Modelling and control of switch-mode DC-DC converters using state transition matrices

Switchable DC circuits, extensively used in power electronic devices, have a nonlinear response even when all the circuit elements are linear. A simple but accurate way of modelling the perturbation response of such a circuit is presented. The exact circuit behaviour is first represented by its state transition equation, which is then linearized around a nominal operating point to obtain a linear state space description of the system. In a similar fashion, a linear average value of the circuit output is also obtained. The proposed method of obtaining a perturbation model is tested on a buck-boost converter through two different control designs. The results obtained through this method are compared with those obtained through a standard (state space averaging) technique and are found to be much more accurate.