Reachable Sets of Dynamic Systems

Chapter Eight: PID control: functional sensitivity

Abstract

In this chapter, the sensitivity of a control circuit with anti-windup PID controller is discussed. Instead of classical sensitivity, we use functional sensitivity, defined in terms of variational calculus. The non-local functional sensitivity is given in the form of the system's reachable set. The relation to differential inclusions is explained. The solution to the functional sensitivity is shown, using the differential inclusion solver, which calculates and displays the system's reachable sets. A comparison between functional sensitivity and the classical approach is made. The main simulation tool is the differential inclusion solver.

Keywords

Differential inclusion; Uncertainty; PID ...