Nonlinear analysis of a 1st-order thyristor-bridge control system. Use of difference equations and transition mapping

By considering the solution of the differential equation governing the current delivered, via a thyristor bridge, to a series R-L load, an exact nonlinear difference equation relating the current at consecutive firing instants is established. The behaviour of the system, both statically and dynamically, is thereby examined and use is made of transition-mapping concepts. Perturbational analysis is performed to linearise the equation and it is demonstrated that the system can be considered as a discrete controller with proportional and derivative control having a varying time constant. Computer simulation and experimental results are presented as evidence of the validity of the developed models.