Selecting the Feedback Controller in VS .NET

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1 Selecting the Feedback Controller
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Time (0) Time (b)
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FIG 4.6. Response after startup with (a) no preload, (6) 30 percent preload.
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set point by reset action-a slow procedure. The results of inadequate and sufficient preload in a three-mode controller are displayed in Fig. 4.6. The first crest in the record of Fig. 4.6a is brought about by the sudden activation of derivative as the controller output starts to fall. Proper adjustment of preload will locate this crest right at the set point, as shown in Fig. 4.6b. In the absence of derivative, there is no crest, and the measurement will be found to converge on the set point asymptotically. Some integration must take place, because a sizable error always exists at the time tl when the antiwindup switch activates the reset circuit. The load Q (output at time tz) will differ from the preload b by the amount of this integration:
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100 tz q-b=PR tl e d t
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If the preload is set equal to the expected load, some overshoot will develop. Therefore, if critical damping is to be achieved, the preload setting must be significantly less than the expected load. In Fig. 4.6a, no preload is indicated. Because no preload is less than 0 percent (0 psi compared to 3 psi in a pneumatic system), the proportional band lies below the set point by this difference. When placing one of these controllers into operation, it is first necessary to adjust proportional, derivative, and reset for maximum performance in the steady state, just as would be done for a continuous process. Once these are set, response during startup depends entirely on the value of preload.
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Auto-manual Transfer
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As far as the controller amplifier is concerned, the loop is open when in manual control. The slightest deviation will eventually cause the controller to saturate, because it has no way of satisfying itself in a closed
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loop. For t,his reason, all controllers with an auto-manual transfer feature also have some means of preconditioning the reset so that the proper output will be maintained during transfer to automatic. T h i s is known as bumpless transfer. Some controllers are designed to insure bumpless transfer even if a deviation exists. But each controller design seems to have its own particular transfer procedure, so there is little point in trying to generalize. The reader is advised to consult the instructions supplied by the manufacturer.
The Three-mode Controller An ideal three-mode controller consists of a simple combination of the individual modes as they have already been presented:
de edt+Dz Because the three components of gain at the natural period are out of phase, vector addition is required to determine the resultant phase and gain of the controller. A vector diagram is given in Fig. 4.7. Because of the gain limitation placed on the derivative mode, the latter is not exactly represented by a vertical vector, but the inaccuracy is not severe above a period of 2rD. From the vector diagram of Fig. 4.7, the resultant phase and gain of the ideal controller are $ = tan-l ( &) 2aD Y-&
Control Modes
(4.6) (4.7)
Interaction
between
Whenever reset and derivative operate successively on a signal, they interact with one another. Reset produces a rate of change of output in an attempt to restore the measurement to the control point. But derivative reacts to a rate of change of output.
FIG 4.7. The resultant gain and phase emanates from a vector summation of the individual modes.
1 Selecting the Feedback Controller
When a signal passes through derivative and reset in series, as in Fig. 4.&z, no matter in what order or whether one or two st ages of amplification are used, interaction results-the ultimate control function is not ideal. Figure 4% shows a parallel dynamic operation, followed by summation, producing the ideal (nonint,eract,ing) control response. The block diagram of the noninteracting controller can be reduced mathematically to Eq. (4.5). But reduct ion of the diagram of Fig. 4.8~ to a comparable mathematical expression yields
m=7(l+~)(pf~ledi+llnd~~,R)
(4.8)
A remarkable fact is that at this writing all standard three-mode controllers are interacting. Although the mathematical structure of a noninteracting controller is simpler, its implementation is too costly to be competitive at present. Interaction is manifest in the effectiveness of the three-mode adjustments. Let the effective mode value be indicated by a prime, relative to the settings introduced:
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