Modeling and Control

When does feedforward control do more harm than good? Are there smart techniques to deal with these situations so feedforward is not permanently disabled in a PID controller?

If the feedforward correction arrives too soon, there can be an inverse response where the initial reaction seen in the controlled variable is in the opposite direction of the effect of the disturbance. This causes the feedback controller to make a move in the wrong direction. The solution is to add a delay to the feedforward signal so its correction arrives at the same time or a little bit later than the disturbance at a common point in the process. If the feedforward arrives way too late (after the feedback controller has returned the controlled variable back to set point), the feedforward creates a second disturbance. If the lateness is due to a lag in the feedforward path, a lead-lag can be added to the feedforward signal for dynamic compensation. If the lateness is due to a transportation delay or dead time in the feedforward path, the delay or dead time must be reduced by making changes to the process or the feedforward measurement choice or location.

Excessive feedforward measurement noise can show up as an increase in variability of the controlled variable. A simple fix is to add a filter to the feedforward signal with the filter time set to keep the fluctuations from the feedforward noise in the controller output within the resolution limit of the control valve. If the feedforward measurement is below its low rangeability limit, its signal can become bizarre. This is a common problem with flow measurements. The best solution is to use a better sensor and transmitter technology and scale range, but given you are stuck with the situation, the feedforward action can be programmatically turned off when too erratic. Sometimes flow controller set points instead of flow measurements are used to get around flow measurement noise and erratic behavior.

A more interesting problem is when unmeasured disturbances have caused a deviation in controlled variable that is in the same direction as the feedforward correction. Here a smarter technique would programmatically turn off the feedforward when its correction would make the existing control error worse. Next week I will propose some ways to predict this scenario.

It is important that the turning “off and on” of the feedforward action be bumpless, automatic, and tested. A dead band in the trigger for “off and on” is advisable. Finally, model predictive control inherently deals with many of these issues through its use of disturbance variables.

Maybe I have just been unlucky or maybe the plants I worked in were as stressed as the typical project schedule these days but often for column temperature, boiler level control, and neutralizer pH, feedforward control didn’t live up to expectations. The problem was abusive unmeasured disturbances. The feedforward signal is often flow, which doesn’t tell the whole story. If there were only flow disturbances, life sure would be simple.

Consider a distillation column with a feedforward of feed flow corrected by a tray temperature controller output that manipulates steam flow. For an increase in feed flow, the feedforward initiates an increase in steam. Seems great but what if the tray temperature is rising because of a change in feed concentration Adding steam adds to the rate of rise of temperature toward a possible product spec limit plus wasting steam.

Consider a boiler drum with a feedforward of steam flow corrected by a drum level controller that manipulates feed water flow. For an increase in steam flow, the feedforward initiates an increase in feed water flow. Technically sound but what if the drop in drum pressure causes a swell from the expansion of bubbles that is headed for the high drum level trip point set to prevent liquid carry over into the steam header. Adding hot feed water adds to rate of rise of level and the possibility of boiler shutdown.

Consider a neutralizer with a feedforward of acid waste flow corrected by a pH controller that manipulates a basic reagent flow. For an increase in waste flow, the feedforward initiates an increase in base flow. Seems smart but what if the pH is rising because of a decrease in acid concentration in the feed. Adding base adds to the rate of rise of pH toward a possible environmental limit plus wasting reagent.

A smart technique would preemptively correct the feedforward signal by subtracting a signal that is the rate of rise of the filtered rate limited controlled variable multiplied by an adjustable factor. Here, the correction for a positive rate of change only occurs when the controlled variable is above the set point plus some noise band. The correction for a negative rate of change only occurs when the controlled variable is below the set point minus some noise band. In each case, the feed forward is corrected to help deal with an unmeasured upset. If the controlled variable is near the set point, the controlled variable is lined out, or the unmeasured upset is driving the controlled variable back to set point, the feedforward correction is zero. The adjustable factor like the feed forward gain can be initialized based on first principles (e.g. material, component, and energy balances). Note that the above scenario is for a reverse controller and a direct feed forward action.

Concentration and temperature measurements of the feed may help make the feedforward signal calculation inherently smarter and reduce the number and size of unmeasured disturbances. But, there can be extenuating circumstances. For example, cold feed water would cause bubbles to collapse and the inverse response that might counteract steam flow induced shrink or swell. Also, a pH feedforward based on a pH measurement of the incoming waste may do more harm than good because the electrode error and failure rate in low or high pH streams is larger and error in reagent demand greater because the titration curve is flatter. Testing is always a must before putting even the best idea online.

In many of the plants I worked in the production capacity had been increased over the years by a series of debottlenecking projects. Unfortunately the surge tanks volumes were not increased probably because of a lack of understanding of dynamics. Consequently, unit operations upstream and downstream of the surge tank had to be decreased because of high and low levels, respectively. Also, abrupt changes in the surge tank’s discharge flow which are unavoidable as these level limits are approached were disruptive to nearly every type of unit operation.

If batch units or continuous units that are going up and down are dumping into a surge tank, you have a tough scenario to achieve both maximum availability of the surge volume and maximum smoothing of the outlet flow by feedback control alone. Notch gain and error squared level controllers can help but are difficult to tune. Also, low controller gains cause slow oscillations from reset action unless the reset time is also increased so that the product of the reset time and controller gain stays above a minimum. The fact that a low PI controller gain for an integrating process, such as level, can cause oscillations is not well recognized. For more details on this source of oscillations see the equation on page 109 of Good Tuning - A Pocket Guide (2nd Edition) and Equation 3-3j on page 81 of New Directions in Bioprocess Modeling and Control published by ISA. These equations are consistent once you consider the maximum integrating process gain is the inverse of the fastest full scale ramp time.

One solution is to add a velocity limited feedforward. For a surge tank level controller that manipulates the tank’s discharge flow, the total flow of all units that are dumping into surge tanks is a feedforward signal to set the discharge flow. If the flow engineering units are consistent and there is cascade control of level to discharge flow the feedforward gain is one. The big question is what is the velocity or rate limiting needed to spread the disturbance from batch and on-off operations over the available surge volume.

A material balance and dimensions of the tank can be used to compute the velocity or rate limit on a first principle basis. The attached file shows the calculation and implementation in a graphic representation of a Function Sequence Table (FST). Furthermore, the calculation offers continuous directional adaptation of the velocity or rate limit. The only adjustment is to set a filter time for the feedforward measurement that is equal to the normal time that the feedforward flow could be zero. For a single batch operation upstream, this time would be the batch cycle time plus the normal time between batches. For more info on this technique see Appendix B - Batch to Continuous Transition in Advanced Control Unleashed published by ISA.

BatchToContinuousTransition

One of the simplest and easiest techniques to evaluate and implement is set point feed forward. The maximum feedforward gain is the inverse of the process gain. You just need to make sure the process gain is converted to the same units used for the feedforward gain and only a fraction of the maximum is used as the actual feedforward gain to allow for nonlinearities, errors, and PID action. New adaptive controllers such as DeltaV Insight can find and schedule the process gains and hence the set point feedforward.

If the controller gain is large (> 1.0) and the controller structure has proportional action on error, set point feed forward has little value because there is already a sizeable step in controller output from a set point change. However, large dead times can cause low controller gains. Here, set point feedforward can get you to a set point much faster, which can be useful for loop set points driven by batch, cascade, or advanced control.