An incremental encoder disk is patterned with a track of slots along the periphery, as shown in Figure 15-1. These slots create an alternating pattern of dark and light lines. The disk count is defined as the number of dark and light line pairs that occur per revolution (lines per revolution). As a rule, a second track is added to generate a signal that occurs once per revolution (index signal: QEPI), which can be used to indicate an absolute position. Encoder manufacturers identify the index pulse using different terms such as index, marker, home position, and zero reference

Figure 15-1 Optical Encoder Disk

To derive direction information, the lines on the disk are read out by two different photo-elements that "look" at the disk pattern with a mechanical shift of 1/4 the pitch of a line pair between them. This shift is detected with a reticle or mask that restricts the view of the photo-element to the desired part of the disk lines. As the disk rotates, the two photo-elements generate signals that are shifted 90° out of phase from each other. These are commonly called the quadrature QEPA and QEPB signals. The clockwise direction for most encoders is defined as the QEPA channel going positive before the QEPB channel and conversely, as shown in Figure 15-2.

Figure 15-2 QEP Encoder Output Signal for Forward/Reverse Movement

The encoder wheel typically makes one revolution for every revolution of the motor, or the wheel can be at a geared rotation ratio with respect to the motor. Therefore, the frequency of the digital signal coming from the QEPA and QEPB outputs varies proportionally with the velocity of the motor. For example, a 2000-line encoder directly coupled to a motor running at 5000 revolutions-per-minute (rpm) results in a frequency of 166.6kHz, so by measuring the frequency of either the QEPA or QEPB output, the processor can determine the velocity of the motor.

Quadrature encoders from different manufacturers come with two forms of index pulse (gated index pulse or ungated index pulse) as shown in Figure 15-3. A nonstandard form of index pulse is ungated. In the ungated configuration, the index edges are not necessarily coincident with A and B signals. The gated index pulse is aligned to any of the four quadrature edges and width of the index pulse and can be equal to a quarter, half, or full period of the quadrature signal.

Figure 15-3 Index Pulse Example

Some typical applications of shaft encoders include robotics and computer input in the form of a mouse. Inside your mouse you can see where the mouse ball spins a pair of axles (a left/right, and an up/down axle). These axles are connected to optical shaft encoders that effectively tell the computer how fast and in what direction the mouse is moving.

General Issues: Estimating velocity from a digital position sensor is a cost-effective strategy in motor control. Two different first order approximations for velocity can be written as:

Equation 11.

Equation 12.

where:

• v(k) = Velocity at time instant k
• x(k) = Position at time instant k
• x(k-1) = Position at time instant k-1
• T = Fixed unit time or inverse of velocity calculation rate
• ΔX = Incremental position movement in unit time
• t(k) = Time instant "k"
• t(k-1) = Time instant "k-1"
• X = Fixed unit position
• ΔT = Incremental time elapsed for unit position movement

Equation 11 is the conventional approach to velocity estimation and requires a time base to provide a unit time event for velocity calculation. Unit time is basically the inverse of the velocity calculation rate.

The encoder count (position) is read once during each unit time event. The quantity [x(k) - x(k-1)] is formed by subtracting the previous reading from the current reading. Then the velocity estimate is computed by multiplying by the known constant 1/T (where T is the constant time between unit time events and is known in advance).

Estimation based on Equation 11 has an inherent accuracy limit directly related to the resolution of the position sensor and the unit time period T. For example, consider a 500 line-per-revolution quadrature encoder with a velocity calculation rate of 400Hz. When used for position, the quadrature encoder gives a four-fold increase in resolution; in this case, 2000 counts-per-revolution. The minimum rotation that can be detected is, therefore, 0.0005 revolutions, which gives a velocity resolution of 12rpm when sampled at 400Hz. While this resolution can be satisfactory at moderate or high speeds, for example 1% error at 1200rpm, this resolution clearly proves inadequate at low speeds. In fact, at speeds below 12rpm, the speed estimate is erroneously zero much of the time.

At low speed, Equation 12 provides a more accurate approach. It requires a position sensor that outputs a fixed interval pulse train, such as the aforementioned quadrature encoder. The width of each pulse is defined by motor speed for a given sensor resolution. Equation 12 can be used to calculate motor speed by measuring the elapsed time between successive quadrature pulse edges. However, this method suffers from the opposite limitation, as does Equation 11. A combination of relatively large motor speeds and high sensor resolution makes the time interval ΔT small, and thus more greatly influenced by the timer resolution. This can introduce considerable error into high-speed estimates.

For systems with a large speed range (that is, speed estimation is needed at both low and high speeds), one approach is to use Equation 12 at low speed and have the DSP software switch over to Equation 11 when the motor speed rises above some specified threshold.