Inverse response is deceptive

Most industrial processes respond to the actions of a feedback controller by moving the process variable in the same direction as the control effort. The temperature goes up when a controller feeds more fuel to the burners in a furnace, the flow rate drops when a controller closes the valves in a pipeline, and the speed increases when a controller revs up the motor driving a conveyor.

By Vance VanDoren, Ph.D., P.E., Control Engineering April 1, 2007

When the controller dumps a slug of cold water into a drum of boiling water, the level inside will actually drop before rising to its final value. The controller will ignore the inverse response if it is tuned to accomodate a fictitious deadtime equal to the duration of the inverse response.

Most industrial processes respond to the actions of a feedback controller by moving the process variable in the same direction as the control effort. The temperature goes up when a controller feeds more fuel to the burners in a furnace, the flow rate drops when a controller closes the valves in a pipeline, and the speed increases when a controller revs up the motor driving a conveyor. Some processes will oscillate both upwards and downwards in response to the controller’s actions, but the process variable’s first reaction will usually be in the same direction as the control effort.

However, there are some rare exceptions where the process variable first drops then rises after an increase in the control effort. Consider an industrial boiler. As the steam leaves the drum to satisfy downstream demand, liquid water is added to keep the level inside more-or-less constant. This is typically accomplished with a feedback controller that measures the height of the boiling water and manipulates an inflow valve to return the level back to its former value.

Unfortunately, the hot water inside the drum will cool and condense if the incoming water is cold enough. That will cause the water level to drop, even as more water is added. The problem becomes even more acute if the controller’s level-sensing technology treats the top of the froth as the water level. The inflow will tend to collapse the froth and dampen the boil, exaggerating the apparent drop in the water level.

Misdirection

This “inverse response” phenomenon is shown in the trend charts. As the controller increases its control effort by adding more water to the drum, the process variable will initially decrease before beginning to rise. In academic parlance, a process that demonstrates an inverse response is said to be “non-minimum phase.” In the boiler business, this phenomenon is known as “shrink-swell.”

An inverse response fools the controller into believing that the process variable is headed in the wrong direction. Unless the controller knows that the process variable is about to reverse course all by itself, the controller will typically react by reversing its own direction. It will be able to put the process variable back on track for a short while, but the process variable will eventually reverse course and force the controller to do the same. The two will continue to chase each other, causing the process to oscillate ad infinitum .

Patience for the controller

Fortunately, a controller can be endowed with the patience to wait out the process’s temporary misdirection. With a PID controller, that can be accomplished by tuning the controller as if the process included a deadtime (see “Dealing with Deadtime,” Control Engineering , July 2005). Doing so makes the controller slow enough to ignore the process’s temporary misdirection but lengthens the time required for the process variable to reach the setpoint thereafter.

Author Information
Vance VanDoren is consulting editor to Control Engineering . Reach him at controleng@msn.com .