An Introduction to System Modeling and Control

17Robustness and Sensitivity of Feedback

Chapters 8, 9, 11, and 12 of this text make up “classical control theory”. These methods of Bode [47], Nyquist [48], and Evans [53] (root locus) were developed in the 1930s and 1940s. Most applications of these techniques were to single‐input single‐output (SISO) control loops. The statespace approach appeared in the 1960s and 1970s and is usually referred to as “modern control theory”. A great advantage of the statespace method was that it could easily deal with multi‐input multi‐output systems. However, design for robustness (i.e., good gain and phase margins) was not so manageable in the statespace. The 1980s and 1990s saw the return of the frequency domain as the Nyquist theory gives a way to measure robustness.

An alternative way to view classical control has been given by Bruce Francis [62] as follows.

The subject of this first course is classical control. That means the systems to be controlled are single‐input, single‐output and stable except possibly for a single pole at the origin, and design is done in the frequency domain, usually with Bode diagrams.

We make a slight addition to this view by letting the open‐loop system (system to be controlled) have up to two poles at the origin along with the inclusion of root locus as a usual design method. Controllers for such systems can be designed using the methods of output pole placement (Chapter 10), Bode/Nyquist (Chapter 11), root locus (Chapter 12), or the statespace (Chapters ...