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PRECAUTIONS TO TAKE IN APPLYING THE Z-N METHOD. Some discussion
is needed to avoid some pitfalls in applying step 2 of the Z-N method to obtain K cu and P, . These precautions are concerned with the type and size of the disturbance that induces the response and with the avoidance of using a limit cycle as the indication that the system is on the threshold of instability. The simplest way to introduce a disturbance is to move the set point away from the control variable for a short time and then return the set point to its original value. This procedure, which is equivalent to introducing a pulse function in the error, causes the system to respond and yet stay within a narrow band surrounding the normal operating point of the process. An alternate type of disturbance would be to introduce a small step change in set point. If step changes in set point are used to induce transients, the successive step changes should alternate around the normal operating point of the process. It is also important to make the disturbance as small as possible, especially as the gain of the controller is increased, so that the valve and other components do not exceed their physical limits. When the valve moves to its limits during a closed-loop transient, we say that the valve saturates. Under these conditions, a sustained oscillation occurs, which is called a limit cycle. The limit cycle that is caused by saturation is a nonlinear phenomenon, which will be covered in Chap. 33 on nonlinear control. If a limit cycle occurs, the gain that produces it and the period of the cycle should not be used in the Ziegler-Nichols rules. Since the limit cycle will appear to the observer to be the same as a sustained oscillation when the system is on the verge of instability, the novice will often mistakenly use the information derived from the limit cycle (controller gain and period) to obtain controller settings. A simple way to know if one has a limit cycle is to observe the swing in pressure to the valve. If the limits of the valve (e.g., 3 psi to 15 psi) are reached repeatedly during the oscillatory response, one has a limit cycle and the controller gain and period should not be used to determine controller settings. It is for this reason step 2 states that K, should be increased in small steps until the response first exhibits a sustained oscillation. To appreciate the use of step 2 of the tuning method, one should have some laboratory experience in tuning a real process, or at least a computer simulation of a process. The experienced operator can develop some short cuts to finding the ultimate gain and ultimate period.
PROCESS
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Cohen and Coon Rules (C-C)
The next method of tuning to be discussed is an open-loop method, in which the control action is removed from the controller by placing it in manual mode and an open-loop transient is induced by a step change in the signal to the valve. This method was proposed by Cohen and Coon (1953) and is often used as an alternative to the Z-N method. Figure 19.3 shows a typical control loop in which the control action is removed and the loop opened for the purpose of introducing a step change (M/s) to the valve. The step response is recorded at the output of the measuring element. The step change to the valve is conveniently provided by the output from the controller, which is in manual mode. The response of the system (including the valve, process, and measuring element) is called the process reaction curve; a typical process reaction curve exhibits an S-shape as shown in Fig. 19.4. After presenting the Cohen and Coon method of tuning, the basis for their recommendations will be discussed. The C-C method is summarized in the following steps:
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