Filter Algorithm Types

This topic describes the different types of filter algorithms in the RMC and lists where they can be applied. For more general information on filtering in the RMC, see the Filtering topic.

The RMC offers the following input filter algorithms in the following areas:

Filter Type	RMC75/150			RMC200
Filter Type	Feedback (Control)	Feedback (Display)	Control Output	Feedback (Control)	Feedback (Display)	Control Output
Low Pass, Single Pole
Low Pass, 2-pole Butterworth
Low Pass, 4-pole Butterworth
Low Pass ABG
Low Pass ABGD
Model

Phase Delay and Attenuation Comparison

The filters exhibit the following frequency response and phase delay at the cut-off frequency:

At Cut-off Frequency:	Magnitude	Phase Delay
Low Pass, Single Pole	-3 dB (0.707)	45º
Low Pass, 2-pole Butterworth	-3 dB (0.707)	90º
Low Pass, 4-pole Butterworth	-3 dB (0.707)	180º
Low Pass ABG	4 dB (1.56)	- 20º (leading)
Low Pass ABGD	4.5 dB (1.67)	0º

Cut-off Frequency Limits

The filter cut-off frequencies are limited to the ranges listed below, based on the frequency of the selected controller Loop Time.

Filter Type	Min Cut-off Frequency	Max Cut-off Frequency
Low Pass, Single Pole (1P)	0.01	50% x loop frequency
Low Pass, 2-pole Butterworth (BW2)	0.01	25% x loop frequency
Low Pass, 4-pole Butterworth (BW4)	0.01	25% x loop frequency
Low Pass ABG	0.01	10% x loop frequency
Low Pass ABGD	0.01	7.5% x loop frequency

For example, the frequency of a 1 msec loop time is 1 kHz, so the ABG filter would be limited to 100 Hz. The frequency of a 0.5 msec loop time is 2 kHz, so the ABG filter would be limited to 200 Hz.

Filter Descriptions

Low Pass

A low-pass filter passes filters out high frequencies, and passes through lower frequencies. The cut-off frequency defines which frequencies are passed through.

Low Pass, Single Pole (1P)

This is the most simple of all filters. A single-pole filter has a small phase delay, but the amplitude starts dropping off with frequency immediately.

Low Pass, 2-pole Butterworth (BW2)

The main advantage of Butterworth filters is that they have unity amplitude out to the cut-off frequency. However, they have a large phase delay. Therefore, a Butterworth filter works very well for viewing signals, since the human eye doesn't mind some delay. Butterworth filters are not so good for high-speed control applications where phase delay cannot be tolerated.

The 2-pole Butterworth has a more gradual cut-off than the 4-pole, and less phase delay.

Low Pass, 4-pole Butterworth (BW4)

Same as the 2-pole Butterworth, but a sharper cut-off and more phase delay.

Low Pass, ABG

The Alpha-Beta-Gamma filter is a simplified form of observer and is closely related to Kalman filters and linear state observers. The ABG filter has very little phase delay, actually leads for some frequency ranges, and the amplitude is above unity for some frequency ranges. This means the filtered signal can overshoot the input signal.

Low Pass, ABGD

The Alpha-Beta-Gamma-Delta filter extends the ABG filter (above) one more level, using a "delta" term for a fourth jerk state. This helps provide more filtering without significantly increasing the phase delay, but also makes this filter a bit more finicky, with a lower maximum filter cut-off frequency.

Model

The Model-base filter uses a model of the system to calculate the Actual Velocity and Actual Acceleration, factoring the Control Output into the model. The Tuning Wizard generates the system model. See Modeling for details.