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asp net display barcode h = rnl(PO  Pl) = rnn(P1  Pz) = m1m(po  Pz) ml + m2 in Visual Studio .NET
h = rnl(PO  Pl) = rnn(P1  Pz) = m1m(po  Pz) ml + m2 QRCode Reader In VS .NET Using Barcode Control SDK for .NET framework Control to generate, create, read, scan barcode image in Visual Studio .NET applications. QRCode Encoder In .NET Using Barcode printer for VS .NET Control to generate, create QR Code image in .NET applications. (7.2) Decoding Quick Response Code In .NET Framework Using Barcode reader for .NET framework Control to read, scan read, scan image in Visual Studio .NET applications. Bar Code Generator In VS .NET Using Barcode printer for .NET framework Control to generate, create barcode image in .NET applications. The gain with both loops open is the partial derivative in terms of m: c3h am 1 nl2 = m&h7  7d ml + m2 Barcode Reader In Visual Studio .NET Using Barcode recognizer for VS .NET Control to read, scan read, scan image in VS .NET applications. QR Code 2d Barcode Creation In C# Using Barcode generator for VS .NET Control to generate, create QR image in Visual Studio .NET applications. m;Iy(y $ = (PO  P2) (*2)2 QR Code 2d Barcode Creator In .NET Framework Using Barcode drawer for ASP.NET Control to generate, create QR image in ASP.NET applications. QR Code ISO/IEC18004 Encoder In VB.NET Using Barcode printer for Visual Studio .NET Control to generate, create QRCode image in .NET applications. (7.3) The gain with the pressure loop closed is in terms of p,: Generating Code128 In .NET Using Barcode maker for VS .NET Control to generate, create Code128 image in .NET applications. Matrix Barcode Generation In .NET Using Barcode creation for Visual Studio .NET Control to generate, create Matrix Barcode image in Visual Studio .NET applications. 1 = PO  P l = (PO  Pz) (Aam1 p ah
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The resulting matrix is: hp
PO  Pl Pl  pz PO  Pz PO  pz Pl  Pz PO  Pl ~ ~ IPO  Pz po  p2
(7.7) Choice of particular cm pairs for this application depends on the pressure distribution. The matris indicates that the valve with the greater pressure drop is better for flow control. But if p, is midway between po and pi, all elements in the matrix are 0.5, so it does not matter which pairs are chosen. Multivariable Process Control 1
The sum of each row and each column is unitythis is one of the features of the relativegain matrix. In a 2 by 2 matrix such as (7.7), it is only necessary to solve for one element, the others being equal or complementary. example 7.4
Another common twoloop process is the blending system shown in Fig. 7.4. Two streams, X and Y, are blended to a specified total flow F of composition 2. Let the flow of stream X be designated ml and the flow of stream Y be m2. The following equations describe the process: F=ml+m2=~= X ml _ im
l  x ml =l!l$ F
(7.8) (7.9) Only one element of the matrix need be found: (7.10) (7.11) The matrix then takes on the appearance: gg+
(7.12) For values of x less than 0.5, m, should be used for composition control and m2 for flow control. There is no limit to the number of variables that can be displayed by a matrix, although some difficulties may be encountered in making the differentiations. To this extent, an analog computer would be helpful. Or a numerical solution may be found by incrementing each manipulated variable, although general solutions like those above have more value. Instead of using mathematical models, as was done here, an existing plant may be tested to generate a matrix of gains. This requires a series FIG 7.4. A typical twocomponent blending system in which both total flow and composition are to be controlled. 1Multipleloop Systems
of openloop tests, in which ml is first incremented and changes in all the controlled variables observed. Then openloop gains (Ac,/Am,),, and so on, can be calculated. The other manipulated variables are then incremented and their effects calculated in the same manner. Fortunately it is not necessary to make closedloop tests to determine (Ac,/A&, since enough data have already been gathered. AIatrix manipulation can do the rest. Let the values of (ACi/Amj), be arrayed in a matrix identified as M. A complementary matrix C, of elements (AVtj/ACi),, can be generated by inverting, then transposing matrix M : C = (M )T (7.13) Rules for performing this operation can be found in reference (5) and in most texts on modern algebra. Finally, each relativegain term Xij is found by wcultiplying each element in matrix M by its corresponding element in the complementary matrix C. It is also possible to prepare a matrix of relative gains from the elements (ACi/Amj), alone. The procedure is the same as that described by Eq. (7.13), except that the elements of matrix M are inverted, i.e., they appear as (A nj/Aci),. Coupling
Whenever a single manipulated variable can significantly affect, two or more controlled variables, the latter are said to be coupled. This interaction between control loops can be troublesome. Some variables are difficult enough to control without being subject to upsets from other loops. For this reason, proposed composition loops should always be examined for evidence of coupling. When the gain matrix contains numbers approaching 1 and 0, the loops will be largely independent. But values approaching 0.5 indicate a strong mutual coupling. To gain an appreciation of the effects of coupling, consider the pressureflow system of Fig. 7.3. Let p, be midway between p, and p2, so that all elements in the gain matrix equal 0.5. The flow cont roller will manipul a t e m2. With the pressure controller in manual, the flow controller could be adjusted as if it were alone, i.e., as if there were no coupling. And, in fact, there would be no coupling because only one loop is closed. But under these circumstances, any change in po, pz, or flow would affect pl. Next, think of the pressure controller being in automatic, but with a wide band and long reseti.e., very loose settings. But should the set point of the flow controller be changed, pressure will be upset nearly as much as when its loop was open. The pressure error will eventually be

