how to use barcode scanner in asp.net c# T+ UA + FpC VPC - H,Fx,,(dy/aT),dt = Tr in .NET framework

Creating Quick Response Code in .NET framework T+ UA + FpC VPC - H,Fx,,(dy/aT),dt = Tr

T+ UA + FpC VPC - H,Fx,,(dy/aT),dt = Tr
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The thermal time constant is rT = UA + FpC - H,Fx,,(ay/c T).
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(10.19)
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If T, is the manipulated variable, t,he steady-state process gain turns out to be UA UA + FpC - H,Fxo(ay/aT), (10.20)
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If the reactor is unstable, bbth the gain and the time constant will be negative. The denominator in both expressions is the difference between the slopes of the heat-removal and heat-evolution curves, as in Fig. 10.3. If both denominators are positive, the reactor behaves as a simple firstorder lag. If both are negative, positive feedback dominates; the dynamic gain is the same as a simple lag, but the phase angle goes from -90 at zero period to -180 at an infinite period: 4~ = -7r + tan- 2n z 70 (10.21)
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The - r indicates a negative steady-state gain, while the plus sign in front of the tan- indicates a negative time constant. Both the time constant and the steady-state gain can also approach infinity, in which case the reactor acts as an integrator whose dynamic gain at period ~~ is To .+EE2nVpC/ CIA 277TT (10.22)
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Equation (10.22) defines the dynamic asymptote of process gain for all conditions of stability, exhibiting an effective time constant of VpC/UA. A stable reactor can operate without temperature control; regulation of T, alone is ordinarily sufficient. But an unstable reactor will drift away from the control point in either direction at an ever-increasing rate, unless feedback control is enforced. Unfortunately, it may not always be possible or economical to design for stability. Enough heat transfer area must be provided so that only about 50 to 60 F differential is required across it to remove the rated flow of heat. (This is an estimate of the T - T, ordinarily required to exceed dT/dy, such as that given in Fig. 10.2.3) Stability will be assured if heat is removed by boiling one or more of the ingredients in the reaction, since this makes the system almost isothermal. On the other hand, if heat is removed by a mechanism like evaporation of liquid into a dry gas stream, its flow may change very little with temperature. In this case the slope of the heat-removal curve would be slight, and the reactor could be expected to be unstable. All of the foregoing statements on stability were used to describe openloop situations. Some unstable reactors can be given steady-state stability by applying enough negative feedback from the control system to overcome the positive feedback of the reaction. To visualize how this is possible, consider the proportional control loop of Fig. 10.4 for steadystate conditions only. Figure 10.4 can be represented mat.hematically by
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T c = (,
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-T)=x
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FIG 10.4. Negative feedback of the controller must overcome positive feedback in the reactor in order to attain steady-state stability.
FIG 10.5. The dynamic gain varies almost linearly with the amount of dead time in the loop.
The closed-loop steady-state gain is found by solving for T/T,: 1 1 ;, = 1 + P/100& Steady-state stability is identified by positive gain. to be positive, (10.23)
111 order for T/T,
i&P-
If KT were posit ive, P could have any value, because the reactor would be stable with the loop open. But with KT negative, P cannot be greater than -100 KT: if KT = -2, P < 2007& This sets an upper limit on P. The dynamic properties of the rest of the loop set a lower limit on P. The nat ural period of the temperature-control loop is found by equating the sum of the phase lags of all dynamic elements to 180 . Since the phase of a negative lag is between -90 and -180 , there is little room for other elements. This clearly rules out integral control. If all the other dynamic elements in the loop can be lumped toget her as dead time rd, t he period of oscillation can be found by equating the sum of the phase lags to -180 : -r = -242 - r + tan-1 2=721 70 To Having found 70, determined : the dynamic gain of the unstable reactor can be
A plot of dynamic gain vs. the ratio of Td/rT is given in Fig. 10.5. dynamic gain of a stable react,or is included for comparison.
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