Ziegler-Nichols method controller

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. 

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. 

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. 

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... 

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

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... 

In this section, we decide on exactly which two frequencies to use in Equations (6.52)-(6.54) in order to solve for the PID controller parameters. Our ultimate objective is to produce a PID controller that achieves a close match between the actual and desired closed-loop performemce in the time domain. Which frequencies to use for PID design has been and remains an interesting question. The well-known Ziegler-Nichols frequency response PID tuning method is based on the crossover frequency of the process. However, we have found that, although the crossover frequency is very important from a stability point of view, lower frequencies are far more important from a closed-loop performance point of view. 

The Ziegler and Nichols method is difficult to apply in a plant environment, since no process operator would allow a control loop to oscillate. 

When tuning using the Ziegler-Nichols closed-loop method, values for proportional, integral, and derivative controller parameters may be determined from the ultimate period and ultimate gain. These are determined by disturbing the closed-loop system and using the disturbance response to extract the values of these constants. 

The following is a step-by-step approach to using the Ziegler-Nichols closed-loop method for controller tuning ... 

The Ziegler-Nichols process reaction curve tuning method for a PI controller is as... 

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