Analysis and simple design using the Nichols chart

Abstract

In previous chapters on Bode plot design, we met a class of control design problems which were based on manipulating the open-loop transfer function characteristics to achieve some desired closed-loop performance. For example, we adjusted the open-loop phase to improve the closed-loop system stability margins. We then have to form the closed-loop transfer function and check whether the open-loop control design meets the design specification. Hence there is a need to establish a relationship between the open-loop characteristics, G_OL(jω), and the closed-loop characteristics, G_CL(jω), in our control design problems. In many cases we have complicated models or sets of frequency response data and the problems of manipulating unwieldy transfer functions or frequency response data files are not easy. However, control design packages like MATLAB make the calculation of response information as simple as typing

$$gcl = gol/\left( {1 + gol} \right);$$

where gol and gcl are the open and closed-loop transfer functions respectively. However, traditionally the problem of gaining closed-loop information easily was solved by using a Nichols chart. The Nichols chart is still part of control design packages, since it gives valuable information by graphically relating open-loop and closed-loop information on one plot. We find that Nichols charts are less commonly used than the Bode plot techniques we have been dealing with, but particular industries, such as the aerospace industry, often use Nichols charts to a greater degree. We present here an introduction to the Nichols chart and give several examples of simple design.