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barcode reading in asp.net After the process reaches steady state at the normal level of operation, switch in Software
1. After the process reaches steady state at the normal level of operation, switch Code 128C Decoder In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Code 128 Code Set A Creator In None Using Barcode printer for Software Control to generate, create Code 128 Code Set B image in Software applications. the controller to manual. In a modem controller, the controller output will remain at the same value after switching as it had before switching. (This is called bumpless transfer.) 2. With the controller in manual, introduce a small step change in the controller output that goes to the valve and record the transient, which is the process reaction curve (Fig. 19.4). 3. Draw a straight line tangent to the curve at the point of inflection, as shown in Fig. 19.4. The intersection of the tangent line with the time axis is the apparent transport lag (Td); the apparent firstorder time constant (7) is obtained from Code128 Scanner In None Using Barcode scanner for Software Control to read, scan read, scan image in Software applications. Code128 Maker In Visual C#.NET Using Barcode maker for .NET framework Control to generate, create Code 128 Code Set B image in .NET framework applications. T = B,IS
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Generate EAN / UCC  13 In Java Using Barcode creator for BIRT reports Control to generate, create GS1128 image in BIRT reports applications. EAN 128 Maker In ObjectiveC Using Barcode creator for iPad Control to generate, create USS128 image in iPad applications. (19.5) Encoding EAN13 Supplement 5 In ObjectiveC Using Barcode generator for iPad Control to generate, create GTIN  13 image in iPad applications. Reading Data Matrix 2d Barcode In Visual C#.NET Using Barcode scanner for .NET Control to read, scan read, scan image in .NET applications. FIGURE 193 Block diagram of a control loop for measurement of the process reaction curve.
Making EAN 13 In None Using Barcode generation for Font Control to generate, create EAN / UCC  13 image in Font applications. Data Matrix 2d Barcode Decoder In Java Using Barcode decoder for Java Control to read, scan read, scan image in Java applications. CONTROLLER
TUNING
PROCESS
IDENTIFICATION
FIGURE 194 Ifrpical process reaction curve showing graphical construction to determine firstorder with transport lag model. input
4. Using the values of K,, T, and Td from step 3, the controller settings are found from the relations given in Table 19.2. Notice in Table 19.2 that all of the controller settings are a function of the dimensionless group Td/T, the ratio of the apparent transport lag to the apparent time constant. Also K, is inversely proportional to K,. TABLE 19.2
CohenCoon controller settings
Qpe of control Proportional (P) Proportionalintegral (PI) Parameter setting
71 = Td
Proportionalderivative (PD) 30+ 3TdfT 9+2OTd/T
70 = Td
Proportionalintegralderivative (PID) 6 2TJT 22+ 3Td/T
71 = Td TD = T, 32+6Td/T 13 +&'d/T 4 11 + Z Td/T
PROCESS
APPLICATIONS
The rationale for the CC tuning method begins with the representation of the Sshaped process reaction curve by a firstorder with transport lag model; thus (19.6) Using the system expressed by Eq. (19.6)) Cohen and Coon obtained by theoretical means the controller settings given in Table 19.2. Their computations required that the response have $ decay ratio, minimum offset, minimum area under the loadresponse curve, and other favorable properties. In applying the CC tuning method, an important task is the graphical construction, shown in Fig. 19.4, which reduces the process reaction curve to the firstorder with the transport lag model given by Eq. (19.6). To understand the basis for the graphical procedure, consider the response of the transfer function of Eq. (19.6) to a step change in input; the resulting transient is shown in Fig. 19.5. After t = Td, the response is a firstorder response. The point of inflection of the curve in Fig. 19.5 occurs at t = Td and the slope of the tangent line at this point is related to the time constant by the relation: S = B,IT
Solving for T gives the expression in Eq. (19.4). The response after t = Td, shown in Fig. 19.5, was also presented in Fig. 5.6. The attempt to model the process reaction curve by the method shown in Fig. 19.4 is crude and does not give a very good fit. Finding the point of inflection and drawing a tangent line at this point is quite difficult, especially if the data for the process reaction curve are not accurate and if they scatter. A better method for fitting the process reaction curve to a firstorder with transport lag model is to perform a leastsquare fit of the data. The disadvantage to this fitting procedure is the time and effort required. An example to be presented later will study the effect of the type of model fitting procedure on the selection of controller parameters. f& m  _. Tangent line, slope = !$
FIGURE 195 Step response for a firstorder with transport lag model.
CONTROLLER TUNING AND PROCESS IDENTIFICATION
More recently, Lopez et al. (1967) studied the tuning of controllers with errorintegral criteria for the firstorder with transport lag model of Eq. (19.6). The errorintegral criteria that they considered were ISE, IAE, and ITAE. In their work, a search procedure was used to find the controller parameters that minimized each particular figure of merit. Their results, developed for Td/T varying from 0 to 1.0, were presented in graphical form and as empirical equations that were fitted to their graphical results. Their results, which can be considered as a variation of the CC tuning method, were not compared with the CC method. The interested reader may wish to compare the method of Cohen and Coon and the method of Lopez et al. as a project. To illustrate the two methods of controller tuning just presented, the system shown in Fig. 19.1 was simulated by use of a computer program called TUTSIM. (This simulation software is described in Chap. 35.) Table 19.3 gives the values of the controller parameters obtained by applying each tuning method; Figure 19.6 shows the resulting transients. Since the ZN method does not give a rule for a PD controller, the settings listed for a PD controller udder the ZN heading of Table 19.3 were obtained by using a theoretical frequency response calculation in which the design was based on 30 phase margin and a maximum K,. No general conclusions can be made about the relative merits of the two tuning methods from the results shown in Fig. 19.6, since these results apply to one specific example. About all that can be said is that for this specific example, both methods give reasonable first guesses of the control parameters.

