Minimum-Time Control of a Buck Converter for Bipolar Square-Wave Generation

The application of optimal control theory concepts justifies the use of a bang-bang control to reach in minimum time a desired steady-state value of the output voltage in the buck converter. The converter trajectories in the phase-plane are used as control functions and sliding-mode control is introduced to regulate the output voltage. Analytic approximations of the optimal control law are investigated to generate a bipolar square-wave in the converter output. SPICE simulations and experimentals waveforms are in good agreement with the theoretical predictions of the analytic approximations. Main features of the proposed control are the following: i) Minimum transient time in the polarity change of the output voltage. ii) Output regulation in steady-state by means of sliding-mode control to reject load perturbations iii) Minimum-time transient regime to reach steady-state values of voltage and current for specified values of load resistance and desired output voltage.