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

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.