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Resolution, Accuracy, and Repeatability
Resolution, Accuracy, and Repeatability
While evaluating encoders, a few common terms are important to specify the best encoder for a specific application. These terms are often misinterpreted or misused, which can lead to confusion when motion control systems are designed.
This article describes these key terms and how they are related to MicroE encoders. Understanding these terms helps to define the role of the encoder in the overall servo performance of a system. It is to be noted that even the most accurate and repeatable encoder is only a trivial part of the servo performance of a system.
Resolution is the smallest physical movement measurable, and it is defined as the distance of a single count. Resolution is expressed in µm/count or nm/count for linear encoders, and for rotary encoders resolution values are measured in counts/revolution, arc-seconds/count, or µradians/count.
It is necessary to carefully consider the final resolution needed for an application when specifying encoder resolution. The servo control system is likely to dither between two counts. If the resolution needed for an application is 1 micron and a 1 micron encoder is chosen, the final system could dither between two counts (2 microns).
The magnitude of the dither will be reduced when a higher resolution encoder is selected. Choosing a higher resolution encoder also brings with it a few factors to consider in the design of the motion control system.
A primary consideration is that motion controller and servo drive encoder inputs have a maximum frequency that can be supported on their encoder inputs. This limit is clearly specified by most controllers and drives. A common maximum specification is 20 million counts/sec.
For a rotary encoder system with a 5.5” diameter rotary scale like the one shown in Figure 1 (20,250 lines), a resolution of 81 million counts/rev is achieved by an encoder read head with 4000x interpolation. However, using a drive or controller with a 20 million counts/sec maximum encoder input frequency restricts the maximum speed to only 4 RPM.
Figure 1. The majority of MicroE's rotary and linear encoders use a 20 µm pitch grating. Reflected light creates a 20 µm period analog signal that is then interpolated by factor of 4 to a factor of 16,384. The Index reference mark is also shown above the main track.
To address this challenge, a common solution is to use an analog sin/cos output encoder rather than a digital A quad B output encoder. MicroE serial interface encoders, such as the MII6800Si, are also a powerful way to attain high resolution without compromising speed.
Accuracy is the difference between the actual “true” position of the motion axis and the position as reported by the encoder read head. A very accurate measurement standard such as a laser interferometer is required to measure accuracy. Accuracy is expressed in values of Sub Divisional Error (SDE), Slope, Linearity, and/or Total Linearity.
Figure 2. Typical error plot of Veratus tape scale
Sub-Divisional Error (SDE)
SDE is a cyclic error caused by imperfections of the Sine/Cosine analog output. This error appears in the interpolated counts created and does not accumulate. It is measured in the <nm range RMS.
It can also be called intra-fringe accuracy, as it repeats with each diffracted fringe period. Plotting sin and cos outputs in an XY format enables the use of the Lissajous pattern for alignment. A perfect 90 degree angle phase shift and 1:1 amplitude, centered on (0,0) will produce a perfect circle and would represent zero SDE.
All encoder systems possess small deviations from perfection as depicted in exaggerated form in figure 3.
Most MicroE encoders provide electronic gain, phase, and offset corrections to optimize the signal and balance the offsets. This, in turn, minimizes SDE.
Figure 3. Lissajous figures of SDE sources. Red circle is DC offset error, Green is gain mismatch, Blue is phase≠90°.
The maximum expected accumulative error is called slope error, which is a value that can be added to a controller to offset the slope in the plotted data.
Linearity error is the total range of non-accumulating positional error plotted over a meter of travel following the removal of the slope error. Typically, it is measured in ≤ ± µm (max/meter).
The stability and process controls behind the production of linear gratings and scales keeps the slope error in the same range as the linearity error, allowing the total linearity to be specified in the ± µm/m range (Figure 2, range between the lowest and the highest error of blue line). This is also a part of rotational error as well.
Repeatability is the total range of positions attained when the system is commanded to one location, multiple times, under all conditions. The repeatability of any digital servo system as measured at the encoder is specified as ± (resolution) and does not take into account the effects of Abbe error, friction, etc.
Figure 4 illustrates a linear stage’s bidirectional repeatability with data points recorded every millimeter. A ball screw drives this linear stage and a linear encoder provides the plot. Again, a laser interferometer was employed as the measurement standard. In a perfect system, all of the readings would sit directly over each other and resemble a single plot.
The actual repeatability is the range between the lowest reading and the highest reading at one position. In this plot, potential sources of repeatability error include the encoder, backlash, bearings, and stiction (the friction that has the tendency to avoid stationary surfaces from being set in motion).
Figure 4. Stage repeatability plot
Understanding resolution, accuracy, and repeatability thoroughly is a key foundation in identifying the optimal encoder specifications. Determining the right balance between all motion control components is an integral part of specifying the motion control system that satisfies all application requirements.
Choosing the best encoder resolution and accuracy is critical but other factors must be taken into consideration. A highly accurate and repeatable optical encoder alone cannot compensate for a poorly designed positioning device nor will a great mechanical design deliver high performance if the encoder is under specified for a specific application.
This information has been sourced, reviewed and adapted from materials provided by MicroE.
For more information on this source, please visit MicroE.