Recursive Distributions of Poles and Zeros for Linear Phase Variations

Abstract

This article discusses two recursive distributions of poles and zeros that permit the synthesis of a transmittance whose phase variations are linear in respect to logarithmic variations of the frequency. Slope and magnitude are adjusted through two parameters. One of the resulting transmittances is particularly attractive for the synthesis of a CRONE controller if constraints on closed loop pole locations or on sensitivity function energies are imposed. The resulting transmittance also permits us to obtain a state space description of the open and closed loop systems, which is required if a linear parameter varying system is to be controlled.