# Tracking Filter Width

March 29, 2018

A tracking filter can be applied to a controller’s input signal to filter out unwanted noise and harmonics, which can affect measurement and control. Engineers can also adjust the width of the tracking filter for a sine sweep test.

To better understand the value of a tracking filter, consider the following:

### The Value of a Tracking Filter

Suppose we run a sine sweep from 5 hertz (Hz) to 100Hz with 1G amplitude. The product resonates at 25Hz, which excites its harmonics: the resonances at frequencies that are multiples of the 25Hz resonant frequency. There is an acceleration at the harmonics in addition to that contributed by the 25Hz vibration.

When the sweep reaches 25Hz, a controller without a tracking filter would read all the accelerations simultaneously and record them at 25Hz.

#### Issues with Noise and Distortion

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 reads 0.4G from the harmonics and 1G acceleration at 25Hz. In other words, the controller measures 1.4G at 25Hz.

The controller wants 1G at 25Hz and decreases the output (drive). The controller was correct when it shook the product with 1G at 25Hz but is now shaking with a lower acceleration. It still reads 1G because it includes the noise and harmonic distortion from other frequencies in the measurement.

#### Uses for Tracking Filters

Tracking filters isolate the pure sine tone 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 acceleration measurement.

Tracking filters are useful in many testing situations. For example, hydraulic shaker tests without a tracking filter may seem capable of controlling vibration at frequencies beyond the shaker’s operating specifications. A vibration at lower frequencies but within specifications could generate an acceleration that the controller reads as high frequencies to control. With a tracking filter, the controller filters out the lower frequency accelerations and will not record them as higher frequencies.

### Comparison of Tracking Filter Widths

Vibration Research ran an experiment to compare tracking filters.

A signal generator output a 1,000Hz sine tone with an amplitude of 1G to the controller’s channel 2 input. The output (drive) of the controller was looped to its channel 1 input. VR was most interested in the channel 2 graph over the course of the controller’s sine sweep test.

VR ran the test with different tracking filter widths. The width of the tracking filter defines the width of the frequency band over which the controller reads acceleration.

For example, take a tracking filter width of 500Hz. When the sine sweep reaches 750Hz, the controller would incorporate some of the 1G acceleration at 1,000Hz from the signal generator into its measurement. Although there was no acceleration at 750Hz, it would appear on the graph as if there was.

#### Results

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

Without a tracking filter, the graph displayed a straight line across the spectrum at 1G. The controller read 1G of acceleration throughout the sine sweep even though the acceleration was at 1,000Hz.

The wider the tracking filter, the wider the curve. With a wider tracking filter, the controller reads the acceleration at 1,000Hz sooner in the 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.

### Tracking Filters in VibrationVIEW

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.

#### Example

If we set the fractional bandwidth to 20%, the width of the tracking filter would be 20% of the sine sweep’s frequency. When the sweep reaches 40Hz, the width of the tracking filter would be 8Hz, and so on.

Then, suppose we ran a sine sweep from 5Hz to 100Hz and set the fractional bandwidth to 20% and the maximum bandwidth to 5Hz.

From 5Hz to 25Hz, the software would use the fractional bandwidth, and the tracking filter width would increase from 1Hz to 5Hz. When the sine sweep reaches 25Hz, the software would switch to the maximum bandwidth because the fractional bandwidth would be the greater of the two over 25Hz. The point at which the fractional bandwidth equals the maximum bandwidth is called the crossover frequency.

### Math Trace for Tracking Filter Width

In VibrationVIEW, a math trace can display the width of a tracking filter during a sine test. This simple trace maps the tracking filter location and width. Additionally, it plots the fixed (or maximum) bandwidth, which is the same throughout the test, and the fractional bandwidth, which increases as the frequency of the test increases.

The correct formula for displaying the width of the tracking filter for a sine test is:

( Freq < ( [PARAM:Frequency] + ((([PARAM:TrackBWFractional]/100) * [PARAM:Frequency])/2) )) && ( Freq > ( [PARAM:Frequency] – ((([PARAM:TrackBWFractional]/100) * [PARAM:Frequency])/2) )) && ( Freq < ( [PARAM:Frequency] + ([PARAM:TrackBWFixed]/2) )) && ( Freq > ( [PARAM:Frequency] – ([PARAM:TrackBWFixed]/2) )) * Demand

See an additional 40 uses for math traces.

#### Example Video

The video below shows the width of a tracking filter with a fixed bandwidth at 50Hz and fractional bandwidth at 20%. The crossover frequency is 250Hz (250Hz * 20% = 50Hz = maximum frequency).

From 10Hz to 250Hz, the tracking filter uses the fractional bandwidth, and the width increases as the frequency of the test increases. When the test reaches 250Hz, the tracking filter uses the fixed (maximum) bandwidth.