A tuning scheme for proportional-and-derivative controllers

A simple way of tuning usual proportional-and-derivative (PD) controllers is presented. The tuning is devised so that the closed-loop system has a speed of response near that of time-optimal bang-bang control during a large portion of the transient period. When the system is near the desired equilibrium it behaves linearly, and thus avoids the problem of being overly sensitive to the disturbances and noise. The idea is rather intuitive. Unlike dual-mode control, the plant is controlled throughout by a PD controller. Numerical results are included.