Ziegler-Nichols 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. 

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. 

Figure 8 Standing oscillations in Continuous Cycling (Ziegler-Nichols) method...

Rules oiThumh/ 3. 3. 2 On-Line Trial antlError / 3.3.3 Ziegler-Nichols Method / 3.3.4 Tyreus- Luyhen Method... 

For optimal adaption of the controller to the control circuit, the behavior of both must be known. Random adjustment of all three parameters is generally not successful. A series of methods are available for determining favorable control parameters [e.g., Ziegler-Nichols method 1. operate the circuit with a pure P controller (T —> oo, Ty = 0), 2. reduce Xp until the control circuit undergoes continuous oscillations], whereby on the basis of targeted adjustments and the resulting reaction of the control circuit, the correct setting of the controller can be found. Some other practical tips (Table 2.8-1) follow ... 

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,... 

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. 

The most well-known tuning guidelines that make use of these concepts are the Ziegler Nichols method and the Cohen-Coon method. There are also other controller tuning guidelines, such as dead-beat tuning and Internal Model Control tuning. It is beyond the scope of this chapter to discuss the last two methods. 

Ziegler-Nichols method, 221,223 Ziegler-Nichols settings, 224 zone control, 399 zone rules, 418 z-transform... 

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