JUL-AUG 2018

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INTECH JULY/AUGUST 2018 17 PROCESS AUTOMATION remove, noise. Here, if the process is steady, with random fluctuations, the relation for variability attenuation is: The user chooses the value of λ (or alternately f or τ) to temper the noise. Although the benefit of the FoF over the MA filter is computational simplicity, the negative is the persisting influence of long past data. In the MA, once a data value is out of the window, it no longer influences the average. However, in the FoF the past values are exponentially weighted, fading in time, but never to tally leaving. Figure 2 illustrates the performance of a FoF. The filtered value makes a first-or - der response to a change in the process. The lambda values of 0.500 (solid line) and 0.0645 (dashed line) are chosen to represent the same noise reduction ob - tained with the N=3 and N=30 values of the MA filter, λ = 2 ⁄ (N+1). Note: l Both filtered values show an expo- nential rise to the new value, requir- ing three-to-four time constants, a period of N ≅ 3.5/λ, to make about 97 percent of the change to reach the proximity of the new value. l After the spike at sample 120, there is a progressive relaxation back to the filtered value. The key advantage of the FoF over the MA filter is that the algorithm is computationally simple. However, the interpretation of the filter factor or time constant is less intuitive than choosing N in a moving average. And, the FoF does not reject outliers. In either the MA or FoF the user must choose the filter coefficient value to best balance the lag or ramp period and to desirably temper the variation. In either case, the user needs to realize that the lag can be detrimental to con - trol if it is similar in magnitude to the primary time constant or dead time of the process. The filter time constant should not be selected to be any great - er than 1/5 the primary time constant. Filtering might be in any number of places (e.g., on the instrument or sen - sor, in the data acquisition transmittal system, on the I/O cards, in the control device, or as an option in the control algorithm). With a correctly imple - mented controller utilizing derivative, mode, filtering of the CV may not be necessary at all. Both algorithms hide the true magnitude and duration of process spikes. Butterworth filter: Butterworth filters are a family of filters for addressing low, high, or band-limited frequency noise. The first-order low-pass Butterworth filter is the same as the FoF. As the or - der of the filter increases, the sharper the magnitude response is at the cutoff frequency, but more lag is introduced into the system. The FoF removes high- frequency noise (data-to-data varia - tion) but tracks the average. However, in some frequency-based electronic applications, the user desires to have both a low-pass and high-pass filter. Although popular in electronic appli - cations, it is rarely relevant in process monitoring or control. Some control systems use a second-order low-pass Butterworth filter due to its truer re - sponse to process changes (i.e., a lower cutoff frequency can be used to get the same desired attenuation). Statistical filter: One of several ap- proaches is based on a Six Sigma (statis- tical process control) desire to prevent tampering. In the filters discussed, even at steady conditions, the filter will con - tinually report small deviations, and if used in automatic control, the con - troller will seek to correct this residual noise. The prevent-tampering concept is to hold a single filtered value until there is statistically confident evidence that the process value has changed, then change the filtered value. In one technique, a cumulative sum (CUSUM) of deviations of measurement from the filtered value is the observed metric. If the CUSUM becomes statistically sig - nificant (perhaps at the three-sigma level), then there is adequate justifica - tion to change the filtered value. Figure 3 illustrates the CUSUM filter on the same data. Note that the filtered signal does not change during the initial steady state period and quickly jumps when there is a real change. It took about five samples to be statistically confident in the change from 2 to 5. In this set of data, the filter did not jump quite far enough, but made a correction after samples in the 40 to 60 period provided adequate confidence. Also note that the outlier at sample 120 was rejected. The statistically based filters are scale independent; they adapt to the noise amplitude. One author often ap- plies the CUSUM filter to the output of a controller to temper control action, rather than to mask the input CV activ- Figure 3. Characteristic performance of a statistical filter (three-sigma, 99 percent confi- dence) to a pro- cess step change and spike

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