative information in the systems analysis. The mathematical connectivity of qualitative and quantitative information is a key feature of this approach. A test problem in resource allocation is used to demonstrate the function and flexibility of the method. This is anchored in connecting qualitative and quantitative information in the analysis.