Basic Math for Process Control

In Chapter 8, which deals with frequency response analysis, the point was made that attempting to obtain frequency response data on actual operating equipment was impractical. Process operators would not allow their equipment to be upset with sine wave disturbances over a lengthy time period, when their job was to ensure production and safe operations.
Nonetheless, the dynamic behavior of most operating equipment cannot be predicted by sitting in front of one's computer and applying theory. Real life operating equipment often consists of multiple time constants, with some dead time thrown in. The only way to get at the dynamic characteristics is with a field test. The question then becomes: Can a field test be devised that would be acceptable to plant operating people and would also yield the required information?
J.G. Ziegler, during his career as a control systems engineer with the Taylor Instrument Companies, answered this question and made a significant contribution to control systems analysis. His method has come to be called the Ziegler Nichols approximation, or for short, the Z N approximation.
The events that led up to the Z N approximation are interesting and deserve some space. During the late 1930s and early 1940s, there was no ISA The Instrumentation, Systems, and Automation Society. In the United States, any technical work on control systems that was felt to be noteworthy was made public through accredited professional societies such as the American Society of Mechanical Engineers or the American Institute of Chemical Engineers, at their national or...