PID tuning rules for SOPDT systems: review and some new results

PID controllers are widely used in industries and so many tuning rules have been proposed over the past 50 years that users are often lost in the jungle of tuning formulas. Moreover, unlike PI control, different control laws and structures of implementation further complicate the use of the PID controller. In this work, five different tuning rules are taken for study to control second-order plus dead time systems with wide ranges of damping coefficients and dead time to time constant ratios (D/tau). Four of them are based on IMC design with different types of approximations on dead time and the other on desired closed-loop specifications (i.e., specified forward transfer function). The method of handling dead time in the IMC type of design is important especially for systems with large D/tau ratios. A systematic approach was followed to evaluate the performance of controllers. The regions of applicability of suitable tuning rules are highlighted and recommendations are also given. It turns out that IMC designed with the Maclaurin series expansion type PID is a better choice for both set point and load changes for systems with D/tau greater than 1. For systems with D/tau less than 1, the desired closed-loop specification approach is favored.