Deadtime, the Simple Easy Key to Better Control

Deadtime is the easiest dynamic parameter to identify and the one that holds the key to better control. Deadtime found visually or by a simple method can tell you what is limiting the ability of the loop and what the remedy is.  In most loops, you as the automation engineer can gain a much greater understanding and make a dramatic improvement. You can become famous by Friday (assuming you read this on a Monday).

You can make a small setpoint change in automatic or a small output change (e.g., 0.5% ) by momentarily putting the loop in manual. The time to a change in the process variable in the correct direction is the deadtime. To detect the deadtime and noise visually, compression must be turned off. The remaining principal limit to identifying the deadtime in fast loops is the update time of the historian. For loops with a relatively large deadtime (e.g., greater than 10 sec), the deadtime can be visually identified assuming the update time is 1 sec or less. For loops with smaller deadtimes, you can put a few function blocks together in a module executing as fast as possible (e.g., 0.1 sec for many DCS) to tell you the deadtime. Of course, good tuning software that is executing very fast can tell you the deadtime and a lot more. The point here is that just knowing the deadtime offers exceptional insight and power to do what is right. So without delay let’s explore how we all can become more responsive.

The sum of all the discrete update times such as PID module execution rate and wireless update time and all the signal filter times and transmitter damping time should be less than 20% of the total loop deadtime to limit deterioration in achievable loop performance to be appreciably less than 20%.  The valve response time should also be less than 40% of the deadtime. This is going to be difficult to achieve and to measure if you don’t have a true throttling valve and is nearly impossible in pressure systems because the process deadtime is usually so small (e.g., less than 1 sec). Almost as difficult but perhaps less important is the size of the valve response time compared to process deadtime in level systems assuming liquid flows into or out of the volume are manipulated for level control and the sensitivity limit and noise in the level measurement is extremely small enabling a detection of a small level change. The time for the level to get through a sensitivity limit or noise band is additional deadtime.

Consider the case where a loop in manual has no oscillations and develops oscillations when the loop is put in automatic. If the period of oscillations is 3 to 4 times the deadtime, the PID gain is too high. If the period is 6 to 10 times the deadtime, the reset time is probably too small.  If the period of a level, gas pressure, or temperature loop on a vessel or column is more than 20 times the deadtime and decaying, it is most likely due to small of a PID gain - actually the product of PID gain and reset time is too small but it is most often caused by a PID gain needed for a normal reset setting being much greater than what is used due to the comfort zone of operations (e.g., many of these loops should have a PID gain that is 50 to 100 unless the reset time is greatly increased). If the period is more than 20 times the deadtime and the amplitude is constant indicating a limit cycle, the source is deadband, backlash, stiction, or resolution limit. If the source is deadband or backlash, increasing the PID gain should be able to reduce the oscillation amplitude and period.

Now let’s look at the situation where a loop in manual has an existing oscillation. If the oscillation period is less than the deadtime, it is essentially noise and the PID should not react to it. If the period is between 2 and 10 times the deadtime, the PID gain must be considerably reduced to prevent amplification of the oscillation due to resonance. If the period is more than 10 times the deadtime, the PID gain should be made as aggressive as possible to reduce the amplitude of the oscillation. Of course, the best solution is to find and eliminate the source of the oscillation.

What the controller sees in the first four deadtimes is most important in terms in controller tuning because unless the PID is seriously detuned, the PID should have reacted to arrest the response from a load disturbance. This corresponds to a lambda setting of 3 or less deadtimes. For a near-integrating, integrating, and runaway process, the maximum ramp rate in % of PV scale (%/sec) in the first four deadtimes divided by the step % change in PID output is approximately the integrating process gain (1/sec) that can be used with the deadtime to tune the PID using integrating process tuning rules. If there is a compound response, having the PID appreciably do its job within 4 deadtime simplifies the tuning and reduces what the PID sees and has to deal with in terms of the consequences of a later response typically due to recycle effects.

The reset time should be greater than 3 deadtimes for a PID with the exception being a truly deadtime dominant process (a rather rare case).  The more likely scenario as mentioned before, is that the reset time must be increased because the product of the PID gain and reset time is too small for near-integrating, true integrating and runaway processes. For many loops on vessels and columns, the reset time is several orders of magnitude too small.

Deadtime also determines the limit as to loop performance even if the loop is tuned aggressively. The minimum peak error is proportional to the deadtime and the minimum integrated absolute error is proportional to the deadtime squared. If a PID gain is detuned, the effect can be equated to an increase in an effective deadtime greater than the actual deadtime. In other words, if you spend money to decrease deadtime in the process by better equipment or piping design or in the automation system by faster valves, measurements and discrete actions, if the PID is not tuned to match the decrease in actual deadtime, you do not see an improvement due to an effective deadtime from sluggish PID control.

For more on how deadtime limits performance, see slides 12-14 of ISA-Mentor-Program-WebEx-PID-Options-and-Solutions.pdf and for much more see the associated ISA Mentor Program Webinars.

The effect of an operating point non linearity is reduced by decreasing the total deadtime. My goal in pH control on difficult systems was to make the total deadtime as small as possible by better mixing and reagent injection so that the excursion on the nonlinear titration curve was as small as possible from tighter pH control. In other words, an increase in deadtime causes an increase in the nonlinearity seen, which causes a further deterioration in control (a spiraling effect, literally and figuratively).

If the deadtime is zero, the controller gain could be theoretically infinite and control perfect. Without deadtime, I would be out of job. The good news is that negligible deadtime only exists in simulations without volumes in series, transport and mixing delays, heat transfer lags and automation system dynamics. Even if the process deadtime is extremely small, just having an automation system creates a deadtime that must be dealt with. The bad news is that deadtime is extremely detrimental and is not given the proper consideration as to what it is telling you and the PID. Also, the misuse of the term of “process deadtime” rather than “total loop deadtime” leads people into missing the important opportunities to reduce deadtime in the valve, measurement and controller, which is usually more readily done, more in your realm of responsibility and typically much less expensive than reducing deadtime in the process.