Ziegler-Nichols Tuning Method

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 ... 

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... 

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

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.

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 ... 

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

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. 

The method should be viewed in the same light as the classical SISO Ziegler-Nichols method. It gives reasonable settings which provide a starting point for further tuning and a benchmark for comparative studies. 

A key to the successful application of a PID control is the tuning of parameters, Xp, Tp and Tp in Equation 13.5. To tune them properly, the Ziegler-Nichols method is used, which includes an ultimate-gain method and a step-response method. 

The tuning settings based on the process reaction curves obtained by the open-loop tuning method, in addition to the Ziegler-Nichols method (Table 2.38), can also be selected by other methods. Figure 2.39 compares the load responses and Figure 2.40 compares the set point responses of these methods. 

In Section 16.5 we discussed a tuning method based on the process reaction curve. The method is primarily experimental and uses real process data from the system s response. In this section we discuss an alternative method developed by Ziegler and Nichols, which is based on frequency response analysis. 

Example 18.4 Controller Tuning by the Ziegler-Nichols and Cohen-Coon Methods... 

One good feature of the Ziegler-Nichols closed-loop method is that it can be learned more quickly than starting with trial and error alone. There is a procedure to be followed, and the pattern of sustained cycling is easy to recognize. The Ziegler-Nichols method is often completely acceptable for tuning control loops that respond quickly, for example, liquid flow rate control loops that respond with an ultimate peak-to-peak time period (UTP) of 5 to 15 s. 

The two previous tuning techniques require a reasonably detailed control-loop analysis. In practice, many controllers are tuned by trial-and-error methods based on process experience. Both the Ziegler-Nichols method and the reaction-curve method are based on the assumption that the disturbances enter the process at one particular point. These methods, therefore, do not always give satisfactory results. In these cases, the final adjustments must be made by trial-and-error search methods. 

If not, the gains maybe experimentally tuned using, for instance, the Ziegler-Nichols method (Frankhn,... 

Automatic tuning needs identify the dynamics of a certain process. Usually Relay was mainly used as an amplifier in the fifties and the relay feedback was applied to adaptive control in the sixties. The exciting to a process loop make it reach the critical point. The critical point, i.e, the process frequency response of the phase lag of pi(it),has been employed to set the PID parameters for many years since the advent of the Ziegler-Nichols(Z-N) rule. From then several modified identification methods are... 

Because a proportional only controller will never reach SP, the quarter decay is determined with respect to the steady state condition. The reciprocal of the coefficient, in this case the reciprocal of 0.5, is known as the gain margin. It is the factor by which the controller gain can be increased before the controller becomes unstable. A proportional only controller tuned according to the Ziegler-Nichols method will therefore have a gain margin of 2. 

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