H∞ optimization of proportional controllers for Unstable-First-Order-Plus-Dead-Time Systems

In this paper, we consider the H
_∞
optimization of proportional controllers for Unstable-First-Order-Plus-Dead-Time Systems (UFOPDT). Based on the existing results on the stability range of proportional controllers for UFOPDT systems, we investigate the weighted sensitivity optimization problem by H
_∞
norm computations. General form of the H
_∞
controllers are derived with numerical approximations, and their accuracy is discussed. The main algorithm is also illustrated by a design example.