Construction and analysis of causally dynamic hybrid bond graphs

Engineering systems are frequently abstracted to models with discontinuous behaviour (such as a switch or contact), and a hybrid model is one which contains continuous and discontinuous behaviours. Bond graphs are an established physical modelling method, but there are several methods for constructing switched or 'hybrid' bond graphs, developed for either qualitative 'structural' analysis or efficient numerical simulation of engineering systems. This article proposes a general hybrid bond graph suitable for both. The controlled junction is adopted as an intuitive way of modelling a discontinuity in the model structure. This element gives rise to 'dynamic causality' that is facilitated by a new bond graph notation. From this model, the junction structure and state equations are derived and compared to those obtained by existing methods. The proposed model includes all possible modes of operation and can be represented by a single set of equations. The controlled junctions manifest as Boolean variables in the matrices of coefficients. The method is more compact and intuitive than existing methods and dispenses with the need to derive various modes of operation from a given reference representation. Hence, a method has been developed, which can reach common usage and form a platform for further study.