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Step response of "Rate of Change" alarms
Rate-of-change (ROC) alarms detect the rate at which the measured variable is changing. Their ability to respond to a step change is limited. This article explains what response can be expected from an ROC alarm.
Rate of change (ROC) alarm systems are expected to measure the difference in the measured variable (MV) over a specified time period. As such they play a role of a 'differentiator', i.e. in mathematical terms their output u equals:
u = d(MV)/dt
This property can have the undesirable effect of amplifying noise, since noisy (fluctuating) signals will exhibit continuous high momentary rates of change (just think of daily currency exchange rate fluctuations!).
To avoid spurious alarms, and to detect the underlying trends in the Measured Variable, a degree of filtering must be added. The simplest form of that is to choose the sampling rate which is appropriate for the real rate of change of interest.
For example: if we need to measure 6 deg C a minute rate, selecting a sampling time of 1 second is not appropriate. The real temperature readings recorded over a whole minute could fluctuate every second like this:
200.0, 200.2, 200.1, 200.4, 200.3, 200.6, 200.5 ....... 206.0, 205.9
If measured every second, the system would indicate between positive 0.2/s (+12 deg C per minute) and negative 0.2/s (-12 deg C per minute). However, if we consider only the first and last samples over one minute, we'll get the correct reading of 6 deg C change over a minute +/-0.1 degree.
The role of a proper rate-of-change filter is exactly to reject these short fluctuations and measure the correct underlying rate at which the signal is changing.
However, the very same methods that suppress fluctuations also limit the ability of the rate-of-change measuring system to respond to step changes in the measured variable.
This is because, with the step change, the actual duration of time over which the change in measured variable actually occurs is very small compared with the period over which the change is being detected.
Example 1: the system described above changes suddenly by 6 degrees in 10 seconds. However, our sampling time is still one minute. Hence the change in measure variable is only checked after a minute and the same 6 degrees a minute result is recorded. The real rate, however, peaked at 6 degrees in 10 seconds, which is 36 degrees a minute. We can say that the measured rate only got to within 1/6 of the actual maximum rate, or alternatively that the step change was suppressed.
Process measurements normally include front end filtering low-pass to prevent fluctuation from affecting any instrumentation, not just the rate of change filter. The presence of the additional filter makes response analysis more complicated. Generally, if the filter response is in the similar range as the rate of change sampling or averaging time, the filter helps.
Example 2: A Maxiflex M1431B 8 channel isolated Voltage/Current input module is being used to detect an abnormal rate-of-change condition. The module is configured for the fast sampling rate of 1 second. If a 10% step change takes place in the input signal, then the recorded rate in the module will reach approximately 8.4%, close to the real figure.
Example 3: If, in example 2, the Maxiflex module is set to the slow sampling rate (which includes additional rate filtering for highest accuracy at slow rates of change), then the same 10% step change of the input will only produce a rate-of-change response peaking at about 2%.
Conclusion: If checking for rate of change, the system tries to reject instantaneous fluctuations and detect the underlying trend (up or down) in the measured variable. However, the same mechanism will partly suppress any step change in the variable and the step change will only appear as a temporary peak at the rate-of-change output. The most accurate detection of rate-of-change will occur when the change occurs over a period of time at least equal to the sampling rate of the instrument.
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