THE INTEGRAL mode of a controller is essential in eliminating offset in any loop subject to load changes—which is almost every loop encountered in process control. Consequently, almost every controller has integral action in one form or another.
However, tireless effort to drive deviation between the controlled variable and its set point to zero presents problems when the loop is open. In an open loop, no amount of control effort will be successful, and continuing to integrate results in “windup” with adverse consequences. The integral component in a “wound-up” controller doesn’t balance the process load, driving the controlled variable away from a steady state when the loop is eventually closed. This imbalance can produce a large deviation, requiring integral action to eliminate, and, if repeated, it results in a limit-cycle immune to correction by tuning the controller. Preventing windup requires reconfiguration of the controller, and external-reset feedback is the most satisfactory method of accomplishing it.
Development of Automatic Reset
The first pneumatic controllers had only on-off action. A mechanical linkage, whose position represented the difference between process measurement and set point, acted on a relay to switch the output pressure between its two states. Proportional control was introduced by negative feedback of that pressure to reposition the linkage through a bellows. The precise value of the output when the deviation was zero could be adjusted by a screw, acting on a spring opposing the bellows, as a bias (Equation 1):
in which m is the controller output, c and r are the controlled variable and set point, P is the proportional band, and b is the bias, with all variables expressed in percent of scale.
Proportional offset develops whenever the process load requires a value of controller output that isn’t equal to the bias. Consider, for example, a proportional-level controller with a 50% bias manipulating the flow entering a tank. If the flow leaving that tank exactly matches the flow entering with the valve 50% open, there will be no offset. However, at any other value of outflow—which requires a matching inflow to reach a steady state—the matching inflow can only be attained by a proportional offset.
In applications where offset was particularly undesirable, a plant operator might reset the set point to position the controlled variable where it was wanted. The offset remained, however, and it was variable. It could be manually eliminated by operator adjustment of the output bias, and this became known as manual reset, but only until the load changed again.
In 1929, “Doc” Mason of the Foxboro Co. came up with the idea of replacing the bias spring with a bellows connected to the controller output. If the bias and controller output could be kept equal in the steady state, Equation 1 shows the offset will be zero. This became automatic reset.
However, simply connecting the two bellows together produces an on-off controller, as the new bellows adds positive feedback to the controller canceling the negative feedback of the proportional bellows. To stabilize this loop, the positive feedback has to be slower than the negative feedback coming from the process. So, a restrictor was inserted between the controller output and the feedback bellows, creating a first-order lag. Initially the restrictor was fixed, then a selection of fixed restrictors was used, and finally an adjustable restrictor. The configuration is shown below in Figure 1, in which time constant “I” was known as the reset time.
FIGURE 1: AUTOMATING RESET
Automatic reset is achieved by positive feedback of the controller output.
This is one of those examples where the idea came first and theory followed. Only much later were equations used to develop the correlation between automatic reset and integral action, and it wasn’t commonly called by the name “integral” until 1970. Substituting controller output m for b in Equation 1, and applying first-order lag I gives (Equation 2):
where s is the Laplace operator. Rearranged, we have (Equation 3):
which is recognizable as the proportional-plus-integral controller algorithm.
The reset feedback path in Figure 1 is shown as a dashed line, indicating that it can be broken to stop integration, and prevent windup for reasons explained in the various applications below. Not all controllers integrate by means of a feedback loop, however, and these require other methods of windup protection that aren’t as effective. So, it may be necessary to build a controller from the elementary function blocks shown in Figure 1 to obtain the capability of external-reset feedback.
An early problem caused by integral windup was temperature overshoot in heating batch reactors. The reactor was charged cold, with the temperature controller in automatic, set point at its desired value, and the steam block valve closed. Opening the block valve started the heating operation. At this point, the reset bellows contained full-supply pressure, keeping the controller output saturated and the steam control valve wide open until temperature crossed its set point. The resulting overshoot was unacceptable. The remedy shown below in Figure 2 breaks the reset-feedback path by a batch switch whenever the controller output exceeds 100% or wherever the manipulated variable limits, and substitutes a manual-loading signal. Suitable adjustment of this preload positions the integral term near the anticipated process load, which can prevent overshoot, and provide a smooth transition from proportional or proportional-plus-derivative to PI or PID control. This same method is now applied to digital controllers with external-reset capability.