Tuning, controller Ziegler-Nichols method

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. 

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. 

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

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. 

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. 

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 ... 

The constants Kp, Kt, and Kd are settings of the instrument. When the controller is hooked up to the process, the settings appropriate to a desired quality of control depend on the inertia (capacitance) and various response times of the system, and they can be determined by field tests. The method of Ziegler and Nichols used in Example 3.1 is based on step response of a damped system and provides at least approximate values of instrument settings which can be further fine-tuned in the field. 

---