A dynamic system model is proper for a particular application if it achieves the accuracy required by the application with minimal complexity. Because model complexity often—but not always—correlates inversely with simulation speed, a proper model is often alternatively defined as one balancing accuracy and speed. Such balancing is crucial for applications requiring both model accuracy and speed, such as system optimization and hardware-in-the-loop simulation. Furthermore, the simplicity of proper models conduces to control system analysis and design, particularly given the ease with which lower-order controllers can be implemented compared to higher-order ones. The literature presents many algorithms for deducing proper models from simpler ones or reducing complex models until they become proper. This paper presents a broad survey of the proper modeling literature. To simplify the presentation, the algorithms are classified into frequency, projection, optimization, and energy based, based on the metrics they use for obtaining proper models. The basic mechanics, properties, advantages, and limitations of the methods are discussed, along with the relationships between different techniques, with the intention of helping the modeler to identify the most suitable proper modeling method for a given application.

A Review of Proper Modeling Techniques

This paper presents a survey of the bond graph method from its conception and creation by Prof. Henry Paynter to the present. A thematic classification of the bibliographical material is given depending on whether work deals with the definition of theoretical details of bond graphs, applications of bond graphs to particular fields, or if it deals with a computer program developed using the bond graph theory. A list of journals which publish bond graph related articles, as well as textbooks is also presented. The survey, though exhaustive, does not pretend to be all inclusive. Some works may have been unintentionally omitted due to obvious limitations on accessing and listing all the relevant literature concerning the topic.

A survey of bond graphs : Theory, applications and programs

A method is presented for the analysis and simulation of the dynamic response of systems containing linked long, flexible bodies driven by actuators at joints and attachement points.

Bond Graphs for Flexible Multibody Systems

Commercial competition demands a reduction in the development time of new products. While it has been recognized for a number of years that the development process can be accelerated with the use of computer simulation based on mathematical models of the product, the lack of appropriate modeling tools has limited the effectiveness of this approach. It is the premise of this work that a new modeling metric able to handle nonlinear dynamic systems and all types of energy elements, will improve the effectiveness of modeling tools.
A new modeling metric, activity, which is based on energy, is developed in this work. This metric is used to rank the importance of all energy elements in a system. The ranking of the energy elements provides the relative importance of the model parameters and this information can be used to reduce the size of the model. The metric is implemented in an algorithm called Model Order Reduction Algorithm (MORA). MORA is applied to a nonlinear quarter car model showing that elements with low activity can be eliminated without any significant change in model accuracy.
MORA is also applied to linear systems, where the steady state activity to sinusoidal inputs is considered. It is shown that the activity varies with frequency, and thus, a series of reduced models can be generated as a function of the excitation frequency.
For multibody systems, the activity metric can be applied to each DOF of the rigid bodies. The activity metric is applied to a heavy-duty tractor-semitrailer to demonstrate that a significant number of the model parameters are insignificant, and therefore, that a substantial reduction in the model size can be achieved.
Finally, an interpretation algorithm based on the activity metric is developed to provide the user with physical meaning of each low activity element eliminated. In addition, the use of the activity metric to rank the energy elements augments the insight into the model, since the engineer can focus on a smaller number of elements that are identified by MORA as important to the system behavior.
In conclusion, this work develops an automated modeling algorithm, MORA, which can be used to rank model parameter importance, reduce model complexity and help provide physical insight into a system. MORA extends the applicability of automated modeling to systems that can be represented by nonlinear dynamic models and it should improve the use of modeling and simulation for product development.

An energy-based model reduction methodology for automated modeling

The singular perturbation method applied to multi-time scale processes enables the reduction of dimensionality by considering only one part of the system—the slow or the fast part—depending on the frequency domain of interest. The fast and slow dynamics of bond graph models can be estimated by determination of causal loop-gains. We define here the notion of a reciprocal system which, with singular perturbation techniques, can obtain more accuracy on the fast time scale behaviour of the system.

Order Reduction of Multi-time Scale Systems Using Bond Graphs, the Reciprocal System and the Singular Perturbation Method

Bond graphs are an extremely useful modeling procedure for representing the actual energy exchange mechanisms of interacting dynamic systems. Governing state equations are straightforwardly obtained from the bond graph; however, for large structures, a restrictively large number of equations can result. A procedure is developed whereby the original equations are reduced to a form suitable for modal decomposition. The resulting modes are reinterpreted in bond graph form with the resulting model being an extremely accurate system representation while requiring only a fraction of the original number of equations. The procedure is demonstrated through example.

D.L. Margolis

Papers

Reduction of models of large scale lumped structures using normal modes and bond graphs