Effect of Noise, Update Rate, Trigger Level, and Stick-Slip on Performance

Since the ultimate limit to loop performance depends upon deadtime, the effect of deadband, noise, update rate, trigger level (threshold sensitivity), and valve sensitivity-resolution (stick-slip) on the best possible performance can be estimated by the amount of equivalent deadtime these terms add to the loop. The dependence of loop performance on deadtime for unmeasured step disturbances is seen in Equations 14-3 and 14-4 on page 3 of Industrial-Applications-of-PID-Control. All loops have some degree of these terms. For flow, level, and pressure loops, the deadtime from the automation system exceeds the process deadtime. The practical limit of loop performance depends upon controller tuning as shown in Equations 14-1 and 14-2. Most loops are tuned slower than optimum in order to provide a smoother and more robust and conservative response. Therefore the practical limit is more often in effect. However, since tuning practices vary so widely, a more common basis for comparing the effects of these terms for system design is to use the ultimate limit. The practical and ultimate limits are reconciled by the amount of equivalent deadtime associated with a detuned controller as expressed in Equation 14-6 on page 5. In other words to see the benefit of a reduction in automation system or process deadtime, one must tune the controller more aggressively to take advantage of the improvement. A finer but important point is that the largest time constant must be in the process downstream of the disturbance to see the benefit from the time constant slowing down the actual disturbance and not just the controller response. Equations 14-1 and 14-2 still hold if the large time constant is in the measurement but the predicted errors are for the measured variable and not the actual process variable because the trend is a filtered version of the real process excursion.

The effect of small controller scan times can be estimated by Equation 14-2 on page 3. For larger values, the effect should be studied in terms of its size compared to the original deadtime and the 63% per cent response time. The scan time can also introduce a resolution error for rapidly changing measurements as exemplified in silicon wafer manufacturing temperature control example in April 2011 Control Talk column “Ultimate Limits to Performance” where a 1 second scan time introduces a 1.6 deg resolution error because the temperature is changing 100 degrees/min

Equations 14-11 through 14-18 on pages 34 – 36 show the effect of noise, wireless settings. and control valve sensitivity-resolution. The absolute effect depends upon increase in the total deadtime as a fraction of the 63% response time. The relative effect depends upon the new versus the original deadtime. For the small deadtime to time constant ratios found in vessel temperature loops, the difference in these perspectives is significant. For a 10 degree open loop error, if the original deadtime is 1 minute and the process time constant is 100 minutes and the additional deadtime is 1 minute, the peak error goes from 0.1 to 0.2 degrees and the integrated error goes from 0.1 to 0.4 deg*min. This doesn’t sound too bad until you realize you have doubled the peak error and quadrupled the integrated error. However, the real limitation is noise because it prevents one from using the high controller gains possible for a small deadtime constant ratio. Consequently, the introduction of a threshold sensitivity setting by the wireless trigger level or an enhanced PID for wireless option can mitigate the effect of noise on controller gain and thus improve actual performance. The resulting increase in the rate of change of the controller output also reduces the deadtime from the control valve sensitivity-resolution limit associated with stiction. The beneficial effects of the threshold sensitivity setting is quantified by Equations 14-18a through 14-18e on page 36. The threshold sensitivity setting with the enhanced PID can also eliminate the limit cycles from valve stiction (stick-slip) and backlash (deadband).

Equation 14-5b on page 4 shows the rise time of the setpoint response (time to setpoint) is the inverse of the product of the near or real integrating process gain and controller gain plus the original deadtime. This is the response of the actual process variable that does not depend upon the wireless update rate. The observed response is delayed by the update rate. If the wireless update rate is larger than the process response time, the enhanced PID controller gain can be set equal to the inverse of the process gain. For a setpoint change, the enhanced PID makes a single move that gets the actual process variable to the setpoint per the process response time. Here again, the observed response will be delayed by the wireless update rate. We have the interesting situation where the actual performance is better than the observed response. The use of a threshold sensitivity to eliminate reaction to noise allows an increase in controller gain and thus a reduction in rise time. Thus, an increase in the wireless update rate and threshold sensitivity setting can improve the setpoint response and might be the right choice if the additional deadtime does not cause an appreciable increase in the errors for unmeasured disturbances.