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Classical PID Control
by Graham C. Goodwin, Stefan F. Graebe, Mario E. Salgado
Control System Design, Prentice Hall PTR
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In this chapter we review a particular control structure that has e almost universally used in industrial control. It is based on a particular
fixed-structure controller family, the so-called PID controller family. The letters ‘PID’ stand for Proportional, Integral and Derivative Control.
They have proven to be robust in the control of many important applications.
The simplicity of these controllers is also their weakness: it limits the range of plants that they can control satisfactorily. Indeed, there exists a
set of unstable plants which cannot be stabilized with any member of the PID family. Nevertheless, the surprising versatility of PID control
(really, PID control simply means: control with an up-to-second-order controller) ensures continued relevance and popularity for this
controller. It is also important to view this second-order setting as a special case of modern design methods, as presented, for example, in
Chapters 7 and 15. This chapter covers the classical approaches to PID design, on account of the historical and practical significance of the
methods and their continued use in industry.
Table of Contents:
● PID Structure
● Empirical Tuning
● Ziegler-Nichols (Z-N) Oscillation Method
● Reaction Curve Based Methods
● Lead-pensators
● Distillation Column
● Summary
● Further Reading
PID Structure
Consider the simple SISO control loop shown in Figure .
Figure . Basic feedback control loop
The traditional expressions for PI and PID controllers can be described by their transfer functions, relating error E(s) = R(s) – Y(s) and
controller output U(s) as follows:
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