Frequency Shaping Tuning

The frequency shaping tuning method is based off of a few basic concepts:

It is an LTI system (or close enough). Required
What is an LTI system?
The frequency response of the system is known.
Use the Bode Tool in MEI's Controls Toolkit to retrieve this data.
The controller's frequency response can be shaped.
Use the Filter Tool in MEI's Controls Toolkit to retrieve this data.

The following example will take you through the major steps in the frequencey shaping method. These following plots were generated using a Trust TA 9000. (www.trustautomation.com)

Get a good model of the plant. What is a plant?

Using the PID algorithm, set Ki and Kd to zero and Kp to a small number (1 or smaller). For Kp, you only need be concerned that the stage is stable. Kp = 1 is convenient for understanding the concepts, but other values or OK. You can set these PID parameters in Motion Console under the Filter Summary Coeffs tab.

After you have set the PID parameters, use the Bode Tool and get a measurement. You will want to run both a sine sweep measurement and a noise based FFT measurement to find out which gives you better result. To learn how to use the Bode Tool, please see the Bode Tool section.

The following plot is a sine sweep measurement.

Sine Sweep Measurement
	Kp = 0 Ki = 0 Kd = 1	Red - Closed Loop Blue - Open Loop

The sine sweep plot gives better data at low frequencies (<5Hz), as shown by less noise and a phase lag closer to -180 degrees (inherent in a motor at low frequencies). This is not a concern, since the system is expected to be fairly insensitive at low frequencies.

Noise-based FFT Measurement
81920/8192
(Measured with 81920 point test length and 8192 point test resolution)

For the sake of visibility, a smoothing factor of 3% will be used with FFT plots unless otherwise mentioned. See the plot below.

Artificially smoothed 3%

The FFT plot shows a resonance at ~685 Hz that the sine sweep misses completely. The sine sweep data is only good for up to about 50 Hz in this system. Although there are several things that can cause high/poor high frequency noise levels, it is most often caused by low encoder resolution.

Generally, sine sweeps measurements are best for low and high frequency systems that have lots of resolution. FFT measurements are best at high frequencies, especially high frequencies when there is little resolution.

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