Ziegler Nichols

Table 4.2 Ziegler-Nichols PID parameters using the Proeess Reaetion Method...

Figure 2.34. Process reaction curve for the Ziegler-Nichols Method.

Obtain the process reaction curve for the process with disconnected controller, as explained in Sec. 2.3.3. Analyse this curve to obtain the parameters for the Ziegler-Nichols Method. Use Table 2.2 to obtain the best controller settings for P and PI control. Try these out in a simulation. 

Figure 6.2. Illustration of fitting Eq. (6-2, solid curve) to open-loop step test data representative of self-regulating and multi-capacity processes (dotted curve). The time constant estimation shown here is based on the initial slope and a visual estimation of dead time. The Ziegler-Nichols tuning relation (Table 6.1) also uses the slope through the inflection point of the data (not shown). Alternative estimation methods are provided on our Web Support.

Using the first order with dead time function, we can go ahead and determine the controller settings with empirical tuning relations. The most common ones are the Ziegler-Nichols relations. In process unit operation applications, we can also use the Cohen and Coon or the Ciancone and Marlin relations. These relations are listed in the Table of Tuning Relations (Table 6.1). 

B. Tuning relations based on closed-loop testing and the Ziegler-Nichols ultimate-gain (cycle) method with given ultimate proportional gain Kcu and ultimate period Tu. 

MATLAB calculation details and plots can be found on our Web Support. You should observe that Cohen-Coon and Ziegler-Nichols tuning relations lead to roughly 74% and 64% overshoot, respectively, which are more significant than what we expect with a quarter decay ratio criterion. 

Cohen-Coon Ziegler-Nichols Ciacone-Marlin Apply empirical design relations. 

Ziegler-Nichols Continuous Cycling (empirical tuning with closed loop test) Increase proportional gain of only a proportional controller until system sustains oscillation. Measure ultimate gain and ultimate period. Apply empirical design relations. 

We have yet to tackle the PI controller. There are, of course, different ways to find a good integral time constant. With frequency response, we have the handy tool of the Ziegler-Nichols ultimate cycle tuning relations. So with Kcu = 60 and cocg = 3.3 rad/min, we find by referring to... 

Using the Ziegler-Nichols tuning parameters, we repeat the proportional controller system Bode plot ... 

Ultimate gain and ultimate period (Pu = 2tt/(0u) that can be used in the Ziegler-Nichols continuous cycling relations. Result on ultimate gain is consistent with the Routh array analysis. Limited to relatively simple systems. 

To use the Ziegler-Nichols rules, it is necessary to plot the open-loop Bode diagram without the controller. All other transfer functions are assumed to be unity. 

From the overall ft plots, at ft = —180°, a>co = 1.3 radians/min and the corresponding value of AR = 0.123. By the Ziegler-Nichols procedure, this means that ... 

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