Control system design using low order controllers: constant gain, PI and PID

Considers the problem of designing low order controllers for linear time-invariant plants. Specific controller structures considered are the constant gain, the proportional-integral (PI) and the proportional-integral-derivative (PID). Utilizing the characterization of all stabilizing constant gain, PI and PID controllers obtained in Ho et al. (1996) and their companion paper, a computer-aided search over the space of stabilizing controller parameter values is conducted to determine fixed order controllers that satisfy given design objectives. Both frequency domain performance measures such as the H_∞ or H₂ norms, as well as time-domain performance measures such as settling time and overshoot to a unit step are considered. Simple examples used in this paper show that the earlier results on stabilization using a fixed order controller can form the basis for carrying out optimal designs while keeping the controller order fixed. The results here should have a widespread impact on industrial applications of control theory