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the process gain: P Gp = rijamz
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Since these tests are made only at one operating point, they will not disclose any nonlinear properties. Closed-loop response should be observed at other flow conditions to detect any change in damping. If the period changes with flow, a variable dynamic element is present. A n extremely nonlinear measurement, such as pH, is identified by the distorted waveform it produces, as in Fig. 2.13. A less severe nonlinear measurement may not be detected without changing the set point. In short, if a thorough analysis is to be made, the closed-loop test should be repeated at other values of flow and set point.
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Testing a Neutralization Process
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This is an actual case history of t,he process upon which this test procedure was first tried. It was a neutralization process in which a reagent was being added to bring the effluent leaving a reactor to pH 7. The pH controller was in manual, simply because aut,omatic control was unsatisfactory. The open-loop test gave a dead time of 40 sec. The volume of the sample piping divided by the sample flow was 15 sec. The remainder was probably distributed through the reactor and associated piping. With a proportional band of 150 percent, the loop sustained uniform oscillation of 2.8-min period. The ratio T,/T~ = 2.8/0.67, or 4.2, indicated essentially a single capacity along with the measured dead time. The reaction vessel contained 200 gal of material, flowing at 2.5 gpm. Therefore V/F = 200/2..5, or 80 min. The dynamic gain of an SO-min capacity at a 2.8-min period is G1 = & = 0.004 P Yet the proportional band for zero damping was 150 percent. This can mean only one thing-extremely high process gain. Dividing Gl int o P/100 yields the gain product of valve, process, and transmitter: 150 G,G,G = 1oo(o,oo4) = 3 7 5 Again the familiar problem of the pH curve appears:: high gain near the control point, low gain elsewhere. But, the situation could be helped. licpiping the sample line reduced it#s dead t,imc to 5 set , bringing the This reduced t,he period to 2 1 min and the total dead time t,o 30 see. proportional band by the same fac%or of Ti. So the controller was
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Characteristics of Real Processes
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adjusted for damping at the new conditions. (A procedure for adjusting three-mode controllers is described in Chap. 1.) A later observation revealed that the loop had become more heavily damped. The only noticeable change since the controller xrs adjusted was a lower value of output. The loop gain apparently had decreased kith load. An inquiry about the valve c~hnracteristic produced the answer: reagent was being delivered through an equal-percentage valve under constant pressure drop. The loop gain therefore varied directly wit h flow, as did the valve gain. Although a pH process is nonlinear, its characteristic curve cannot be corrected with an equal-percentage valve, because the valve acts on the output of the controller, not on the input.4 The valve chnrncteristic, in fact, made matters worse. Sot only did the loop gain beconle variable, but it was higher than it n-ould have been with an cquivnlcnt linear valve. The gain of an equal-percentage valve is four times the fractional flop; fractional flow in excess of O.T,j Tvill cause the gain to exceed unity. If the normal flow is 50 percent of the valve s cxpncGty, the eclual-percentnge characteristic will contribute twice the gain of a linear valve. This necessitates a proportional band twice as wide. The time required to test this process at one operating point K:M 0111~ a few minutes. Yet together with known facts about the plant, and one subsequent observation, the prowss WIS thoroughly dctined and two rcc ommerld:LtioIls made to improve control. .Any other test procedure would have taken longer and might not h:lw :lc*hievrd c~omparnble results.
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