barcode reader using c#.net FIGURE 18-24 Control system. in Software

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FIGURE 18-24 Control system.
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the disturbance will not break through and appear at C until 7~ units of time elapse. Up to time ro. no control action occurs, with the result that the overall closedloop response will be sluggish and generally unsatisfactory. To overcome this difficulty, Smith suggested that G&) be modeled according to Eq. (18.13) and that additional feedback paths be inserted into Fig. 18.24 as shown in Fig. 18.2%. If Gp(s) is modeled exactly by Eq. (18.13), a close study of Fig. 18.25a shows that the signals entering comparator A will be identical; as a result, the signals cancel and cause the output of comparator A to be zero. The net effect is to completely eliminate the outer feedback path; this simplification is shown in Fig. 18.258. The system of Fig. 18.25b is now much easier to control because the transport Iag is not present in the loop. Of course, in the real system the transport lag is still present; we have eliminated it in a mathematical sense from the feedback path by the additional feedback paths of Fig. 18.25~ and the assumption that the process transfer function, Gp(s) can be modeled exactly as shown in Eq. (18.13). To achieve the simplification suggested by Fig. 18.25b we must now face reality and realize that the signal Ct in Fig. 18.25b is not available to feed back. Only the signal C can be measured and fed back to the controller. In terms of controller hardware implementation, the diagram of Fig. 18.25~ is redrawn in Fig. 18.26~ to show which portion of the diagram will be implemented with controller hardware. Figure I8.26b, which is another way to represent Fig. 18.26a, is a form sometimes presented in the literature for dead-time compensation. The reader may legitimately ask whether or not hardware exists to actuahy implement what is shown within the dotted lines in Fig. 18.26. Until the appearance
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(a) Dead-time compensation (Smith predictor) block diagram; (b) Equivalent diagram for part (a) when GP = G(s)e-ws.
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of microprocessor-based controllers, the answer was no. However, today many commercially available controllers provide dead-time [exp(-TgS)] and G(s) in the form of a first-order lag [l/(~s + l)]. Features such as these will be discussed in Chap. 35. The recommended procedure for applying dead-time compensation is as follows: 1. By means of an open-loop test of the process, model Gp(s) by the transfer function 1 -e -TDS 7s + 1 In this step, we have chosen G(s) of Fig. 18.26~ to be first-order. Many processes in chemical engineering can be modeled by a first-order lag with dead-time. 2. By means of appropriate hardware, implement the controller portion of Fig.
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FIGURE 18-26 Hatdwanz implementation of dead-time compensation.
PROCESS
APPLICATIONS
18.26~~ or Fig. 18.26b. If G,(s) can be exactly modeled by a first-order process with dead-time, the response of the control system in Fig. 18.26 will be equivalent to the response obtained for the system in Fig. 18.2% in which the loop involves the control of a first-order process. In most practical situations, there will be some mismatch between GJs) and its model of first-order with dead-time. The greater the mismatch, the greater the deterioration in control response from the ideal situation of Fig. 18.256. The application of the deadtime compensation technique and the effect of mismatch between Gp(s) and its model will be illustrated in the next example.
Example 18.4. Dead-time compensation. Consider the control system shown in Fig. 18.27 in which the process is fourth-order; thus 4
In a practical situation, we would not know the transfer function of the process. In this example, we have taken the process model to be fourth-order to provide a system sufficiently complex to show considerable transfer lag. One can show for the system in Fig. 18.27 that the ultimate gain and the corresponding period are: K,, = 4.0 and P, = 27~. Using the Ziegler-Nichols rules, one gets K, = 2.0. The response for a unit-step change in set point for K, = 2 is shown in Curve I of Fig. 18.29. Notice that the decay ratio is about
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