Combined optimal pulse width modulation and pulse frequency modulation strategy for controlling switched mode DC–DC converters over a wide range of loads

Abstract

This paper develops a combined optimal pulse width modulation (PWM) and pulse frequency modulation (PFM) strategy for controlling switched mode DC–DC converters. The peak ripple magnitudes of both the output–voltages and –currents during all operating modes over a wide range of loads are minimised subject to specifications on the minimum efficiency bounds of the converters. This problem is posed as a multi-objective functional inequality constrained optimal control problem. By expressing the initial state of each operating mode at the steady state as a function of the switched time instants, as well as applying the time scaling transform method and the constraint transcription method, the multi-objective functional inequality constrained optimal control problem is converted to a conventional optimal control problem. Finally, a control parameterisation technique is applied to solve the problem. Computer numerical simulations show that the combined control strategy could achieve low peak ripple magnitudes of both the output–voltages and –currents for all operating modes over a wide range of loads and guarantees the satisfaction of the specifications on the minimum efficiency bounds of the converter over a wide range of loads.