When I was 4 years old and sitting on my Daddy’s knee, he said, “Son, I have just two words for you: dead time.” I did not understand the significance of his words of wisdom for decades. The math in my control theory classes mostly served as a distraction from the essential truth, that if the dead time is zero, the controller gain can be infinite and the reset time zero. The controller has enough muscle for an instantaneous response. The errors from disturbances can be zero.
Without dead time, I would be out of a job. The importance particularly hit home in pH control of systems with steep titration curves where the slope and hence process gain can change by a factor of 10 for each pH unit deviation from setpoint. Minimizing dead time reduces the excursion on the titration curve minimizing the nonlinearity seen by the pH control loop.
You can get a feel for dead time by drinking Hurricanes on Bourbon Street. The time from your first drink to a feeling of being more of a party person than an engineer is dead time. If you drink too many Hurricanes in this dead time, you may be out of control.
The key role of dead time in tuning and loop performance is largely missing in the control literature. Fortunately, I found Greg Shinskey as a guiding light. Shinskey’s articles and books offered the best knowledge of process relationships and dynamics, focusing particularly on dead time as the culprit. Without this essential understanding, you are vulnerable to a lot of misconceptions. For example, I saw an academic paper where there was no dead time in the simulation. The author was proudly showing how his special tuning method could increase the controller gain and reduce the control errors. He did not realize a tuning method was not even required. He didn’t understand you could continually increase the controller gain and improve loop performance.
Concept: Dead time delays the ability of the loop to see a change and make an effective correction. The loop dead time is the total time delay for a complete loop around the block diagram from any starting point. The loop dead time is the sum of actuation, correction, process, recognition, and execution delays and the equivalent dead time from lags (time constants) smaller than the largest time constant in the loop.
For unmeasured disturbances and controllers tuned for maximum disturbance rejection, the peak and integrated errors are proportional to the dead time and dead time squared, respectively (see Tip #71). Process, mechanical, and control system designs should minimize the total loop dead time to fundamentally increase the ability of the control loop to do its job. The ultimate period (inverse of the natural frequency in cycles per sec) is proportional to the total loop dead time. For most processes, the maximum controller gain and minimum reset time are inversely and directly, respectively, proportional to the ultimate period and thus the dead time.
Details: Process delays (e.g., mixing and transportation delays) create a continuous train of delayed values. Digital delays cause a discontinuous update at discrete intervals. The equivalent dead time from digital delays is ½ the cycle time plus the latency (delay from start of cycle time to the report of result). For most digital devices, the latency is negligible. The dead time from wireless devices is ½ of the default update rate for changes that do not exceed the trigger level. The dead time from a PID in a Distributed Control System (DCS) is about ½ of the module execution time.
The dead time from an analyzer where the result is at the end of the analyzer cycle time, is 1½ times the cycle time plus the sample transportation delay. An enhanced PID developed for wireless can enable more aggressive tuning when dead time from the digital device or analyzer is larger than the process time constant. The dead time from actuator and positioner sensitivity limits, valve backlash and stick-slip, and from digital signal quantization, is the deadband, resolution, and threshold sensitivity divided by the rate of change of the input to the respective automation system component.
The dead time from automation system time constants (e.g., sensor lags, transmitter damping, and signal filter times) that are small compared to the rate of change of the process can be taken approximately as equivalent dead time. For large loop dead times, feedforward control is advisable for measureable large and fast disturbances. When the dead time becomes much greater than the open loop time we have a case of dead time dominance. Tuning methods break down and peak errors for step disturbances are as big as if there was no feedback control. For a list of solutions for this unfortunate case, see the Control Talk post Dead Time Dominance Does Not Have to Be Deadly.
Watch-Outs: Field and simulation tests or imagined scenarios where the disturbance always occurs just before the input of the PV will not show the increase in dead time by the digital device. Such tests or scenarios lead to erroneous conclusions that digital delays do not increase the ultimate period or dead time. Disturbances can arrive at any point in a digital device cycle time and should be visualized on the average as arriving halfway through the cycle time.
Tests or scenarios where the input step change is larger than the deadband, resolution, and threshold sensitivity limits will not show additional dead time from these limits. Dead time compensators cannot eliminate the effect of dead time on the ultimate limit. The more aggressive PID tuning possible for dead time compensators is dependent on an exceptionally accurate dead time.
Exceptions: The equivalent dead time from small time constants has a factor that decreases as ratio of the small to largest time constant in the loop increases.
Insight: Dead time is the ultimate limit to how well a loop can reject unmeasured disturbances and how aggressive you can tune the controller.
Rule of Thumb: Minimize the largest sources of dead time and consider the use of an enhanced PID developed for wireless and feedforward control for large dead times.