【作者】 赵欣；

【导师】 常昌远； 李祖华；

【作者基本信息】 东南大学 ， 集成电路工程（专业学位）， 2017， 硕士

【摘要】 数字控制方式具有灵活性好,可编程,易于实现各类高级的控制算法等优点,因此开关型功率变换器的数字化控制逐渐成为一股不可阻挡的发展趋势。但是,一方面,数字控制存在延迟,会给系统的稳定性带来不良影响。另一方面,数字控制功率变换器系统中的模数转换器(Analog-to-Digital Converter,ADC)和数字脉宽调制器(Digital Pulse Width Modulator,DPWM)存在量化效应,在某些情况下会导致系统发生极限环振荡。因此,为了保证系统的稳定工作,设计数字控制器时需要充分考虑延迟和量化的影响。本文以采用数字控制的DC-DC Buck变换器系统作为研究对象,首先考虑采样保持环节,AD转换延时和控制算法计算延时,构造闭环系统模型,给出了基于朱利判据法计算系统稳定工作参数范围的方法。在上述稳定范围内,由于数字控制中量化效应的影响,系统仍可能发生极限环振荡。接下来,对于本文所研究的近似为正弦形式的极限环振荡,采用描述函数法分别建立了 ADC和DPWM的动态量化模型,分析了量化及其所引起的等效动态增益之间的关系。之后,当DPWM的设计分辨率足够高满足避免两占空比级极限环振荡的动静态条件时,考虑ADC和DPWM可能在环路中引入的最大等效动态增益,给出了包含延迟和量化引起最大等效动态增益时的完整闭环系统模型,结合静态无极限环条件对积分补偿增益系数上限的约束综合考虑,可以计算出能充分保证系统稳定的补偿器参数范围。最后,进行了相应的Simulink仿真和基于FPGA的硬件电路测试验证。本文通过研究证实:一、输出电压的低频振荡是由系统的Neimark-Sacker分岔所引起的,系统分岔所导致的输出电压低频振荡振幅很大,因此可以忽略量化引起的动态增益对系统分岔的影响。二、低分辨率的DPWM可能在控制回路中引入很大的等效动态增益,使系统相位滞后达到180°时环路增益等于1,从而引起两占空比级极限环振荡。三、在系统分岔发生之前,受ADC和DPWM的量化效应在环路中引入的等效动态增益影响,系统可能已经发生了极限环振荡。因此,为了保证数字控制DC-DC变换器的稳定性,除了要保证一个高分辨率的DPWM,确定补偿器参数时还要综合考虑数字控制中的延迟和量化对闭环系统稳定性的影响。更多还原

【Abstract】 Digital control of switching-mode power converters has gradually become an irresistible trend for the following advantages:excellent flexibility,programmability,and is easy to implement various kinds of advanced control algorithms.However,on one hand,the delay of digital control may degrade the stability of the system.On the other hand,the quantization effects of the ADC and the DPWM in a digitally controlled power converter system may result in limit cycle oscillations in some situations.As a consequence,the influence of delay and quantization should be taken into consideration when designing the digital controller in order to guarantee the stability of the system.This thesis uses a digitally controlled DC-DC Buck converter as the research object.Firstly,considering the sample-and-hold module,the time delay of the analog-to-digital conversion together with the control algorithm calculation,the closed-loop system model is established and the method to calculate the parameter range that could guarantee the stability of the system based on the Jury test is presented.However,owing to the quantization effects of digital control,limit cycle oscillations may still occur within the stable range discussed above.After that,the describing function method is applied here to obtain the amplitude and offset-dependent gain model of the ADC and the DPWM on account of the limit cycle oscillations studied in this thesis is quasi-sinusoidal.Then,under the premise that the resolution of the DPWM is sufficiently high that satisfies the static and dynamic conditions to eliminate limit cycle oscillations on two duty cycle levels,considering both the ADC and the DPWM in the control loop have maximum equivalent gain,the complete closed-loop system model includes the delay and the quantization effects is presented.Combining the constraint on the upper limit of the integral compensation gain to guarantee a static no-limit-cycle condition,the parameter range of the compensator to ensure a stable system in this situation can be calculated accordingly.Finally,corresponding simulations in Simulink and circuit tests based on FPGA are carried out.It is proved that the low-frequency oscillations of the output voltage are resulted from the Neimark-Sacker bifurcation,and since the amplitude of the low-frequency oscillations is large,the influence of the dynamic gains resulted from quantizations on the bifurcation of the system can be ignored.Secondly,low-resolution DPWM may lead to a large equivalent dynamic gain,and the limit cycle oscillations on two duty cycle levels will occur when the phase lag reaches 180 degrees and the loop gain magnitude equals to unity.Thirdly,it can be noted that the limit cycle oscillations may have already happened before the occurrence of the low-frequency oscillations due to the quantization effects of the ADC and the DPWM.As a consequence,a high-resolution DPWM is necessary to avoid the limit cycle oscillations.Besides,the influence of delay and quantization on the stability of a closed-loop system should be taken into consideration when determining the compensator parameters.更多还原