Once a valve moves it responds as a velocity-limited exponential. For small changes, the response looks like two time constants in series. For large changes, the response looks like a ramp. Stroking time is a consideration for large actuators and compressor surge or pressure control. The addition of a booster will reduce stroking time, but will introduce a relatively large dead band (e.g., 2%), particularly when designed for piston actuators. The use of a booster without a positioner can cause positive feedback and butterfly disc instability from high outlet-port sensitivity. A booster in series with a positioner must have a bypass around the booster adjusted to prevent a limit cycle.
For most applications, slip is worse than stick, which is worse than dead band, which is worse than stroking time, although none of them are desirable.
Uncover Root Causes
Unless otherwise directed, manufacturers and technicians will make large (10%) signal step changes (much greater than dead band or stick-slip) to their valves at 50% position--far from the seating friction problems. For these tests, the response time is at a minimum and almost any valve looks good.
To make the whole situation even more deceptive, smart digital positioners may give the allusion of good response because they measure actuator shaft position and not actual balance, disc or plug position. You can develop a lot of misleading statistics, diagnostics and trends that are blind to dead band and stick-slip.
A good test should use signal changes that are less than 1%. To test to a rotary valve response in the shop, you need a travel gauge on the ball, disc or plug, since positioner feedback is prone to giving erroneous information. The most positive test is when the valve is in the pipeline at operating conditions, since high temperatures and pressure drops can make stick-slip worse. A sensitive low-noise flow measurement shows whether the ball, disc or plug actually moved.
Table I: Know Your Nomenclature
A limit cycle in level can be attributed to valve dead band if its amplitude is proportional to the dead band and is inversely proportional to controller gain, and if its period is proportional to the controller integral time and inversely proportional to the square root of the controller gain (The variables are described in Table I):
For stick-slip, the percent amplitude in the controlled variable seen by the controller is proportional to the product of the slip and open-loop gain, which itself is the product of the gains for the manipulated variable, process variable and controlled variable:
The amplitude in the process variable [in engineering units] seen on a trend recording, is without the controlled variable gain factor that is equal to 100% divided by the calibration span. The manipulated variable gain is the slope of the installed characteristic of the control valve.
For oversized valves and steep slopes, the gain is much larger and consequently the effect of slip is much greater. If you also consider that oversized valves tend to ride the seat where the friction is greatest, you get a double hit. Ideally, the amplitude Ao from slip should be less than A/D or D/A resolution, which for a 12-bit microprocessor with one sign bit is 0.05%. This is essentially impossible for oversized valves, small calibration spans, or high process gains.
The stick-slip oscillation period depends upon the open-loop gain and the controller settings:
An integral time set too fast for a given valve stroking time can cause an unstable (growing) oscillation for large upsets. The integral time must be larger than the product of the controller gain, the full-scale stroking time, and the open-loop error from a load upset. The loop goes unstable for large load upsets:
If an integrating process has rounded oscillations in the controlled variable and controller output, but a clipped oscillation in the manipulated flow, it is caused by valve dead band.
With a little experience, a user can diagnose a limit cycle caused by a control valve. If an integrating process has rounded oscillations in the controlled variable and controller output, but a clipped oscillation in the manipulated flow (Figure 2), it is caused by valve dead band. For dead time-dominant loops, a square wave in the controlled variable and a saw tooth in the controller output (Figure 3) are a sure sign of valve stick-slip.
Calculate the Impact
The additional dead time from valve dead band for load upsets can estimated from: