If the total loop dead time was zero, you could set the controller gain as large and the reset time as small as desired. If there were no disturbances, you could simply sequence the controller outputs for startup, transitions, and shutdown. Process dynamics, controller tuning, and loop performance would be a non issue.
I once had a loop with zero dead time. I was studying the performance of my new algorithm for adaptive pH control in an Advanced Control Simulation Language (ACSL) program for my Master’s Thesis. The larger I set the controller gain, the tighter the control I got. I was ecstatic. I was going to become “way famous”. Then the let down – I had inadvertently turned off the dead time function. All I had left for process dynamics was a single time constant. The operating point nonlinearity of pH had no effect because I could stay incredibly close to set point. Since then I have seen tuning studies for a single time constant that beat to death a scenario where all the normal concerns are non existent. I decided to become sensitive to dead time especially since I could reduce my time on a pH startup by reducing dead time.
Control textbooks and studies tend to focus on set point responses ignoring unmeasured disturbances at the process input (e.g. load upsets). Special algorithms can be designed and tuned to prove a point. This may work well in simulations, aerospace, and hydraulic systems where dead time is either negligible or predicted/compensated and the servo response rules, but the real world of industrial process control isn’t so kind.
The variety and variability of the sources of dead time and disturbances in process control is quite impressive. The following lists are just some major sources that come to mind.
Sources of Disturbances
1) Limit cycles (split ranged point discontinuity, resolution, and cascade dead band)
2) Interaction between loops
3) Slow secondary loops (cascade control)
4) Design limits (equipment operating limits)
5) Low residence times (e.g. undersized feed, recycle, surge, and waste tanks)
6) Manual procedures and manual valves
7) Field switches (e.g. on-off level control)
8) Activity (catalytic and metabolic)
9) Ambient conditions
10) Interlocks and sequences
11) Raw materials
12) Recycle streams
13) Startups, shutdowns, and product transitions
14) Fouling (e.g. process coatings) and frosting (e.g. crystal accumulations)
15) Parallel trains
16) Undersized cooling towers
17) Bored board operators
18) Shift change
20) Goal reviews
My worst experiences have been with undersized recycle, surge, and waste tanks. The residence time (volume divided by throughput rate), which is the process time constant, is so low there is not enough filtering of the changes in stream composition. Also, the level control on these tanks is forced to jockey the feeds to downstream operations to keep the tank from overflowing or running dry. Plants tend to avoid putting in the bigger tank to save money and reduce inventories when they need to debottleneck or push a process.
Sources of Dead Time
1) Discrete execution and communication interval
2) Analyzer cycle time (e.g. chromatograph)
3) Transportation delay (e.g. sample line)
4) Mixing delay (e.g. agitator, eductor, and sparger)
5) Injection delay (e.g. back filled dip tube)
6) Resolution limit (e.g. VSD, control valve)
7) Dead band (e.g. VSD, control valve)
8) Instrument time constants in series (e.g. sensor and signal filter lag)
9) Process time constants in series (e.g. thermal lags and residence times)
10) Lab samples (e.g. sample hold, processing, and analysis time)
Dead time is often inversely proportional to a rate and therefore a function of test conditions. The dead time from transportation delays, sample lines, sensor lags, and residence times in series is inversely proportional to flow rate. Mixing dead time is inversely proportional to agitator pumping rate or eductor flow rate. The dead time from dead band and resolution limits is inversely proportional to the rate of change of the signal (e.g. rate of change of process variable for measurement resolution limits and rate of change of controller output for valve dead band and stick-slip). The time it takes a measurement to get out of its resolution limit or noise band can be significant for level or temperature and depends upon how fast the process is driven to change and hence the step size in the controller output or set point. The dead time for control valves becomes just the summation of the pre-stroke dead time, discrete processing, and communication interval (all usually small) if the step in controller output is larger than the valve dead band or resolution limit. The dead time effect of dead band and resolution limits unfortunately does show up for unmeasured load upsets at the process input.
My intention is now to avoid any further dead time or disturbances to an evaluation of dead time compensators and model predictive control so check here next week for more fun than control engineers should be allowed to have with advanced control.