The Ziegler-Nichols methods for tuning PID controllers

The selection of the PID controller parameters K, T[ and can be obtained using the classical control system design techniques described in Chapters 5 and 6. In the 1940s, when such tools were just being developed, Ziegler and Nichols (1942) devised two empirical methods for obtaining the controller parameters. These methods are still in use. 

The Process Reaction Method assumes that the optimum response for the closed-loop system occurs when the ratio of successive peaks, as defined by equation (3.71), is 4 1. From equation (3.71) it can be seen that this occurs when the closed-loop damping ratio has a value of 0.21. The controller parameters, as a function of R and D, to produce this response, are given in Table 4.2. 

Note that the Proeess Reaetion Method eannot be used if the open-loop step response has an overshoot, or eontains a pure integrator(s). 

The two Ziegler-Niehols PID tuning methods provide a useful rule of thumb empirieal approaeh. The eontrol system design teehniques diseussed in Chapters 5 and 6 however will generally yield better design solutions. 

Of the two teehniques, the Proeess Reaetion Method is the easiest and least disruptive to implement. In praetiee, the measurement of R and D is very subjeetive, and ean lead to errors. 

---