Astatism analysis of time delay controllers towards effective anti-windup schemes

The paper provides astatism analysis of controllers with time delays arising from compensation schemes such as internal model control and Smith predictor. As the rather straightforward result a condition for the astatism is provided. From the spectral analysis, it results that even if all the infinitely many roots of the controller lie on the imaginary axis, the astatism brought by the root at the origin is predominant in the controller responses. Subsequently, applying the final value theorem, a methodology to derive the asymptotic slope of the astatic time delay controller is proposed. Besides, delay approximation based methods such as Maclaurin series and Pade approximation are involved in the analysis. The presented research is motivated by broader analysis of time delay controllers towards effective design of anti-windup schemes. Full understanding of the astatism nature is the key aspect for this research task.