Differential observation and integral action in LTI state-space controllers and the PID special case

Abstract

This paper makes the case that practical differentiation of measured state variables may be seen as an observation or estimation scheme for linear time invariant state space controllers. It is shown that, although not having the separation property, the estimation error of this scheme converges to zero if the resulting closed loop system is strictly stable. On the basis of this concept, it is shown that PID controllers may be interpreted as a special case of state space controllers endowed with differential observation. The interesting consequences of this interpretation are discussed.