The effects of measurement dynamics are similar to the effects of controller dynamics except there are often many more sources of lags and delays and the consequences are generally more severe. Delays are the result of transportation delays and discontinuous updates from periodic sampling and cycle times in digital signals, wireless devices, and analyzers. Lags originate from sensors (e.g. thermowells and electrodes) and fixed or adjustable filtering in the transmitter to reduce noise from the sensor and in calculations.
The dead time from discontinuous signals is the update time plus any latency. For analyzers the latency is the cycle time since the result is available at the end of the analysis cycle time. The resulting dead time is 1.5 times the cycle time. There can be additional dead time from sample transportation and from multiplexing. For wireless transmitters the latency is zero.
The largest lag from sensors and transmitters may be taken as a secondary time constant in a second order plus dead time approximation. More commonly, these measurement lags are taken as additional dead time. If the lag is small compared to the primary time constant, nearly all of the lag can be taken as additional dead time.
If the total dead time as a result of an increase in measurement lags or delays becomes larger than the implied dead time for the present tuning settings, oscillations will develop and the controller needs to be tuned for a slower response.
Equations can also estimate the kicking in a PID output from discontinuous updates. The equation shows that wireless trigger level should be small enough and the update rate large enough to increase the signal to noise ratio for slow processes.
The simple equation to estimate the attenuation of an oscillation by a time constant in the last blog “Effect of Measurement Dynamics Perspective” enables the setting of a filter just large enough to reduce the adverse effects of noise and to predict the behavior of the actual process variable before filtering.
Equations for the ultimate period can be used to determine the adverse effect of measurement dynamics on the ultimate limit to loop performance. More specifically, equations for runaway processes can show how the ratio of the maximum to minimum controller gain changes with temperature measurement lag. The ratio should be around 10 to allow for nonlinearities and non-idealities. For a ratio of 1 the maximum and minimum controller gains are the same and the window of allowable controller gains closes. The open loop unstable process is closed loop unstable regardless of tuning.
Recommendations
- The update time interval should be large enough (update rate slow enough) to minimize resolution or threshold sensitivity errors (particularly in slow loops). The goal here is to make the real change in the process approach or exceed the resolution or threshold sensitivity to improve the signal to noise ratio.
- The update time interval should be small enough (update rate fast enough) to minimize the peak and integrated errors (particularly in fast loops). The goal here is to minimize the increase in total loop dead time.
- Use the equation for the integrated error (Equation 2 in PID Tuning Rules) to determine if the digital device and wireless update rate and measurement filter time are too large.
- Estimate the worst case increase in peak error as the sum of the digital device and wireless update rate (update time interval) plus the measurement filter time multiplied by the maximum rate of change of the process variable.
- If the measurement lag becomes the largest time constant in the loop, use given equation to compute actual process variable amplitude from measured amplitude.
- Set the transmitter damping just large enough so fluctuations in the controller output from noise do not cause a change in valve position or prime mover speed or an unnecessary wireless transmitter update.
- Estimate the increase in total loop dead time from measurement lags, delays, and discontinuous updates (e.g. analyzers, digital devices, and wireless).
- If the discontinuous update time becomes larger than the process 63% response time (process dead time plus time constant), use an enhanced PID.
- If the measurement lag becomes large enough to be considered a secondary lag in an integrating or runaway process, use the equations for the ultimate period to estimate the severe implications for tuning and the ultimate limit to performance.
- If the measurement lag approaches or exceeds the loop dead time and cannot be reduced, set the PID rate time equal to the lag to compensate for the lag.
- Consider whether a small threshold sensitivity limit would help increase the controller gain or enable an enhanced PID to stop limit cycles.
- For wireless devices on slow processes, set the wireless update rate slow enough and the trigger level small enough where the actual process change in the update time is larger than the trigger level.
- For wireless devices, make sure the wireless trigger level is lower than the measurement tolerance to meet environmental or pharmaceutical regulatory requirements and if permitted higher than sensor or process noise or the threshold sensitivity limit of the sensor.
- For runaway processes, estimate the effect of the sensor lag on the ratio of the maximum to minimum controller gain.
