Time-domain based design and analysis of new PID tuning rules

The time domain PID analysis includes three types of first-order plus time delay (FOPTD) models: (a) zero or negligible time delay (b) low to medium long time delay and (c) very long time delay. The first part of the analysis proves that the optimum PID controller for plants having negligible time delay is a PI controller, and the corresponding PI terms based on the actuator's capacity and set-point overshoot are explicitly derived. For low to medium time delay problems, a new PID tuning scheme is then developed. The proposed tuning rule is capable of accommodating the actuator's saturation and therefore has the ability to select an optimum PID controller. By using a separate time response analysis, a new PI tuning scheme for large normalised time delay is then derived. Numerical studies are made for higher-order processes having monotonic open-loop characteristics. The performance is compared with other commonly available tuning rules. With new tuning rules, better performance is observed and the rules have the capability to cover time delays ranging from zero to any higher value.