A Unified Analytical Design Method of Standard Controllers using Inversion Formulae

TL;DR

This paper introduces a unified analytical method for designing standard controllers like Lead, Lag, and PID using inversion formulae, simplifying parameter computation based on control specifications.

Contribution

It presents a comprehensive set of closed-form formulae for designing common controllers, enhancing educational value and practical application in control system design.

Findings

Provides explicit formulas for controller parameters based on specifications.

Simplifies the design process for standard controllers.

Enhances educational tools for control engineering courses.

Abstract

The aim of this paper is to present a comprehensive range of design techniques for the synthesis of the standard compensators (Lead and Lag networks as well as PID controllers) that in the last twenty years have proved to be of great educational value in a vast number of undergraduate and postgraduate courses in Control throughout Italy, but that to-date remain mostly confined within this country. These techniques hinge upon a set of simple closed-form formulae for the computation of the parameters of the controller as functions of the typical specifications introduced in Control courses, i.e., the steady-state performance, the stability margins and the crossover frequencies.