Linear in a Nonlinear World

Control systems assume linearity. Unfortunately the world is basically nonlinear. For the next few weeks we are going to explore how gains, process time constant, and dead times change with plant design and operating condition. This week we start out looking at valve gains.

A plot of the flow versus valve position (installed characteristic) of most control valves is nonlinear. Here the slope is the valve gain. If we were to plot a process variable versus this flow, such as temperature or composition, it would also be nonlinear. Here the slope is the process gain. These are called operating point nonlinearities. If the process variable stays close to its set point, the slope doesn’t change much. Thus, for a constant set point, minimal dead time, and good tuning, the process nonlinearity is not much of an issue. On the other hand, the control valve may have to move a lot to achieve tight control. The loop is more likely to see the nonlinearity of the control valve. Generally the slope of the installed characteristic gets too flat at low and high positions. Entech published a gain specification that the % flow divided by % signal should be between 0.5 and 2.0 (a gain change of 4:1). The following examples of installed characteristics show that the throttle range is shortest for a butterfly valve and longest for a sliding stem valve. For a detailed discussion of these figures see Chapter 2 of Advanced Control Unleashed.

Valve Gains

The rangeability statements by valve manufacturers are defined in terms the uniformity of the inherent characteristic. These statements do not take into account a gain specification, an installed characteristic, or the increased stick-slip at low valve positions from friction of the seating and sealing surfaces, particularly for tight shutoff valves.

A signal characterizer block can be inserted between the controller output and analog output block to compensate for the nonlinearity of the control valve gain. The characterizer is set up to calculate the % flow from % position (the Y axis from the X axis of the installed characteristic). The input signal to the control valve is now % desired flow rather than % desired position. This can confuse operations and maintenance if not adequately documented and displayed. The accuracy of this gain compensation depends upon the knowledge of the system pressures and friction losses that affect the pressures at the inlet and outlet of the control valve. Software can predict the installed characteristic but this is done typically offline with manual entry of data. There is an opportunity for pressure measurements upstream and downstream to provide better compensation of the valve nonlinearity besides facilitate the monitoring and trouble shooting of disturbances. Many times I wished more pressure transmitters were installed to figure out why a loop just got clobbered, but this is another story.

Another practical issue relates to valve stick-slip and backlash, whose effect and compensation we alerted readers to in our Dec 4 and 11 blogs. For operation on the steeper portion of the installed characteristic, the characterizer makes the change in signal to the control valve smaller. Thus it takes longer for the signal to work its way through the resolution limit and dead band. However, for operation on the flatter portion of the installed characteristic, the change in the control valve signal is larger reducing the dead time from the resolution limit and dead band. If you ever waited for the controller output to work its way along the upper flat portion of a butterfly valve characteristic for a process unit operating at or beyond its design limit, you can appreciate the acceleration offered by the signal characterizer. Of course, at some point you just run out of valve and need to take a look at the pump and piping system design besides the valve size.