PID controller tuning for desired closed‐loop responses for SI/SO systems

TLDR

Two‑degree‑of‑freedom PID controllers are essential for unstable processes and can significantly improve dynamic performance over single‑degree‑of‑freedom controllers for stable processes when disturbances enter through the process. The study proposes a new design method for two‑degree‑of‑freedom PID controllers. PID parameters are derived by approximating the IMC controller’s feedback form with a Maclaurin series in the Laplace variable, and the method extends to a two‑degree‑of‑freedom controller design. The resulting PID parameters yield closed‑loop responses closer to desired targets than other tuning methods, with the advantage growing as process dead time increases.

Abstract

Abstract Proportional, integral, and derivative (PID) parameters are obtained for general process models by approximating the feedback form of an IMC controller with a Maclaurin series in the Laplace variable. These PID parameters yield closed‐loop responses that are closer to the desired responses than those obtained by PID controllers tuned by other methods. The improvement in closed‐loop control peformance becomes more prominent as the dead time of the process model increases. A new design method for two degree of freedom controllers is also proposed. Such controllers are essential for unstable processes and provide significantly improved dynamic performance ouer single degree of freedom controllers for stable processes when the disturbances enter through the process.