# Tracking Filter Width

March 29, 2018

The width of the tracking filter can also be adjusted in a sine sweep test. A tracking filter is used on the controller’s inputs to filter out unwanted noise and harmonics from the input signal. This noise can affect the controller’s measurement and control. To better understand the value of a tracking filter, consider the following:

Suppose we run a sine sweep from 5Hz to 100Hz with 1G amplitude. In this example, the sweep is at 25Hz. Additionally, the product resonates at 25Hz, which excites the product’s harmonics—resonances at frequencies that are multiples of the 25Hz resonant frequency. There is acceleration at these other frequencies in addition to the acceleration contributed by the 25Hz vibration.

Without a tracking filter, the controller would read all of these accelerations at the same time and record those accelerations as all occurring at 25Hz. For instance, suppose that when the controller shakes the product at 25Hz with an amplitude of 1G, there is an acceleration of 0.1G at 50Hz and 0.3G at 100Hz (both harmonics of the 25Hz resonance). Without a tracking filter, the controller would “see” 0.4G from those harmonics in addition to the 1G acceleration at 25Hz. In other words, the controller would measure 1.4G, and would consider that acceleration to be occurring at 25Hz. But the controller wants to see 1G at 25Hz, so it decreases the output (drive). The problem is that the controller had actually been doing its job and shaking the product with 1G at 25Hz, but now is shaking the product with, say, 0.6G at 25Hz, even though it is reading 1G, since the noise and harmonic distortion from other frequencies are being included in the measurement.

A tracking filter isolates the pure sine of interest. As the sine sweep progresses, the tracking filter follows the frequency of interest and filters out noise and harmonics from other frequencies. In doing so, the other frequencies do not contribute to the controller’s measurement of the acceleration.

Tracking filters are useful across a variety of testing situations. For example, hydraulic shaker tests without a tracking filter may indicate a capability to control vibration at frequencies beyond the shaker’s operating specs. What is happening is a vibration at lower frequencies, within the shaker specs, generates acceleration that the controller records as acceleration for the high frequencies it is attempting to control. When a tracking filer is applied to this test, the lower frequency accelerations are filtered out and the controller will record no acceleration for higher frequencies.

We ran an experiment to compare tracking filters. A signal generator output a 1000Hz sine tone with amplitude 1G into channel 2 input of the controller. The output (drive) of the controller was looped to the channel 1 input of the controller. Our interest was in the graph of the controller’s channel 2 over the course of the controller’s sine sweep test. The test was run with different tracking filter widths. The width of the tracking filter defines how wide the frequency band is over which the controller reads acceleration. If, for instance, the width of the tracking was 500Hz, then when the sine sweep was at 750Hz, the controller would read some of the 1G acceleration at 1000Hz from the signal generator into its measurement, so that even though there really was no acceleration at 750Hz, it would appear on the graph as if there was.

The results of the experiment at different tracking filter widths are given in Figure 3.1.

Without a tracking filter, the graph displays a straight line across the spectrum at 1G. This makes sense. Without a tracking filter, the controller reads 1G of acceleration throughout the sine sweep, even though this acceleration is at 1000Hz, and therefore plots 1G over the whole spectrum. With a tracking filter, the wider the filter, the wider the curve in the figure above. This makes sense. The wider the tracking filter, the sooner the controller will “see” the acceleration at 1000Hz in the course of the sine sweep. The narrower the tracking filter, the longer it will take in the course of the sweep for the tracking filter to encounter that acceleration.

In VibrationVIEW, the width of the tracking filter can be set in Edit Test > Parameters > Input Filter Parameters. Here, both the fractional bandwidth and the maximum bandwidth of the filter are set. The width of the tracking filter is the lower of the two. Suppose, for instance, we set the fractional bandwidth at 20%. According to this parameter, the width of the tracking filter will be 20% of the frequency of the sine sweep. So, when the sweep is at 40Hz, the width of the tracking filter is 8Hz. The maximum bandwidth defines just that, the maximum bandwidth of the tracking filter throughout the sine sweep. Suppose, for instance, we ran a sine sweep from 5Hz to 100Hz, setting the fractional bandwidth at 20% and the maximum bandwidth at 5Hz. From 5Hz to 25Hz, the fractional bandwidth would be in effect. Over this range, the tracking filter width would increase from 1Hz to 5Hz. When the sine sweep reached 25Hz, the maximum bandwidth of the tracking filter would be in effect, since beyond 25Hz the fractional bandwidth of the tracking filter would exceed the maximum bandwidth, 5Hz. The point at which the fractional bandwidth equals the maximum bandwidth is called the crossover frequency.

The math trace available here shows the width of the tracking filter during a sine test. This simple trace maps the current tracking filter location and width in aqua blue. In addition, this trace plots the fixed (or, maximum) bandwidth in pink (which remains the same throughout the test) and the fractional bandwidth in dark brown (which increases as the frequency of the test increases). The video below shows the width of the tracking filter during a test in which the fixed bandwidth is set at 50Hz and the fractional bandwidth at 20%. The crossover frequency is 250Hz (250Hz * 20% = 50Hz = Maximum frequency). Notice that from 10Hz to 250Hz, the tracking filter takes on the width of the fractional bandwidth, the width increases as the frequency of the test increases. When the test reaches 250Hz, however, the tracking filter takes on the width of the fixed (maximum bandwidth).