Deadband and Resolution Limit Cycle Causes and Fixes
Deadband and resolution cause sustained equal amplitude oscillations called limit cycles that cannot be eliminated by controller tuning. A resolution limit causes limit cycles if there is integrating action at just one point in the control loop either in the process (e.g. level), positioner, or the process controller (e.g. PID). Deadband requires integrating action at 2 or more points in the control loop. The best solution is to eliminate the source of the problem but there are fixes.
Deadband comes from backlash caused by links, levers, sand shaft connections in valves and dampers and a deadband configuration parameter in the setup of variable frequency drives (VFD). Resolution comes from stiction (stick-slip) in valves and I/O cards for the VFD.
Upon a change in signal direction, a final control element does not respond until the change in signal exceeds the deadband. Control valve manufacturers define deadband for a full scale stroke as shown in slide 2 of Deadband-Resolution-Compensator.pdf . However deadband can occur at any point in the stroke when the signal reverses direction. The valve smoothly follows the signal once it starts to move unless there is a resolution limit.
Often a deadband configuration parameter is really a deadzone, where the action is suspended when the input is within the deadzone. Deadzone and deadband create the limit cycles shown in slide 4 for a level loop.
The change in signal must exceed the resolution limit, at which time the final control element takes a step equal to the resolution limit. The quantization of signals by I/O cards creates a resolution limit. For some strange reason, the standard input card supplied by VFD manufacturers had a resolution limit of about 0.35%. When resolution is used to approximate stick-slip, the slip equals the stick creating a staircase of steps in the response of the valve as shown in slide 1. A closer approximation might be a threshold sensitivity limit or trigger limit where the valve moves smoothly without steps once the trim breaks free. Resolution, threshold sensitivity, and trigger limits create the limit cycle shown in slide 3 for a flow loop.
The control loop deadtime is increased by a delay time that is the % deadband, deadzone, resolution, threshold sensitivity limit, or trigger limit divided by the %/sec ramp rate of the signal. The additional deadtime is not seen for a step change. As a controller is detuned, the additional deadtime increases because the controller output ramp rate is slowed down.
On-off rotary valves posing as control valves are notorious sources of deadband from links, levers, and shaft connections and extreme sources of resolution limits from piston actuators, high seal friction, and shaft windup. The use of digital positioners does not eliminate the problem and may be oblivious to the problem when the position feedback is the shaft of the actuator. The shaft moves in response to the actuator but the rotary plug, ball, or disk does not. Diagnostics do not show the deadband or resolution. You see the effect as a delay to disturbances and as limit cycles. See the Chemical Processing Oct 2007 article "Improve Control Loop Performance" and the Control Design May 2004 article "What is your Flow Control Valve Telling You". The ISA book Essentials of Modern Measurements and Final Elements has much more information but Equation 7-10b for the limit cycle amplitude on a level loop with deadband should have a plus "+" sign as seen in the Control Design article.
To eliminate a limit cycle you need to turn off integral action in the controller and/or the positioner. In cascade loops, integral action in both the primary and secondary controllers must be turned off. You can do this by selecting a structure that does not use the integral mode or judiciously setting an integral deadband equal to the deadband or resolution limit. You can also use an enhanced PID with a threshold sensitivity limit just large enough to screen out noise to suspend integral action until there is a real change in the process stopping the limit cycle. Finally, you can carefully try out a deadband and resolution compensator shown in slides 5 and 6. If the deadband and resolution is set too high, the compensator will create slip. The deadband and resolution limit from backlash and stiction are extremely variable but are generally worse for undersized actuators, piston actuators, spool type pneumatic positioners, operation near the closed position, and high temperature. The best way to see limit cycles and to test for deadband and resolution is to have a sensitive low noise flow measurement. Remember that position readback for an on-off rotary valve posing as a control valve may be useless. If you don't want to see the limit cycles on a trend chart, hope for a lot of disturbances and noise to confuse the pattern or increase the data historian compression to be greater than the amplitude of the cycles.