barcode reader project in c#.net Integral Control in Software

Painting Code 128 Code Set A in Software Integral Control

Integral Control
Code 128 Recognizer In None
Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications.
Generating Code 128C In None
Using Barcode generation for Software Control to generate, create Code 128 Code Set B image in Software applications.
A considerable improvement may be obtained over the proportional control system by adding integral control. The controller is now instructed to change the heat input by an additional amount proportional to the time integral of the error. Quantitatively, the heat input function is to follow the relation
Decoding Code 128 Code Set B In None
Using Barcode recognizer for Software Control to read, scan read, scan image in Software applications.
Code 128B Encoder In Visual C#.NET
Using Barcode generation for Visual Studio .NET Control to generate, create Code 128C image in .NET applications.
T ,-kiz- T-l4
Printing Code 128A In VS .NET
Using Barcode maker for ASP.NET Control to generate, create USS Code 128 image in ASP.NET applications.
Code128 Encoder In VS .NET
Using Barcode encoder for VS .NET Control to generate, create Code-128 image in .NET framework applications.
The response, without control action, to a fluctuating
USS Code 128 Generator In VB.NET
Using Barcode printer for .NET Control to generate, create Code 128B image in .NET applications.
Creating USS Code 39 In None
Using Barcode generation for Software Control to generate, create Code 3 of 9 image in Software applications.
AN JNTRODLJ(JTORY
Print UCC - 12 In None
Using Barcode encoder for Software Control to generate, create UCC-128 image in Software applications.
ECC200 Drawer In None
Using Barcode drawer for Software Control to generate, create Data Matrix 2d barcode image in Software applications.
JXAMPLE
Bar Code Maker In None
Using Barcode encoder for Software Control to generate, create bar code image in Software applications.
Code128 Creator In None
Using Barcode encoder for Software Control to generate, create Code 128 image in Software applications.
0 Time -
Encoding Identcode In None
Using Barcode printer for Software Control to generate, create Identcode image in Software applications.
Bar Code Reader In None
Using Barcode scanner for Software Control to read, scan read, scan image in Software applications.
FIGURE 1-7
UPCA Maker In None
Using Barcode maker for Word Control to generate, create UPC-A image in Microsoft Word applications.
Create Data Matrix 2d Barcode In Java
Using Barcode printer for BIRT Control to generate, create DataMatrix image in Eclipse BIRT applications.
Tank temperature versus time: step input for proportional and integral control.
Bar Code Generation In Java
Using Barcode maker for Eclipse BIRT Control to generate, create barcode image in BIRT reports applications.
Making UPC A In .NET
Using Barcode printer for ASP.NET Control to generate, create UCC - 12 image in ASP.NET applications.
q(t) = qs + K,-(TR - T) + KR
Linear 1D Barcode Generation In Visual Studio .NET
Using Barcode generation for ASP.NET Control to generate, create Linear 1D Barcode image in ASP.NET applications.
UCC - 12 Drawer In Visual C#.NET
Using Barcode generation for .NET framework Control to generate, create UPC-A Supplement 2 image in .NET applications.
(TR - T)dt
This control system is to have two adjustable parameters, K, and KR. The response of the tank temperature T to a step change in Ti, using a control function described by (1.9), may be derived by solution of Eqs. (1.3), (1.6), (1.7), and (1.9). Curves representing this response, which the reader is asked to accept, am given for various values of KR at a fixed value of Kc in Fig. 1.7. The value of K, is a moderate one, and it may be seen that for all three values of KR the steady-state temperature is TR; that is, the steady-state error Z S zero. From this standpoint, the response is clearly superior to that of the system with proportional control only. It may be shown that the steady-state error is zero for all KR > 0, thus eliminating the necessity for high values of Kc. (In subsequent chapters, methods will be given for rapidly constructing response curves such as those of Fig. 1.7.) It is clear from Fig. 1.7 that the responses for KR = K,Q and KR = KR, are better than the one for KR = KR~ because T returns to TR faster, but it may be difficult to choose between KR~, and KR, . The response for K,Q settles down sooner, but it also has a higher maximum error. The choice might depend on the particular use for the heated stream. This and related questions form the study of optimal control systems. This important subject is mentioned in this book more to point out the existence of the problem than to solve it. To recapitulate, the curves of Fig. 1.7 give the transient behavior of the tank temperature in response to a step change in Ti when the tank temperature is controlled according to Eq. (1.9). They show that the addition of integral control in this case eliminates steady-state error and allows use of moderate values of Kc.
More Complications
At this point, it would appear that the problem has been solved in some sense. A little further probing will shatter this illusion. It has been assumed in writing Eqs. (1.4~) and (1.9) that the controller receives instantaneous information about the tank temperature, T. From a physical standpoint, some measuring device such as a thermocouple will be required- to
PROCESS SYSTEMS
ANALYSIS AND
CONTROL
measure this temperature. The temperature of a thermocouple inserted in the tank may or may not be the same as the temperature of the fluid in the tank. This can be demonstrated by writing the energy balance for a typical thermocouple installation, such as the one depicted in Fig. 1.8. Assuming that the junction is at a uniform temperature T,,, and neglecting any conduction of heat along the thermocouple lead wires, the net rate of input of energy to the thermocouple junction is hA(T - T,) where h = heat-transfer coefficient between fluid and junction A = area of junction The rate of accumulation of energy in the junction is
where C, = specific heat of junction m = mass of junction Combining these in an energy balance,
dTm -+T,,,=T Q dt
where 72 = mC,lhA is the time constant of the thermocouple. Thus, changes in T are not instantaneously reproduced in T,,, . A step change in T causes a response in T, similar to the curve of Fig. 1.4 for K, = 0 [see IQ. (1.5)]. This is analogous to the case of placing a mercury thermometer in a beaker of hot water. The thermometer does not instantaneously rise to the water temperature. Rather, it rises in the manner described. Since the controller will receive values of T,,, (possibly in the form of a thermoelectric voltage) and not values of T, Eq. (1.9) must be rewritten as 1 (1.9a) 4 = 4s +KATR - TA+KR V~-Tddt I0 The apparent error is given by (TR - T,), and it is this quantity upon which the controller acts, rather than the true error (TR - T). The response of T to a step
,Thermccouule iuidon,
FlGURE l-8
Copyright © OnBarcode.com . All rights reserved.