# Proportional Droop Cause and Cure

## Often precision—repeatability—is more important than accuracy

##### By Gary Steinbaugh

If you have experience with proportional controllers, then you have probably witnessed the

 Fast Forward Geometry and the laws of physics dictate proportional droop must occur. Droop will occur regardless of the technology—mechanical, pneumatic, electronic—used to implement the control loop.

phenomenon of proportional droop. It occurs when the load on a proportional loop increases; the loop recovers, but at a point below the set point.

All that money and trouble for a throttling valve, a continuous sensor, and a controller, and the loop still doesn’t hold the set point? What went wrong?

Nothing. Geometry and the laws of physics dictate proportional droop must occur, although it is not easy to understand why by just observing the mathematics.

Here is an easy way to visualize why proportional droop is inevitable:

Figure 1A (above) depicts a simple tank level control that uses a float as the level sensor. The float attaches to a rod to the handle of a valve that controls the flow of supply water.

A second, identical valve is at the bottom of the tank; moving its handle varies the demand on the system. If the level were to drop, the float would drop, pulling on the supply valve handle and increasing the inflow.

Obviously, for the level to be constant, the inflow must equal the outflow, which is to say, the position of the supply valve handle must match the position of the demand valve handle.

Now, if the demand valve opens as in Figure 1B, the tank will begin to empty, since the outflow exceeds the inflow.

As the level drops, the float follows, opening the supply valve as in Figure 1C. Eventually the level will stabilize, with the inflow matching the outflow, and with the valve handle positions matching again, as in Figure 1D.

However, notice that for the supply valve to open, the level must drop. This will occur regardless of the technology (mechanical, pneumatic, electronic, etc.) used to implement the loop.

What can be done to get the level back to the set point? One approach is to move the point where the float rod attaches to the valve handle, as in Figure 2A (above).

You can see how the level will be raised; but now the valve will react to every splash or ripple, and may start chasing the level. This situation equates to excessive proportional gain with consequent classical oscillations.

A better approach is periodically to reset the length of the rod so the level returns to the desired position, as shown in Figure 2B (on page S24). This must take place slowly, however, or the level may overshoot the intended target, again resulting in oscillations. This situation equates to excessive integral gain (too many resets per minute), and the cure can be worse than the disease.

Is it necessary for your loop to exactly track the set point? Often, precision (repeatability) is more important than accuracy. Your loop will be more stable if you can live with a little proportional droop.

Gary Steinbaugh (Gary.Steinbaugh@jacobs.com) is an ISA Senior member and a registered professional engineer.

### Terminology

Droop (offset) is a sustained deviation of the controlled variable from set point. This characteristic is inherent in proportional controllers that do not incorporate reset action.

Reset action (integral control mode) is a control action that produces a corrective signal that is proportional to the length of time the controlled variable has been away from the set point.

Proportional control is a control mode in which there is a continual linear relationship between the deviation computer in the controller, the signal of the controller, and the position of the final control element.

### Resources

Is it time to replace PID? Applying model-predictive control at the single-loop level may yield the next big leap in performance gains. http://www.isa.org/intech/050301

Process control diagnostics http://www.isa.org/intech/proccontroldiag

Heat is on: Feedforward improves temperature control.  http://www.isa.org/intech/040201