Development of the analytical design method for single stage phase lead and phase lag compensators

The design of phase lead and phase lag compensators in the frequency domain, using the Bode diagram, is a commonly used method of designing control systems and is taught in many undergraduate and postgraduate courses in control engineering. The graphical trial and error procedure used may be replaced by an analytical procedure. However, the analytical approach tends to be formulated as a “black-box” approach in textbooks, without engineering insight. This paper presents the full development of the analytical design procedure. The instructional approach has been successfully used by the author over the past two academic years.