Proportional-integral-derivative λ-tuning for integrating processes with deadtime

Over the past 15 years, a number of model-based proportional-integral-derivative (PID) tuning methods have been developed for systems that can be described as integrating-with-deadtime. This was motivated by the observation that the initial open-loop response of lag-dominant processes, such as tray temperature in high-purity distillation columns, resembles that of a delayed ramp variable. This study compares the behaviour of several PID lambda-tuning rules with the Skogestad internal model control (or SIMC) proportional-integral (PI) controller on simulated integrator-plus-deadtime and lag-dominant first-order plants. Guidelines are provided for selecting the most appropriate tuning method for a given application based on the primary function of the feedback loop (servo against regulatory) as well as the relative importance of control effort and robustness. In contrast, the PID version of the Tyreus-Luyben controller, a popular strategy for this class of models, was found to yield excellent setpoint following but sluggish rejection of unmeasured disturbances acting at the plant input.