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Several years ago, tests were carried out on a polymerization reactor, where batch temperature was controlled by manipulating jacket outlet temperature in cascade with the controllers connected as in Figure 7. The value of could be varied over a range of 4:1 by changing batch size M and area A. It was expected that a different set of tuning constants would be required for each combination, but the same controller settings produced acceptable results over the entire range of thermal time constants. A larger time constant meant slower heating and cooling, and slower integration as well. With this configuration, retuning wasn’t required with changes in recipe or heat-transfer coefficient, both variations common to batch reactions.
Accommodating Velocity Limit
The velocity-limit or rate-limit property of a final element can pose a danger to a control loop, if the integral time of the controller is shorter that the stroking time of that element. However, the danger is hidden while the loop is operating around set point because the actuator takes little time to move only a short distance. When a sufficiently large disturbance strikes, the actuator may fall behind the controller output enough to cause more integral action and further falling behind. This triggers an expanding cycle (Figure 8A) that requires operator intervention to stop.
FIGURE 8 A AND B: STOPPING EXPANDING CYCLES
Velocity limit can trigger an expanding cycle following a large disturbance, while feedback of the measured actuator position prevents the cycle from developing.
Figure 8A is the simulated response of a level-control loop, where the integral time of the controller is set at half of the stroking time of the valve actuator. The first disturbance is a step-load change of 10%, which isn’t large enough to destabilize the loop. Next, a 17% step is large enough to trigger the expanding cycle. This is particularly insidious behavior because the response of the loop to normal variations in load is quite acceptable, which gives false confidence, while masking a potentially fatal instability.
The ideal correction is to speed up the actuator, but this option often isn’t available. The simplest remedy is to increase integral time until the loop is stable following the largest conceivable disturbance. This requires extensive testing, and may not provide complete assurance that the cycle won’t recur. It also degrades the performance of the controller in response to normal low-level disturbances because integrated error varies directly with integral time.
External-reset feedback of the measured position of the final element can eliminate the danger without compromising controller performance. In Figure 8B, the actuator’s actual position is fed back to the integral term of the level controller, with the disturbances repeated. Integral action is now paced to the actuator’s movement, which avoids any risk of an expanding cycle, no matter how large the disturbance or how slow the actuator. This is simply the same principle applied to cascade control in Figure 7. To avoid offset there must be a secondary controller to force the final element to follow the primary output precisely in the steady state.
The need for external reset became clear during a recent startup of a nuclear power plant, where the level in a boiling-water reactor was controlled by manipulating the speed of up to three feedwater pumps. The integral time of the feedwater flow controller was set at 0.18 min, the expected rate limit of the pump-speed governor. When first operating with one pump on line, control was acceptable, until a disturbance triggered an expanding cycle. Review of the records indicated a much slower response of pump speed than expected, requiring an integral time in the flow controller of 1.6 min to stabilize, which was unusually high for a flow loop.
Oddly, the dynamic causing the cycle disappeared when multiple pumps were on-line, so the problem is a variable one. The solution is external-reset feedback of measured pump speed to the flow controller, allowing it to integrate as fast as pump speed can follow. Implementation is complicated by the use of three pumps, with their characterizers. To avoid offset, all calculations performed in the controller output path have to be reversed in the feedback path as described earlier for feed-forward control.
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