To view the recording of Deminar #10, click on the above picture. If you want to just view the slides click on Deminar #10 – PID Deadtime Compensation
The results of some of the tests in Deminar #10 even surprised me even though I had explored and documented some of the unusual features of deadtime compensators in Advanced Application Note 003. Let’s review some of the myths busted.
(1) Deadtime is eliminated from the loop. The smith predictor, which created a PV without deadtime, fools the controller into thinking there is no deadtime. However, for an unmeasured disturbance, the loop deadtime still causes a delay in terms of when the loop can see the disturbance and when the loop can enact a correction that arrives in the process at the same point as the disturbance. The ultimate limit to the peak error and integrated error for an unmeasured disturbance are still proportional to the deadtime, and deadtime squared, respectively.
(2) Control is faster for existing tuning settings. The addition of deadtime compensation actually slows down the response for the existing tuning settings. Setpoint metrics, such as rise time, and load response metrics, such as peak error, will be adversely affected. Assuming the PID was tuned for a smooth stable response, the controller must be retuned for a faster response (see slide 11). For a PID already tuned for maximum disturbance rejection, the gain can be increased by 250%. For deadtime dominant systems where the total loop deadtime is much greater than the largest loop time constant (hopefully the process time constant), the reset time must also be decreased or there will be severe undershoot. If you decrease the reset time to its optimum, undershoot and overshoot are about equal. For the test case where the total loop deadtime to primary process time constant ratio was 10:1, you could decrease the reset time by a factor of 10, smaller than what was noted on slide 11. Further study is needed as to whether the ratio of the old to new reset time is comparable to the ratio of deadtime to time constant and whether the PID module execution time (0.5 sec) is the low limit to the reset time for an accurate deadtime estimate.
(3) Compensators work better for loops dominated by a large deadtime. The reduction in rise time is greatest and the sensitivity to per cent deadtime modeling error particularly for an overestimate of deadtime is least for the loop that was dominated by the process time constant. You could have a deadtime estimate that was 100% high before you would see a significant jagged response when the process time constant was much larger than the process deadtime. For a deadtime estimate that was 50% too low, some rounded oscillations developed for this loop. The loop simply degrades to the response that would occur from the high PID gain as the compensator deadtime is decreased to zero. While the magnitude of the error in deadtime seems small, you have to remember that for an industrial temperature control application, the loop deadtime and process time constant would be often at least 100 times larger. For a 400 second deadtime and 10,000 second process time constant, a compensator deadtime would need to be 200 seconds smaller or 400 seconds larger than actual to start to cause a problem. In contrast, the deadtime dominant loop developed a jagged response for a deadtime that was high or low by just 10%. I think this requirement is unreasonable in industrial processes. A small filter of 1 second on the input to the deadtime block in the BKCAL path may have helped.
(4) An underestimate of the deadtime leads to instability. In tuning calculations for a conventional PID, a smaller than actual deadtime can cause an excessively oscillatory response. Contrary to the effect of deadtime on tuning calculations, a compensator deadtime smaller than the actual deadtime will only cause instability if the controller is tuned aggressively after the deadtime compensator is added.
(5) An overestimate of the deadtime leads to sluggish response and greater stability. In tuning calculations for a conventional PID, a larger than actual deadtime can cause an excessively slow response. Contrary to the effect of deadtime on tuning calculations, a compensator deadtime greater than the actual deadtime will cause jagged irregular oscillations.