Ziegler-Nichols tuning

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.

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. 

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

Equations for Calculating the Ziegler-Nichols Tuning Parameters for an Interacting Controller... 

Table 1 Continuous cycling (Ziegler-Nichols) tuning parameters...

Unlike the process reaction curve method which uses data from the open-loop response of a system, the Ziegler-Nichols tuning technique is a closed-loop procedure. It goes through the following steps ... 

For systems with transfer functions that are very difficult to factor and consequently very hard to complete the frequency response analysis, Luyben [Ref. 7] discusses various numerical solution techniques. He has also included a computer program in FORTRAN which uses the stepping technique to develop the Bode and Nyquist plots for a distillation column. More details on the philosophy of the Ziegler-Nichols tuning method can be found in the original work ... 

IV.66 Repeat Problem IV. 39 but use the Ziegler-Nichols tuning technique instead of the ISE criterion. Compare the Ziegler-Nichols settings found here with those found in Problem IV. 39. 

There are two very popular ways to control systems with inverse response the first uses a PID feedback controller with Ziegler-Nichols tuning and the second uses an inverse response compensator. 

Describe the Ziegler-Nichols tuning methodology. This procedure is often called the continuous cycling tuning method. Why ... 

The value of the gain at the limit of stability is 64. It is called the ultimate ain K . The (O at this limit is the value of the imaginary part of. Y when the roots lie right on the imaginary axis. Since the real part of s is zero, the system will show a sustained oscillation with this frequency called the ultimate frequency, in radians per time. The period of the oscillation is exactly the same as the ultimate period that we defined in Chapter 2 in the Ziegler-Nichols tuning method... 

The TC2 temperature controller is tuned at the low-flow conditions since this is where it is active. Ziegler-Nichols tuning is used so that the tightest possible temperature control is achieved. Base and reflux-drum level controllers are proportional with Kq = 2. 

Zeolite catalyst, 4 Zeroing instruments, 510 Ziegler-Nichols tuning method, 509... 

Blickley, G. J., Modern Control Started with Ziegler-Nichols Tuning, Control Eng., 38 (10), 11 (1990). 

Compare the results of using both the ATV and Ziegler-Nichols tuning techniques. 

The developed control system exhibited good performance in all the tested conditions however, it was necessary to perform a more rational choice of the controller parameters so as to obtain improved closed-loop responses of the present membrane system. The Ziegler-Nichols tuning technique was initially used. The value of the proportional gain providing an oscillatory response was equal to 4.508, whereas the oscillation period... 

Table 16.1 Settings of both PI and PID controllers calculated by the Ziegler-Nichols tuning rule...

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