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.