Improved Control through Multiple Loops in .NET

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FIG 6.4. loop.
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Gain and phase of a typical damped
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in the response of the secondary loop will be where its phase lag is less than 90 . Notice that gain and phase of the closed loop go in opposite directions in this region. This was not true of the common open-loop elements-capacity and dead time. Therefore trouble will be encountered in the primary loop as 701 approaches 702. But the closed-loop characteristics have three very important advantages over the corresponding open-loop characteristics, at relatively high values of T,~: 1. The gain of the closed loop approaches 1.0, which is not only less than the gain of the open loop, but is not subject to variation. 2. The phase of the closed loop is less than that of the secondary process. 3. Where ~~1 is much greater than ~~2, the secondary part of the process is effectively nonexistent.
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example 6.2
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As a case in point, compare the open- and closed-loop phase in the cited example at 701 = 10~~~:
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Loop Open........... C l o s e d . Gain 5.0 1.01 Phase, deg -99 -11
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In estimating the performance of a cascade cont,rol loop, the following procedure is useful:
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158 1Multiple-loop Systems
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1. Determine the period of the inner loop ro2. 2. Determine the period of the outer loop rol, allowing no phase shift for the inner loop. 3. From Fig. 6.4, read the phase lag corresponding to the ratio ~~~ 1~~~. 4. Recalculate ~~1 after including the phase shift of the inner loop. 5. Include the gain of the inner loop at 70, (from Fig. 6.4) in estimating primary-loop gain.
Valve Position as the Secondary Loop
A positioner is used to close the loop around a valve motor. It drives the motor until a mechanica measurement of stem position is balanced against its input signal. In this way, forces that would act to impede the motion of the stem are overcome. A positioner is essentially a highgain proportional controller closing the loop around what is essentially single capacity pIus hysteresis. The forces affecting the motion of a valve stem are principally friction and pressure drop. It has been pointed out that friction is the cause of hysteresis. And hysteresis can cause limit cycling in the presence of two integrating elements, such as a liquid-level loop with proportionnlplus-reset control. But a positioner is stable in the presence of hysteresis and will succeed in eliminating from the primary loop that, source of phase shift. High pressure drop across the seat of a control valve acts against the area of the seat in opposing the force of the valve motor, It can easily be suflicient to keep the valve from closing tightly. A positioner will place as much pressure on the valve motor as is available if the stem is very far from its directed position and so is able to overcome this difficulty. The natural period of a valve with positioner will be in the order of 0.5 to 2.0 set, depending on the size of the valve. It is the fastest loop But it is not fast, enough to be ca~~~ar~~~~encountercd in process work. ui%e valve contributes more phase iag and attenuation than any other element in the loop. A positioner of l.O-set period would reduce the period of the flow loop to perhaps 4 sec. From I;ig. G.-l, the position loop gain at a ~~~~~~~~ of 4 is about 1.07, three times the gain of the valve itself. so in this case the cascade loop is a hindranc~e rather than :L help. The fault lies in plnring the inner loop around the largest time const:mt. But in any system where the valve is not the slowest element, a positioner is beneficial.
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