Stability of a Hamiltonian observer applied to a resonant converter

A series loaded resonant converter is used in a high voltage and a high power application. A transformer in the resonant converter makes a significant contribution to the dynamics by a high leakage capacitance and a high magnetising inductance. The converter runs both in continuous and discontinuous conducting mode. The converter is a full bridge converter and its controller will be based on the states of the converter. In our case there are five states; the resonant current, the current through the magnetising inductance, the voltage across the series capacitor, the voltage across the leakage capacitance, and the voltage across a capacitive load. It is not possible to measure all states, in fact only one state is measured. We propose a nonlinear observer, called a switched Hamiltonian observer, to estimate the states. A stability analysis of the observer is based on modelling of the observer error process as a Hamiltonian system. By use of this method we are able to prove global stability and suggest a design method of the switched Hamiltonian observer. Simulation is performed for illustration of the stability properties of the observer. The simulations show also that the observer estimates converge to the true state values.