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If a feedback controller containing the integral mode is unable to bring the measurement to the set point, say, due to a valve being at a limit, there will be a sustained error in the loop. The integral mode will eventually drive the controller output to a saturation limit, such as 0 percent or 100 percent. Such a condition is called “reset windup,” or merely “windup.” Reset windup is especially bothersome in analog controllers where there are no hard limits on the output at 0 percent and 100 percent (3 and 15 psig, or 4 and 20 mA). For example, a pneumatic controller output can go beyond the 15 psig limit, all the way to the supply air pressure, which may be 18 to 20 psig. Similarly, an electronic analog controller output can go to about 24 mA. When the controller does regain control of the loop, there must be a significant error in the opposite

old C ,old old

new old de D,old D,new

b b ( T T )

= + dt × −

come back within sight, that is, within the 3–15 psig or 4–20 mA nominal range. With a con-troller that is implemented in a digital processor, if there is a sustained error, and in the absence of other provisions, the integrator output will continue to grow without limits. Clearly, a mech-anism for avoiding reset windup in such situations is desirable.

There are several methods for preventing reset windup; some are only applicable in certain cir-cumstances. All the techniques we will mention here assume that the controller is imple-mented in a digital processor.

One of the simplest methods for anti-reset windup protection is to simply stop the integration if the controller output reaches a limit. When the condition that causes the windup is removed, the controller output will recover back to a normal operating point, at a rate dependent prima-rily on the integral tuning.

Some manufacturers offer a considerable improvement over this technique. If the controller output reaches a limit and then begins to recover, the integral action is accelerated by a factor of sixteen until the process variable has returned to its normal operating point. This permits the system to recover much faster from a windup condition.

 External Reset Feedback

Override (or selector) control systems have a unique need for reset windup protection. (Over-ride control is discussed in detail in chapter 12). In a typical over(Over-ride control application, one controller controls the valve in normal circumstances. In abnormal circumstances, however, this controller’s output is “overridden” by another controller, which then takes control of the valve. If an ordinary PI (or PID) controller’s output is overridden by another controller, it will be unable to achieve its set point; consequently, it will wind up. This is a problem posed by using ordinary PI controllers in override applications.

Some manufacturers provide a modified controller form to overcome this problem. This modi-fication is said to use “external reset feedback,” “external reset,” or simply “reset feedback.”

Since the derivative mode does not contribute to the problem of reset windup, we will use only the P and I modes in our discussion of this modification.

For a PI controller, the modification that uses external reset feedback is indicated in transfer function form by the block diagram of Figure 5-12 and by Equation 5-23.

(5-23)

This equation and figure indicate that the controller output is computed as the sum of the con-troller gain times error, plus a lagged value of its own output. The concon-troller output is fed back into a first-order lag whose time constant is the desired integral time of the controller.

C I

M ( s ) K E( s ) 1 M ( s ) T s 1

= +

+

Although it is not immediately obvious, a controller that is formulated in this way has exactly the same behavior as a standard PI. One way of demonstrating this is to solve Equation 5-23 for M(s). After a bit of algebraic manipulation, this yields

(5-24)

which is exactly the same transfer function as for the standard PI (see Equation 4-4).

The internal formulation of the controller would be of no interest to us if its only attribute were that it behaved the same as a standard PI. The real benefit occurs if the manufacturer has con-figured the controller, either in hardware or software form, so that the link from A to B in Fig-ure 5-12 can be removed. Then we can input the signal to the external reset feedback port B from anyplace we choose. A common configuration in override control is to take the reset feedback from the output of the selector device that selects between the normal controller and an abnormal controller (see Figure 12-4). Since there is no explicit integrator in the controller, the nonselected controller will not wind up, even in the presence of a long-term error because of the overriding action of the alternative controller.

 Batch Switch

For batch process applications, as well as for similar applications such as process startups or significant changes in operating point (grade changes), the measurement value may be in tran-sition between an old set point and a new one for a considerable duration. During this time, the action of the integral mode will cause windup. For example, suppose the set point of a temper-ature loop is raised significantly. The integral action of the controller may cause the valve to open fully long before the measured temperature reaches the new set point. Then, getting the valve back to its normal operating range will require a significant overshoot of the set point.

Recall from chapter 4 that the position of the proportional band is shifted by integral action (see Figure 4-12). Thus, the reason for the overshoot is that during the temperature rise the integral action shifts the proportional band so it lies entirely above the set point. To bring the valve back from its wide-open position, the measurement must be somewhere within the pro-portional band, and hence must exceed the set point. Only then does the reversal of the sign of Figure 5-12. PI Controller Formulated with External Reset Feedback

;₆₃ 3

ing region.

Windup can also occur if there is a limitation in the controlling medium itself. For instance, if there is a loss of steam supply, a temperature-control loop will wind up simply by attempting to achieve a constant set point. When the deficiency is corrected, there will be a significant overshoot of the set point before the valve gets back to its normal operating point.

Anti-reset windup techniques for this application generally consist of forced-shifting of the proportional band by some means other than the normal integral action. This can be accom-plished either in hardware controllers or in software control algorithms. We will present the functional details here, which can be implemented in either technology. This anti-reset windup technique is often called a “batch controller” or a “controller with a batch switch” (Ref. 5-1).

With this controller (as with every PI controller), in normal operation the controller output is determined by the following:

where b is the integral-mode contribution.

With the batch switch feature, however, if a sustained error causes the controller output to reach a maximum value, the contribution of the integral mode is back-calculated so as to hold the controller output at this maximum value.

(5-25) The effect is to shift the proportional band downward during the period of noncontrol. When control can be resumed, the measurement value will already be within the proportional band, so the controller output will start to cut back right away. The net result is a reduction in over-shoot when control is resumed.

Figure 5-13 shows the results of a simulation-generated demonstration of this “batch control-ler” technique. The simulation scenario is that of a temperature controller controlling a steam valve. During a period of normal control, the steam supply is interrupted, causing the control-ler output to wind up to a maximum value (set at 90 percent). The characteristic of interest is the recovery of the control loop when the steam supply is resumed.

In Figure 5-13a, the controller is a conventional PI controller without anti-reset windup. Note that when control is lost, the integral action shifts the proportional band upward so that most of it lies above the set point. (Had the maximum output been set at 100 percent, the PB would have been entirely above the set point.) When the steam supply recovers, the measurement must rise to within the PB before the controller output starts decreasing. Note that there is a significant overshoot before normal control is reachieved.

m = K eC + b

max C

b = m − K e

In Figure 5-13b, the controller has been modified to a PI with anti-reset windup. Note that when control is lost, the PB is initially shifted upward. However, once the controller output reaches the maximum the PB is shifted downward, as a result of back calculation of the output bias (Equation 5-25). Upon recovery, the measurement must still rise to within the PB before the controller output is reduced, but this occurs much quicker; consequently, the overshoot is reduced.

Figure 5-13. Overshoot Reduction Using the Batch Switch













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derivative and anti-reset windup will produce very dramatic results. If the proportional band is shifted downward too far, the result will be a “negative overshoot” (i.e., the measurement will not initially reach the set point). Consequently, batch controllers of this type have a lower limit on b. This is called the “reset preload” value; it is user adjustable.

Other tuning parameters that must be adjusted on a batch controller are maximum controller output and preload settings. In a given situation, the batch controller’s performance depends greatly on these settings as well as on the process load. The batch controller works best when it is adjusted for one repeatable situation, including set point and process load.