boost小信号建模参照.pdfVIP

3 （30 分） Project: Control Loop Design and Simulation of a Boost Converter Fig.1 shows a circuit diagram of a boost converter and the parameters for circuit elements. Fig.1. Boost converter circuit diagram and system parameters 1）Derive the large-signal average model of the boost converter and draw the corresponding circuit diagram. 2 ） Derive the small-signal model of the boost converter and draw the corresponding circuit diagram. vd 3 ） From the small-signal model, derive the control to output transfer function (G ) and plot its frequency-domain response (Bode plot) with MATLAB ,bode? command. 4 ）Design a controller to compensate the open-loop Bode plot with MATLAB ,sisotool? toolbox. Clearly mark the poles and zeros of the designed controller and the phase margin of the compensated system.Write down the controller transfer function. 5 ）Simulate the performance of the compensated converter system in MATLAB/Simulink with the converter average model and the designed controller. Add disturbances to the input voltage and load power and record the output voltage waveforms. A report containing the above five aspects is required. 准备工作：小信号模型是一种平均模型，它是假设在稳态情况下，对系统加 一低频的交流扰动信号，然后可以得到扰动信号之间的传递函数。对于 boost电路 来说，由于开关频率很高（ 220kHz），所以，可以利用小信号的方法，来得到系 统中各量之间的传递函数。 另外可以看到， 电容 C 上的内阻 R 相对于负载电阻 R c L 来说非常小，因此在建模的时候可以直接忽略。 1、大信号平均状态方程的建立 假设有一开关函数 s(t ) ，当开关管导通时，为 1，挂断时为 0 。 当 s(t ) 1时，根据电感两端电压和通过电容的电流列方程： diL (t ) u (t ) L V (t )