Of late there has been much advancement in automatic control theory. It is not easy to provide an fair analysis of an field whilst it is still developing; nevertheless, looking back on the progress of feedback control theory it is by now possible to distinguish some main trends and point out some key advances.
The era after the Second World War can be called the classical period of control theory. It was characterized by the appearance of the first textbooks (MacColl, 1945; Lauer, Lesnick, & Matdon, 1947; Brown & Campbell, 1948; Chestnut & Mayer, 1951; Truxal, 1955), and by simple design tools that provided great perception and definite solutions to design problems. These tools were employed using hand calculations, or at most slide rules, with graphical techniques.
With the dawn of the space era, controls design in the United States prevented from the frequency-domain practices of classical control theory and back to the differential equation techniques of the late 1800's, which were inherent in the time domain. The reasons for this development are as follows.
The model of classical control theory was very fitting for controls design problems during and immediately after the World Wars. The frequency-domain approach was suitable for linear time-invariant systems. It is at its best when managing single-input/single-output systems, for the graphical techniques were problematic to use with numerous inputs and outputs.
Classical controls design had some successes with nonlinear systems. ...