CohenCoon

CohenCoon, commonly referred to as the Cohen–Coon tuning rules, is an empirical method for setting PID controller parameters in industrial control systems. Developed to provide practical starting values for controllers, it targets processes that can be approximated by a first-order plus dead time (FOPDT) model.

The method uses a simple plant representation: Gp(s) = Kp e^{-Ls} / (Ts + 1), where Kp is the steady-state gain, L is the process dead time, and T is the time constant. These three parameters are typically estimated from a step response, known as the process reaction curve. L is taken as the delay before any output change, T is inferred from the slope of the response after the delay, and Kp is the steady-state change in output per unit input.

From Kp, L, and T, Cohen–Coon provides explicit tuning formulas to compute the gains of a PID controller. The method has separate formula sets for PID, PI, and P configurations, with the resulting gains expressed in terms of the dimensionless ratios L/T and Kp. The goal is to deliver reasonably good performance across a range of processes without extensive iteration.

Practical use and limitations: Cohen–Coon is widely taught and used as a practical starting point, especially for systems with noticeable dead time. It tends to yield aggressive settings for fast processes and more conservative ones for large dead times. However, its accuracy relies on the FOPDT approximation and it may be less suitable for higher-order, highly nonlinear, or multi-branch dynamics, where refinements via simulation or manual tuning are common.

See also: Ziegler–Nichols tuning, internal model control, process control.