Controller Attenuation and Resonance Tips

When is a controller in automatic not able to do anything to reduce an oscillation? When will a controller amplify an oscillation? In both of these cases, the controller is doing more harm than good by wearing out valves and upsetting other loops. Here we look at how to tell if an oscillation is likely to cause either of these scenarios and what we can do to reduce the detrimental effect on the process.

For oscillation periods between ½ and 2 times the ultimate period (e.g. 2 to 8 dead times), resonance can be occurring. Figure 8.1 in the file Attenuation-and-Resonance-Amplitude-Ratio shows the general effect of resonance where feedbacks control action becomes in phase with the disturbance causing an amplification of the oscillation amplitude. The amplification becomes greater as the PID is more aggressively tuned. Note that abscissa (X axis) of this plot is the log of the ratio of oscillation period to ultimate period whereas the literature uses an abscissa that is the log of the ratio of the oscillation frequency to the natural frequency. An abscissa in the time domain enables a better visualization from trend chart oscillation periods and estimating the ultimate period as simply 4 times the dead time but the result is horizontal flip of what is normally seen in the literature.

For oscillations periods much less than the ultimate period, the process provides significant attenuation by the process time constant acting as a filter. The equation in the previous blog Measurement Attenuation and Deception can be used to estimate the attenuation by the process.

The PID provides no feedback correction for a fast load oscillation as seen in Figure 8.4a in the file Attenuation-and-Resonance-Test-Results. A trend of the PID in manual eliminates the feedback correction so that only the effect of the attenuation by the process time constant is seen. These extremely fast oscillations can be effectively considered to be noise and the best thing the PIUD can do is ignore it. While the oscillation is not made worse by PID control, Figure 8.4b shows how more aggressive tuning cause unnecessary extra movement of the valve that can prematurely wear out packing and can upset other loops particularly when there is no large process time constant acting as a filter of the process variability introduced by the oscillations in the manipulated flow.

For oscillation periods between ½ and twice the ultimate period, the aggressive tuning causes amplification from resonance where the feedback correction oscillation gets in phase with the load oscillation. Here the PID is clearly doing more harm than good and the more aggressive tuning is clearly detrimental.

When the load oscillation period becomes greater than twice the ultimate period the most aggressive tuning settings noticeably decreases the amplitude of the process variable oscillation compared to the PID in manual oscillation. The oscillation in the PID output is larger for the most aggressive settings.

For oscillations periods much greater than the ultimate period the process provides no attenuation. Here PID feedback correction can be significant. More aggressive tuning provides a greater reduction in the oscillation amplitude as seen in the Figure 8.5a test results for a slow load oscillation. The benefit from aggressive tuning is not as noticeable as the load oscillation period increases toward the point where PID control can make the oscillation in the process variable disappear to the point of being lost in noise and measurement or final control element precision limit cycles. The oscillation will be totally visible in the PID output. Tight PID control will almost completely transfer variability from the process variable to the manipulated variable as seen in the valve movement in Figure 8.5b. This transfer has many implications in terms of tracking the path of variability propagation and what variables are chosen for developing neural network models and projection to latent structures (partial least squares) models. The benefit of more aggressive tuning will not be so clear for oscillations with a period that is incredibly long (e.g. 1000 times the ultimate period), which might be the case for day to night effects on operating conditions.

So what can we do about fast oscillations? The best thing to do is mitigate the source of the oscillation. See my 5/30/2013 blog Causes and Fixes for Fast Oscillations for some tips.

We can also judiciously add a signal filter just large enough to prevent wearing out the valve and upsetting other loops. For a slow process (e.g., liquid temperature), a velocity limit can screen out noise without adding a measurement lag. See my 12/12/2012 blog What are Good Signal Filtering Tips? for some ideas. Note that for wireless transmitters, the filtering is best done via a transmitter damping adjustment to reduce unnecessary updates. The wireless trigger level should be set to be larger than noise amplitude after the judicious use of transmitter damping. An enhanced PID in conjunction with a threshold sensitivity limit can stop reaction to noise.

Given that we are stuck with an oscillation that is causing resonance, the next step is to decrease the PID gain. This can be done by increasing lambda to 3 or more dead times.