Integral-proportional derivative controller tuning rules obtained from optimum responses for set-point tracking of unstable processes with time delay

This paper introduces the design of integral–proportional derivative (I-PD) controllers for unstable first-order plus time-delay and integrating-unstable first-order plus time-delay processes. Minimization of the error based on integral performance criteria is performed to derive analytical rules using curve fitting techniques. Obtained analytical formulas may be used to determine the necessary tuning parameters of the I-PD controller from the known plant transfer function parameters. Advantages of the introduced tuning of I-PD controllers are shown by comparisons with other existing ones in terms of unit step responses, measurement noise, control signals, perturbations in plant transfer function parameters, and integral performance indices. Results have shown that some significant advantages have been achieved with the introduced tuning of I-PD controllers when compared to others in the literature.