ADRC for Uncertain Systems with Time-Delay

Abstract

The majority of control systems are operated by proportional-integral- derivative (PID) controllers, which dates back to 1922 ([135], [110], [220]) well before classical and modern control theory were born. Today, much work has been done related to systems with time-delays, see for example, ([188], [189], [154], [126]) and references therein. It should be noted that PID still remains as the preferred controller in over 95% of industrial applications, as generally a good performance can be achieved [22], [162]. Given the wide spread industrial use of PID controllers, it is clear that even a small percentage improvement in the design, a PID controller could have a tremendous impact on practical applications. Despite this, it is unfortunate that currently there is not much theory dealing with PID designs. Indeed, most of the industrial PID designs are carried out using only empirical techniques and the mathematically elegant and sophisticated theories developed in the context of modern optimal control cannot be applied to them. This represents a significant gap between the theory and practice of automatic control.