6.3 Tuning Rules for First-Order + Dead Time Processes

The previous tuning rules were based on tests that forced a process into a continuous oscillation. Obvious disadvantages to the techniques are that the system is forced to the edge of instability, and it may take a while to iteratively adjust the controller to obtain a continuous oscillation. In this section we present tuning rules based on process models that have been obtained through the open-loop step tests presented in Chapter 4.

Ziegler-Nichols Open-Loop Method

Ziegler and Nichols also proposed tuning parameters for a process that has been identified as integrator + time-delay based on an open-loop process step response,

Since first-order + time-delay processes have a maximum slope of k = k_p/t_p at t = q for a unit step input change, these same rules can be used for first-order + time-delay processes,

Their recommended tuning parameters, which should give roughly quarter-wave damping, are shown in Table 6-3. We see a potential problem for systems with a low time-delay/time-constant ratio, since this causes the proportional gain to become very large. Similarly, the integral time tends to be low, causing oscillatory behavior.

Cohen-Coon Parameters

The method developed by Cohen and Coon (1953) is based on a first-order + time-delay process model. A set of tuning parameters was empirically developed to yield a closed-loop response with a decay ratio of 1/4 (similar to the Ziegler-Nichols methods). The tuning parameters as a function of the model parameters are shown in Table 6-4.

A major problem with the Cohen-Coon parameters is that they tend not to be very robust; that is, a small change in the process parameters can cause the closed-loop system to become unstable.

Table 6-3. Ziegler-Nichols Open-Loop Tuning Parameters

Controller type	kc	tI	tD
P-only		—	—
PI		3.3q	—
PID		2q	0.5q

Table 6-4. Cohen-Coon Tuning Parameters

Controller type	kc	tI	tD
P-only		—	—
PI			—
PID