Dynamic modelling of switching systems

A generalized approach for obtaining a small-signal model of linear switching systems is described. Starting from a piece-wise constant linear description of the system, a concise, discrete-time model is obtained using the augmented state vector method. This model together with a generalized description of the transition conditions between the modes is used to obtain the cyclic state of the system. Linearization of both the model and the transition conditions yields a linear small-signal model, which is valid in the vicinity of an operating point. Due to the augmented state form of the system, this linearized model can easily be calculated. This method for obtaining a small-signal model is applicable to a large class of systems. As an example, the advantages of the method are shown in an experiment with a DC-motor drive