The purpose of this thesis is to design and implement a linear quadratic optimal controller for a twin-buck converter with zero-voltage-transition (ZVT). The controller calculates duty ratio every cycle based on voltage and current feedback, as well as estimates the time instances when the synchronous rectification power switch current is zero. These time instances are crucial for ZVT operation. Via frequency modulation, the controller is designed to automatically regulate the output voltage to a desired value under load and voltage source variation. Simulations indicate that the proposed control design works. The controller is implemented using a Field Programmable Gate Array (FPGA). The experimental results match the simulations, which further verifies the applicability of the proposed voltage regulation strategy.

In the thesis, we apply the state average method to model the time-average linear dynamic equation, which is used to design a gain scheduled linear quadratic optimal controller. Because the standard modulation method of the twin-buck converter is PFM(Pulse-Frequency Modulation) and twin-buck converter owns the soft-switching characteristic, the voltage step-down ratio, that is, control force can not be lowered less than 0.5. For expanding the range of control force of converter, we modulate the converter by means of mixed modulation of PWM/PFM. With the former odulation method, we have to calculate the discharging time of synchronous switch taken by controller to achieve zero-voltage-transition (ZVT). In the last part of this thesis, we verify the practicability of the controller and modulation method through soft simulation coded by MATLAB and hardware implementation of FPGA driven by Verilog.