PID Tuning Method Based on IMC for Inverse-Response Second-Order Plus Dead Time Processes

This work addresses a set of tuning rules for PID controllers based on Internal Model Control (IMC) for inverse-response second-order systems with dead time. The transfer function, and some time-response characteristics for such systems are first described. Then, the IMC-based methodology is developed by using an optimization objective function that mixes performance and robustness. A correlation that minimizes the objective function and that allows the user to compute the controller's tuning parameter is found. The obtained expressions are mathematically simple, which facilitate their application in a ten-step systematic methodology. Finally, the proposed tuning method is compared to other well-known tuning rules that have been reported in literature, for a wide range of parameters of the process. The performance achieved with the proposed method is very good not only for disturbance rejection but for set-point tracking, when considering a wide-range of parameters of the process' transfer function.