Ultimate gain method

While this method is very simple it can be quite time consuming in terms of number of trials required and especially when the process dynamics are slow. In addition, it may be hazardous to experimentally force the system into unstable operation. 

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Operate with proportional control only and a step change in flowrate (set rj very high, controller 1 stepflow=l steptemp=0). Increase KP until oscillations in the response occur at KP0. Use this oscillation frequency, f0, to set the controller according to the Ultimate Gain Method (KP=0.45 KP0, rj = 1/(1.2 f0)), where f0 is the frequency of the oscillations at KP = KP0 (see Sec. 2.3.3). How high is EINT2 ... 

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 ultimate gain method is performed by the following steps. 

Figure 13.6 compares the typical response of P, PI, and PID controllers against the step change of a set-point. As can be seen, a well-tuned PID controller realizes Table 13.2 Determination of parameters of PID control by ultimate gain method. 

Determine the parameters, K, T, and Tp, in PID controller by the ultimate gain method when the ultimate gain and the oscillation cycle time, T, are 4.0 and 30 s, respectively. 

This chapter described the concept of a self-regulating process response and an integrating process response. Several methods were described for tuning a control loop while the controller is in automatic output mode. These include the trial-and-error method, the Zlegler-Nlchols ultimate gain method, and the Robbins pattern recognition methods. 

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. 

We may want to find the ultimate gain when the loci cross the imaginary axis. Again there are many ways to do it. The easiest method is to estimate with the MATLAB function rlocf ind (), which we will introduce next. 

Astrbm and Hagglund (Proceedings of the 1983 IF AC Conference, San Francisco) suggested an autotune procedure that is a very attractive technique for determining the ultimate frequency and ultimate gain. We call this method ATV (autotune variation. The acronym also stands for all-terrain vehicle which makes it easy to remember and is not completely inappropriate since ATV does provide a useful tool for the rough and rocky road of process identification. 

Simulate several first-order lag and second-order lag plus deadlime processes on a digital computer with a relay feedback. Compare the ultimate gains and frequencies obtained by the auto-tune method with the real values of cu and obtained from the transfer function. 

A few comments about the method are warranted. The controlled (dominant) variables, Ycd, should be measured such that they belong to the set Yd for rapid control. Similarly, the manipulators in the feedback control loops should belong to the set, Ud. The feedback controllers should have integral action (PI controllers). These can be tuned with minimal information (e.g., ultimate gain and frequency from a relay test). The model Ms is usually quite simple and can be developed from operating data using statistical regressions. This works because the model includes all the dominant variables of the system, Y d, as independent variables by way of their setpoints, Y. The definition of domi-... 

An alternative closed-loop approach called the relay method uses temporary narrow limits on the controller output and toggles between output limits each time the controller error changes sign. The ultimate period is determined as before and the ultimate gain is computed as Ku = 4process measurement, both in percent. 

The ATV (autotune variation) method determines the ultimate gain and period in a manner similar to the ultimate method, but ATV tests can be implemented without unduly upsetting the process. Controller settings can be calculated, and the controller can then be tuned on-line to meet the selected dynamic performance. 

In another method, called ATV (auto-tune variation), the controller is replaced by a relay of amplitude h%. The period is divided in each cycle by two up to the occurrence of oscillations. If a is the amplitude of oscillations, the ultimate gain can be calculated as ... 

The method (B. D. Tyreus and W. L. Luyben, Z EC Research 31 2625, 1992) uses the ultimate gain and the ultimate frequency The formulas for P[ and PID controllers are given in Table 3.1, and the TLC settings for the three-heated-tank process are given in Table 3.2. The performance of these settings is shown in Fig. 3.16. 

The four composition control loops each have a 5 min deadtime. They were tuned using a sequential method. Because reboiler heat input affects aU of the controlled variables fairly quickly, the Xb(x/<2r loop was tuned first with the other three controllers on manual. Relay-feedback testing was used to find the ultimate gain and period. Tyreus-Luyben tuning rules were used. Next, since reflux affects all compositions, the Xixt)IR loop was tuned using the same procedure with the Xb(j) Q loop on automatic. Then the Xs(x> loop was tuned with the two loops on automatic. Finally, the ypio(x) loop was tuned with the other three loops on automatic. Table 12.2 gives controller tuning results for aU four loops. 

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