Bond Graphs and Lagrange Equations as Aids in Analytical Studies of Electro-Mechanical Systems

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AbstractA well-known advantage of bond graph models of electro-mechanical systems is that they can be manipulated manually or with the aid of computer programs to yield first order state equations useful for numerical studies. A causal analysis can show in advance whether derivative causality will cause practical difficulties in the equation formulation which might be best circumvented by modification of the model.Numerical studies are sometimes of limited use in preliminary investigation of the feasibility of a design because the large number of parameters involved precludes a general understanding of the limits of the concept being studied. Analytical studies of simplified models may find the existence of parameter combinations which are crucial to the successful operation of the system or fundamental limitations to performance not obvious in purely numerical studies.Although the first order nature of the normal bond graph state equations are advantageous for numerical simulation, they are not necessarily the most convenient form for analytic studies using pencil and paper. In many cases, the use of Lagrange equations, based on energy state functions and degrees-of-freedom rather than state variables are advantageous for analytic work. Bond graph models and a special form of causality can be used to advantage, particularly when derivative causality is present, to yield sets of second order dynamic equations based on Lagrange equations, which are often easier to work with than their first order equivalents. This will be illustrated by an example by the analysis of the use of a rotary electric motor as an actuator in semi-active or active suspension element in a vehicle suspension.