脉宽调制控制系统的适定性

On Well-posedness of PWM Control System

不连续动态系统的适定性(即解的唯一存在性)问题是混合系统研究的基本问题之一.脉宽调制控制系统可以表示成具有时变仿射不等式约束的分段仿射系统.该文首先在Caratheodory的解定义下导出了脉宽调制控制系统无滑模和跳跃的解的适定性的充分必要条件.然后利用该结果对PWM型DC-DC降压变换器的适定性的研究表明当载波信号h(t)=0时闭环PWM DC-DC变换器总是不适定的,当载波信号h(t)的参数和比例控制器的参数满足一定的条件时,比例控制的闭环PWM DC-DC变换器是适定的.

One of the basic issues in the study of hybrid systems is the well-posedness (existence and uniqueness of solutions) problem of discontinuous dynamical systems. This paper addresses this problem for a class of piecewise affine discontinuous systems with affine inequalities such as systems with pulse-width modulator under the definition of solutions of Caratheodory in terms of an analysis based on Lexicographic inequalities and the smooth continuation property of solutions. Furthermore, it is clear that when carrier signal h(t)=0, closed loop PWM DC-DC converters are not well-posed and when some condition is satisfied, closed loop PWM DC-DC converters with P controller are well-posed.