Continuous approximation and the stability of averaging

Averaged models do not always correctly represent the stability of the systems being modeled. A well-known example is the peak-current controlled PWM converter in which subharmonic oscillation occurs when the duty ratio is larger than 50%. This paper is an effort to understand how stability might be changed in the process of averaging, and to develop alternative continuous-time models that preserve system stability. The basic approach taken here is based on sampled-data modeling and continuous approximation. In the process, we also established a link between state-space averaging and continuous approximation based on forward Euler transformation, providing a possible explanation for the inability of averaged models to predict system instability, especially in the case of peak current control. Use of bilinear transformation is then suggested for continuous approximation of sampled-data models as a means to avoid stability changes. Limitations of this approach are discussed pointing to the needs for new direct continuous-time modeling methods.