Sensitivity integrals and related inequalities for process control systems

TL;DR

This paper develops generalized sensitivity integral inequalities for linear feedback systems, incorporating non-analytic and analytic sensitivity functions, to improve robustness against disturbances and uncertainties, with practical validation on chemical control systems.

Contribution

It introduces new sensitivity integral inequalities for non-analytic and analytic sensitivity functions, enhancing robustness analysis and controller design for process control systems.

Findings

Derived generalized sensitivity integral inequalities.

Rephrased inequalities in plant parameter context.

Validated results through numerical simulations on chemical systems.

Abstract

This paper exhibits the closed-loop design constraints using the non-analytic function theory. First, the paper generalizes the sensitivity integral for linear feedback systems with the non-analytic sensitivity function. Sensitivity inequalities are determined by the integral relationships based on the presence of non-minimum phase zeros and right half plane poles. These inequalities are rephrased in plant parameter context, which must be satisfied by the feedback design. That indicates the ability of controllers under the influence of input disturbances and plant parameter variations. The paper then extends the integral to the analytic sensitivity function of the augmented linear feedback systems. This is useful to augment the ability of a linear feedback system to handle input disturbances and plant uncertainties, via modified sensitivity function theory. Numerical simulations are carried out to perform sensitivity analysis on three chemical control systems. That describes the usefulness and demonstrates the applicability of the result of this paper to examine and augment the ability of linear feedback system.