Sensitivity Analysis of Continuous-Time Systems based on Power Spectral Density

TL;DR

This paper demonstrates that for wide sense stationary disturbances, the sensitivity and complementary sensitivity Bode integrals are equivalent, and derives a lower bound relevant to control system performance, illustrated with an aircraft example.

Contribution

It establishes the equivalence of sensitivity integrals under stationary disturbances and provides a new lower bound, enhancing understanding of control limitations.

Findings

Sensitivity and complementary sensitivity integrals are identical for stationary disturbances.

A lower bound for the complementary sensitivity-like Bode integral is derived.

Application to F-16 aircraft control demonstrates practical relevance.

Abstract

Bode integrals of sensitivity and sensitivity-like functions along with complementary sensitivity and complementary sensitivity-like functions are conventionally used for describing performance limitations of a feedback control system. In this paper, we show that in the case when the disturbance is a wide sense stationary process the (complementary) sensitivity Bode integral and the (complementary) sensitivity-like Bode integral are identical. A lower bound of the continuous-time complementary sensitivity-like Bode integral is also derived and examined with the linearized flight-path angle tracking control problem of an F-16 aircraft.