| In this dissertation, a digital control approach is introduced to realize near time optimal control (TOC) in synchronous buck DC-DC converters. The proposed controller is a combination of a standard constant-frequency pulse width modulated (PWM) control in the vicinity of a steady-state operating point and a bank of switching surface controllers (SSCs) away from the reference. The SSC is a nonlinear controller that ideally provides an ON/OFF sequence resulting in the fastest, i.e., time-optimal rejection of large-signal step load disturbances. The SSC is implemented as a small Verilog HDL module, and can be easily added to an existing digital PWM controller. A hybrid capacitor current estimator enables switching surface evaluation and eliminates the need for current sensing. In contrast to the conventional near time-optimal controllers, this method incorporates the inductor current limitation, as is necessary in practical DC-DC converter designs, and also exhibits good performance even when the output voltage is sampled using a relatively low-resolution, narrow-range window analog-to-digital (A/D) converter. A method is also presented to incorporate the A/D quantization effects in the SSC, which may improve the controller design and performance. A global stability analysis is described in the context of discrete-time piecewise linear (PWL) systems for three possible arising modes in transient operations including sliding mode, asymptotic mode, and mixed mode (including both sliding and asymptotic modes). In the sliding mode, the stability on the switching surface is shown using Lyapunov method. In the asymptotic mode, quadratic piecewise Lyapunov functions are employed to verify the stability. Finally, an approach is proposed to address stability in the mixed mode.Effectiveness of the proposed control method and results of the stability analysis are verified by simulation and experimental results on a 1.3 V, 10 A synchronous buck DC-DC converter. |
