Positioning: Resolution and Accuracy

An application’s required positioning resolution dictates the choice of encoder resolution. A well-tuned system can maintain the position within one encoder state (quadcount). Therefore, the encoder resolution in quadcounts (states) should at least correspond to the maximum permissible positioning error. Depending on the response time of the system, a higher encoder resolution should be chosen for the controller to detect deviations faster and counteract quicker.

Observe that it’s not only the resolution of the encoder that influences accurate and dynamic positioning and speed control. It’s the reaction of the system as a whole. The response time may be limited by current and voltage restrictions of the power supply and controller, the sampling rate of the control loop, mass inertias, friction variation, and mechanical play.

Signal jitter — particularly if large compared to the nominal state width of the encoder — reduces the accuracy in terms of the repeatability that can be achieved. In this respect, direct sensing optical encoders have advantages over interpolated magnetic encoders. Direct sensing larger optical encoders also have advantages concerning the absolute accuracy. Their integrated non-linearity (INL) is very small.

Mechanical transformation

Very high accuracy in positioning is difficult to achieve with mechanical transformation and the associated play. Therefore, high-resolution encoders only make sense on direct drive applications. Very often, high-precision positioning not only requires a high number of states, but also a high absolute accuracy. Optical encoders have advantages here, both due to a high resolution and a low INL.

Drive systems with mechanical transformations such as gearheads or lead and ball screws do not require a high encoder resolution. The resolution of the encoder mounted on the motor will be multiplied by the gear reduction. Similarly, on a screw with 5-mm pitch, a moderate encoder resolution of 512 quadcounts (128 CPT) will result in a theoretical position accuracy of the nut of about 10 microns. That’s often much less than the mechanical play in the coupling and nut, and the accuracy of the screw thread.

Absolute encoders

Incremental encoders measure only changes in position and require a homing procedure for absolute position reading. Homing procedures are typically performed at low speeds, taking time that is not available in some applications. In multi-axis systems — for example, in kinematically complex robotic applications with mechanically interdependent axes — homing could cause collisions and damage. In such cases, absolute encoders can be used as an alternative to incremental models. After being switched on, absolute encoders provide the actual position directly (without a homing procedure) within one motor turn (single turn) or multiple turns (multi turn).

In industrial applications, absolute encoders with a serial interface (SSI or Biss-C) are often used, transmitting the actual position as a bit-stream. A total of only six lines is sufficient for the supply voltage, data transmission, and synchronization of the transmission timing.

For single-turn absolute encoders, one axis revolution is coded in N steps. The coding repeats when rotating more than 360°. Typical resolutions are 12-bit (4096 positions) and more per revolution. In multi-turn absolute encoders, the numbers of revolutions are additionally coded and stored in the same bit stream. Multi-turn encoders are required when the number of measurement steps of a single-turn encoder is not sufficient, for instance for longer paths.

A classic application with absolute encoders is the tracking mechanism of solar installations. Homing with an incremental coder would be too time consuming, as the speeds used for such installations are very slow. For all types of flow regulators, filling systems, and conveyor equipment, it is important to know the exact flow rate from the start. A homing procedure would mean an uncontrolled flow of material. Additional applications with absolute encoders include robotics; handling machines and positioning of machine tables; and spotlights and other stage elements. The maxon positioning controllers (EPOS, MAXPOS) support the use of many variants of absolute encoders.

Encoders for Speed Control

The highest encoder resolutions are required for very precise speed control. The encoder resolution increases with the square of the demanded speed accuracy. In addition, a fast speed-control loop is needed and a high mass inertia has a beneficial effect on speed stability.

How does speed evaluation with incremental encoders work?

Figure 4. Velocity signals recorded on a motor with maxon MR encoder (screenshot from the EPOS2 Studio Data Recorder). The black line is the speed reading of the sensor. It jumps in steps of 30 RPM corresponding to the 1qc/ms resolution. In addition, the signal exhibits a period of 30 ms stemming from the time for 1 motor revolution. The green averaged velocity shows this periodicity more clearly. This average speed signal is closer to the real speed of the motor. However, in this case it instead reflects the imperfections of the encoder.

The speed is evaluated in the controller by counting the number of state changes within a given time interval. An EPOS2, for example, has a speed controller sampling rate of 1 kHz. Therefore, the internal speed is measured in integers of quadcounts per ms (qc/ms) corresponding to a speed resolution of 30 RPM on a 500 CPT encoder (2000 qc per turn). The lower the encoder resolution, the higher this speed quantization.

It must be emphasized that this is a metrology problem due to the digital acquisition. The values measured is not actually how the system behaves. The actual speed of the motor will assume the set value and will maintain it because of the mechanical inertia (flywheel effect). It’s just the measured values that fluctuate around the average speed (Figure 4).

Speed control at high speeds

The electronic components of the encoder limit the maximum pulse frequency that can be handled and, therefore, restrict the maximum speed of the encoder. In some cases, this restriction stems from mechanical considerations such as unbalance and mounting tolerances.

The frequency constraints at the encoder input on the controller side should also be considered. If very high speeds are required, a correspondingly low encoder resolution must be chosen. A relative speed variation of a few percent at high speeds of several thousand RPM corresponds to tens of RPM absolute accuracy, and is quite easy to achieve.

Speed control at low speeds

While the state counting type of speed evaluation results in good speed control at high speeds, it becomes difficult at very low speeds. Imagine a speed of 60 RPM (one turn per second) to be maintained with an accuracy of 5%, or 3 RPM. With the same 500 CPT encoder and 1-ms control cycle time as previously mentioned, it would not be possible to get a stable and smoothly controlled speed.

To reduce the absolute speed variation, a higher encoder resolution and a faster controller are needed. Imagine an encoder with 5000 CPT in the situation described; there would be ten times more feedback. However, at low speeds, the control loop should be able to react faster for keeping the absolute speed deviation small. Both requirements increase the demands on the encoder. The encoder resolution increases with the square of the absolute speed stability — half the permitted speed variation requires a four times higher encoder resolution.

At very low speeds, some controllers allow an alternative method of speed evaluation. They measure the time that elapses between two states. The speed feedback values will be more homogeneous, allowing a stiffer and more dynamic control.

The EPOS4 controller supports another method at low speeds, called speed observer. The speed observer is an element in the control loop that calculates the observed speed in two steps. First, the speed, position, and external torque are predicted based on the parameters that define the mechanical transfer function of the system. Second, the predicted values are corrected based on the newly measured rotor position.

NASA Tech Briefs Magazine

This article first appeared in the January, 2017 issue of NASA Tech Briefs Magazine.

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