Ziegler-Nichols closed-loop tuning method

The Ziegler-Nichols closed-loop tuning method for a PI controller is as follows ... 

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. 

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 and Nichols closed-loop method requires forcing the loop to cycle uniformly under proportional control. The natural period of the cycle—the proportional controller contributes no phase shift to alter it—is used to set the optimum integral and derivative time constants. The optimum proportional band is set relative to the undamped proportional band P , which produced the uniform oscillation. Table 8-4 lists the tuning rules for a lag-dominant process. A uniform cycle can also be forced using on/off control to cycle the manipulated variable between two limits. The period of the cycle will be close to if the cycle is symmetrical the peak-to-peak amphtude of the controlled variable divided by the difference between the output limits A, is a measure of process gain at that period and is therefore related to for the proportional cycle ... 

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. 

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 ... 

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. 

In 1942, Ziegler and Nichols [1] changed controller tuning from an art to a science by developing their open-loop step function analysis technique. They also developed a closed-loop technique, which is described in the next section on constant cycling methods. 

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