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FIG 5.21. A three-mode nonlinear controller exhibits better set-point response but poorer load response than its linear counterpart.
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Nonlinear Control Elements
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FIG 5.22. The nonlinear two-mode controller is superior in all respects on a noisy flow loop. Flow Control
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A flow measurement is always accompanied by noise. This noise is attenuated somcwhnt by the wide proportional band of the controller and passed on to the valve. If the noise is of any magnitude, the valve may be stroked suflicicntly to introduce ac+ual changes in flow. The nonlinear function is an efficient noise filter, in that, it rejects small-amplitude signals. The result is smoother valve motion and a more stable loop. Figure 5.22 shows comparative records for linear and nonlinear control of a noisy flow loop. The nonlinear controller has proven to be quite effective on pulsating flows too, where the disturbance is periodic rather than random.
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J,evel measurements are often noisy because of splashing and turbulence. In addition, the surface of a liquid tends to resonate hydraulically, producing a periodic signal superimposed on the average level. Since the liquid-level process cannot respond fast enough for a change in valve position to dampen these fluctuations, they ought to be disregarded by the controller. A nonlinear controller does just this, sending a smooth signal to the valve. It was pointed out in Chap. 3 that many tanks with level controls are intended as surge vessels. In these applications, tight control is inadmissible because it frustrates the purpose of the vessel. A wide proportional band with reset was suggested for control. But the nonlinear controller is, in fact, ideal for this application for two reasons: 1. 1Iinor fluctuations in liquid level will not be passed on to the valve, providing smooth delivery of flow. 2. lllajor upsets will be met by vigorous corrective action, ensuring that the upper and lower limits of the vessel will not be violated. This application is often referred to as LLaveraging level control, because it is desired that the manipulated flow follow the avcragc level in
1 Selecting the Feedback Controller
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FIG 5.23. The nonlinear two-mode controller prevents minor fluctuations in level from affecting delivery of flow.
the tank. Averaging is really a dynamic process and can be accomplished with a suit able lag. But adding a lag would only serve to reduce the speed of response. The nonlinear function, however, provides filt,ering without sacrificing speed. A typical record of level in a surge vessel and the corresponding output of its nonlinear controller are presented in Fig. 5.23.
pH Control
The neutralization process has been described as unusually diffkult to control because of the extreme nonlinearitjy of the pH curve. Limit cycling (*an he encountered when a linear controller is used, because loop gain varies inversely with deviation. This, t,hen, is a natural application for t,he nonlincnr (*ontroller whose gain varies directly with deviation. In fact, any process prone to limit cycbling can benefit by its USC. The nonlinear function in the controller need not be a perfect complement
FIG 5.24. A nonlinear controller can give uniform damping to a pH loop.
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FIG 5.25. A discontinuous nonlinear controller employs a high-low limiter.
to the process curve, because any contribution it can make will be an improvement over a linear function. And if the linearity, p, is adjustable, a reasonable fit can be made. The input-output graph of Fig. 5.24 shows how a constant loop gain is achieved.
A Discontinuous Nonlinear Controller
The nonlinear function shown in Fig. 5.19 can be approximated by three straight lines. The center is essentially a dead zone where little or no control action takes place. This function is not difficult to introduce into a linear controller; it involves sending the controlled variable to the set-point input through high and low limits. Within the limits, there is no error signal; elsewhere an error is developed as the differenw between the measurement a n d the neartir limit. ITigure 5.25 describes the arrangement of the instrument and its proportional function. Proportional, rcsct, high, and low limits are adjustable. This nonlirwnr coiltrollcr is often used in nvernging lcvcl npplic*ations. Its dead zone is also a vnluablr feature in the pH-caontrol system dcwribcd in Chap. 10.
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