When specifying a position sensor, it's critical to understand how resolution, accuracy and repeatability impact overall system performance. Precision is affected by the entire motion system and is commonly influenced by mechanical errors like eccentricity, backlash and bearing runout. Eccentricity and backlash are the most significant contributors to mechanical errors and require calibration to correct.

Our blog series considers optical encoders to review resolution, accuracy and repeatability. We will also review eccentricity and backlash, the most significant contributors to mechanical errors, as well as how to correct them with calibration. To begin, we review position sensor resolution.

Encoder Basics

Whether designed with optical, magnetic, inductive or capacitive technology, all rotary encoders generate sine and cosine signals as they rotate. While a resolver has one sinusoidal cycle per revolution, an optical encoder can have thousands.

Figure 1.

As the scale moves relative to the first sensor, the incident light intensity changes and produces a sinusoidal voltage. The sinusoidal shape is due to the geometric design of the sensor. The second sensor is positioned 90 degrees out of phase of the first sensor so that it generates cosine voltage. Pitch-per-revolution, pitch uniformity, signal magnitude and sinusoidal fidelity play a critical role in measurement precision.

Resolution

An encoder's resolution is the shortest distance it can detect. A rotary encoder's resolution is expressed as the number of units of measure within 360 degrees, and each unit is referred to as a “count.” For absolute encoders, resolution is often expressed in binary with “bits.” A 16-bit encoder has 216 (65,536) counts per revolution (CPR).

Figure 2 depicts Encoder A with 360 CPR (1°) resolution and Encoder B with 90 CPR (4°) resolution. The numbers in each box indicate what count the encoder reads. The range covered by an encoder count is often referred to as the “bin.” For example, in Encoder A, count 1 is the bin ranging from 1 to 2°. A blue dot represents the true position to be measured. In this first example, the blue dot is located at 1.5°.

Encoder A reads the blue dot's location as a count reading of “1” because it is positioned between 1° and 2°. Encoder B reads “0” because the blue dot is positioned between 0° and 4°. Encoder A clearly gives more precise position information.

Figure 2.

Now consider one count of movement for both encoders, shown by Figure 3, which is the smallest movement possible. The blue dot's new location after moving one count is represented by the green dot. For Encoder A, the new position would be 2.5° and for Encoder B, 5.5°.

The yellow dot indicates the position where the servo “believes” the movement is completed because the encoder reading increased by one count. This example shows that it is impossible for Encoder B to move by 1 degree because its resolution isn't fine enough to measure a 1-degree movement. Increasing encoder resolution aligns the encoder reading closer to the true position of the green dot.

Make a note that the yellow dot's true position depends on the latency (position capture, processing and communication delay) involved before the servo sees a position change.

Figure 3.

Practical Resolution

The objective of generating sin/cos signals is to interpolate the angle within the scale pitch:

$$ \emptyset=\arctan \left(\frac{\text { SIN Magnitude }}{\operatorname{COS} \text { Magnitude }}\right) $$

It is theoretically possible to have an encoder with infinite resolution. But in practice, resolution is limited by digital-to-analog converter resolution because signals are digitized for processing, and it is also limited by signal-to-noise ratio (SNR).

Figure 4 shows two sinewave segments with the same amount of noise. The sinewave on the right can be digitized into more steps (higher resolution) because the signal is larger relative to the noise floor. Maximizing SNR is critical in high-performance encoder design.

Figure 4.

Encoders with higher resolutions are desirable because they allow for the highest performance with position control. If a servo dithers between two counts, the dithering will be smaller with a higher resolution.

High resolution is also important for precise velocity control at low speeds because of “resolution noise,” which is a variation in the counts of the velocity loop sampling period. This can be represented in Figure 5, where the evenly spaced counts depict a constant velocity. Sample 1 reads three counts while Sample 2 reads four counts which equates to a 33% increase in speed. Higher resolutions significantly diminish this effect.

Figure 5.

At high speeds, high-resolution incremental encoders may generate data rates beyond the controller or servo drive's tracking capability. To avoid this, be sure to check the servo drive's maximum input frequency.

Encoder manufacturers often push the limits of resolution relative to SNR, resulting in the least significant bits of position data bouncing around when there is no motion. It is possible to extract higher resolution from noisy position data by averaging multiple samples. A technique often used in metrology, it is generally impractical in servo systems because the averaging delay compromises servoloop stability.

Stay tuned for our next installment on accuracy, repeatability, eccentricity errors and calibration.

Technology Blog

How Resolution, Accuracy and Repeatability Affect System Performance: Part I