Nonlinear Controllers

Special controllers have been developed to compensate for the nonlinearity of most pH neutralization processes. These nonlinear controllers change their gain characteristics proportionally to the ion load (pH) of the process. The characteristics of the controller are as shown in Figure 7.40.3. The diagonal line represents the error-output relationship for the controller (in response to an error, a cor

DEAD BAND (MAXIMUM)

DEAD BAND (MAXIMUM)

DEVIATION FROM SETPOINT, PERCENT

FIG. 7.40.3 Nonlinear controller characteristics.

DEVIATION FROM SETPOINT, PERCENT

FIG. 7.40.3 Nonlinear controller characteristics.

rective signal is generated—the output—which eliminates the deviation from setpoint) with a 100% proportional band (gain = 1.0) without the nonlinear adjustments available with this controller. The first available adjustment is a slope adjustment that allows the proportional band to be increased (gain reduced) about the zero deviation point by a factor of 50. This means that when the gain setting of the controller is 1.0 (100% proportional band), the effective proportional band is 5000%, or a gain of 0.02 (insensitive controller) at the zero deviation point. The slope can be adjusted manually or by an external signal. The second adjustment is the error deviation range, over which the slope adjustment is operative; this is referred to as dead band.

The dead band is adjustable from 0 to ± 30% error (deviation from setpoint). This latter feature allows the gain of the control loop to be adapted proportionally to the ion load. If the process to be controlled resembles Figure 7.40.4, a reagent flow rate or valve position signal can automatically adjust the dead band. At high ion loadings (curve A) the controller gain will be low, a desirable condition when the process gains are high. At lower ion loadings (curve B) the dead band can be reduced, thereby increasing the gain of the controller, a condition that is desirable when the process and valve gains are low. The effectiveness of this type of controller and the benefits achieved by adapting the control loop characteristics to those of the process have been demonstrated on operating installations.

Adaptive controllers are also available for the automatic adjustment of the dead-band width, based on the condition of the pH loop. When the adaptive controller notices

FIG. 7.40.4 Typical acid-base titration curves: Key: A = 9.9 ml HCl + 50 ml of 0.1N KHC8H4O4 per 100 ml solution; B = 6.7 ml of 0.1N HCl + 50 ml of 0.1N KHC8H4O4 per 100 ml solution; C = 100 ml of 0.1N HCl.

that the pH is cycling, it slowly widens (integral action only) the dead band and thereby extinguishes the oscillations after a few cycles. To do this the controller uses a discriminator, which increases its output (the dead-band width) when the oscillations occur near the natural frequency of the loop. When natural frequency oscillations are absent and the pH variations of the loop are unusually slow, the discriminator narrows the dead band.

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