asp net display barcode Dynamic Elements in the Control Loop in .NET

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Dynamic Elements in the Control Loop
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TABLE 1 .I +R, deg Settings of Proportional and Reset for s/4-amplitude hr deg -180 tan (-@Id 0.000 7dTd Damping
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m 1.29 0.66 0.42 0.28 0.15 1.27*
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200 206 232 283 400 770
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-15 -30 -45 -60 -75 -90
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0.268 0.577 1.000 1.732 3.732 m
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2.00 2.18 2.40 2.67 3.00 3.43 4.00
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* The last row describes integral-only control.
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The gain curve for the proportional-plus-reset controller (Fig. 1.12) can be roughly approximated by the asymptotes:
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G,,+(& > 1)
(1.13)
The largest departure occurs at r0 = 2rR, where GpR = 100 @/P versus 100/P. This controller presents two adjustments, both of which affect the stability of the loop. An infinite number of combinations of proportional and reset settings exist which would provide >i-amplitude damping, the only requirement being that GpR = 0.5. Several such combinations appear in Table 1.1. Obviously an infinite reset time is undesirable, because offset will result. Yet a very low value of reset forces the proportional band to be set very high, and the controller acts very much like a pure integrator. If the recovery characteristic of reset is to be combined successfully with the higher speed of proportional action, the contribution of each should be similar. Of course, this is not at all critical. Reset time can deviate by 2 : 1 with little change in performance, as long as the proportional band has been adjusted for proper damping. This is typically described as a trade-off situation: there is a very broad optimum. Means for determining exact values of the optimum will be given at the beginning of Chap. 4. Figure 1.13 describes the effect of a gradual load change on the loop with proportional-plus-reset control.
FIG 1.13. Various combinations of proportional and reset values can provide ji-amplitude damping, but with different rates of recovery from a load change.
+ 60 5 : a 50
n Ud erstanding Feedback Control
THE EASY ELEMENT-CAPACITY Identification
Capacity appears in many forms, but its properties are universal as far as automatic control is concerned. Capacity is a location where mass or energy can be stored. It acts as a buffer between inflowing and outflowing streams, determining how fast the level of mass or energy may change. In fluid systems, tanks have capacity to hold liquid or gas. In electrical systems, capacitors are used to store nominal amounts of charge. Heat capacity is a factor in thermal systems. And the mechanical measure of capacitance is inertia, which determines the amount of energy that may be stored in a stationary or a moving object. Our principal concern is with fluids, so Fig. 1.14 is an appropriate introduction to capacity. In the system shown in the figure, the met ering pump delivers a constant outflow, while inflow may be manipulated. The rate of change of tank contents equals the difference between inflow and outflow:
d =F.-F
dt Solving for v,
(1.14)
v = J(Fi - F,) dt
(1.15)
If the tank is vertical and of uniform inside area, its fractional liquid level h will equal the fractional volume:
where V is the capacity of the tank. h = $ / (Fi - Fo) dt
Since we are interested in tank level,
In an effort to make the entire equation dimensionless, we can define fi and f,, as fractions of the maximum flow F which the valve can deliver.
FIG 1.14. The rate of change of level is proportional to the difference between inflow and outflow.
Dynamic Elements in the Control Loop
FIG 1.15. The percent level change Eill equal the percent Aow change in time V/F.
Time
Then,
Fi - Fo = F(fi - fo)
and h = ; / (fi - fo) dl This is called an integrating process. Sotice (1.16) its similarity to the inte-
grating controllers: h is the output, J; - fO is the input error, and F ,,Fis
the time constant. The step response is given in Fig. 1.1.5. The level in the tank could be controlled by manually adjusting the valve position, thereby setting inflow. But if inflow varied in the slightest from outflow, the tank would eventually flood or run dry. This characteristic is called non-self-regulation. It, means that the integrating process cannot balance itself-it has no natural equilibrium or steady st ate. The non-self-regulating process cannot be left unattended for long periods of time without automatic control. Most liquid-level processes are non-self-regulating; occasionally other processes will exhibit this characteristic. In general, it is not harmful as long as its peculiarities are taken into accqunt. One of these peculiarities is its phase shift. Like the integrating controller, the non-selfregulating process exhibits a phase lag of 90 to any periodic wave. Consequently: 1. Under proportional control, the loop cannot oscillate because its phase lag never reaches 180 . The proportional band therefore can be set to zero. 2. Under floating (integrating) control, the loop will always oscillate with uniform amplitude,, because the total phase shift of process and controller is 180 at all periods. The loop tends to oscillate at the period where the gain product is unity; the reset time then only affects the period and cannot change the damping. The gain of an integrating process is like the integrating controller:
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