Observability and observer design for hybrid multicell choppers

Multicell choppers are part of a class of hybrid systems in which the continuous state vector is always unobservable, in the sense that the observability matrix never has full rank. Due to their hybrid behaviour, the recent concept of Z(T_N)-observability can be applied and analysed in the context of multicell choppers, which allows to give conditions, in terms of the switching sequence, under which the voltage across each capacitor can be reconstructed, not instantly, but after some number of switchings. The case when a DC-motor is coupled to the multicell chopper is also considered. It is shown that, under certain admissible assumptions, the voltages across the capacitors and the motor speed can be acceptably estimated. Two observers, one based on the super-twisting algorithm and the other one based on an adaptive approach, are designed. Additionally, we design an observer for the partial state observation. Simulations are given where the proposed observers are compared and the effectiveness of both is shown.