PID controller design with time response specifications

This paper considers the problem of determining a set of stabilizing proportional-integral-derivative (PID) controller gains, for a given linear time invariant plant that meets or exceeds closed loop step response specifications. The method utilizes two recent results: for a given system, (1) finding a set of stabilizing PID gains for a given system and (2) the relationship between time response (overshoot and speed) and the coefficients of the characteristic polynomial. The method allows us to extract a subject of PID gains that meets stability as well as time domain performance requirements. The computations involved are the intersections of two-dimensional sets described by linear and quadratic inequalities in the controller design space. It is illustrated by examples.