There is absolutely no potential difference in accuracy between quadrature, co-tangent, and absolute encoders.
True.
But I don't believe that I stated, or implied, that there was any difference in
accuracy among the three rotary position sensors you mention. There can be significant differences in
cost and
required instrumentation for a given resolution and accuracy.
Fortunately, if the OP sticks with Baumer, the cost of the existing but obsolete transducer is nil, and there is a PC (personal computer) module, part number 139338, that directly interfaces with his SSI (Synchronous Serial Interface). It even comes with some software.
There are also other PC modules, from other manufacturers, that will drive various types of motors connected to the gear-train whose backlash you want to test. Or you can roll your own motor drivers, always an interesting project in itself. A PC solution means abandoning the Productivity 1000 PLC and writing a program, which
@Cliff T. may not feel comfortable doing if already experienced with programming the PLC.
If someone can manufacture an optical disk with some arbitrary number of alternating transparent and opaque segments evenly distributed around the circumferance, it is almost trivial to add additional concentric tracks with some sort of binary-coded position information (such as a Gray code), along with appropriately positioned optical sensors for each additional track. Of course the alignment, or run-out, of the disk becomes more difficult as more bits of resolution are added, but this is a presumably solved problem. There is also the possibility of using magnetically encoded disks. Magnetic coding has been used for years as a durable position readout on machine tools, but I have no idea what the state-of-the-art is today.
Things have changed since I had a go at optical encoders, which was sometime in the late 1960s for a stepper motor application driving the sine-bar mechanism that rotated a precision-machined diffraction grating in a
Czerny-Turner monochromator.
The end-user wanted to use his monochromator as an illumination source for measuring transmission losses, as a function of various visible and near-infrared wavelengths passing through sample laser-window materials. We needed to read the grating position to determine amplitude corrections to be applied to a photo-multiplier tube (PMT) output current after analog logarithmic amplification to linearize the illumination intensity as a function of wave length.
The absolute grating position was to be determined by counting up/down pulses from a quadrature encoder connected to the double-ended stepper motor drive shaft. The grating position, digitized to eight bits, addressed a look-up-table (LUT) that stored the correction values as twelve-bit data that was applied to a Burr-Brown multiplying digital-to-analog converter (DAC). The PMT logarithmic amplifier output was the other multiplicand, and the DAC analog output product.was a measure of the window transmission as a function of wavelength. Or so we hoped.
We used a commercial off-the-shelf (COTS) up/down counter with quadrature square-wave inputs and binary-coded-decimal (BCD) display outputs and Nixie tube optical display of the digits, so the operator could "dial in" or see whatever wavelength of illumination the monochromator was producing. We also wired in a second up/down 8-bit binary counter that operated in parallel with the COTS BCD up/down counter. The only function of this 8-bit counter was to address the LUT. There was also a mechanical decimal counter, part of the original equipment, attached to the sine-bar mechanism that also allowed the wavelength to be read visually.
This was a complicated electro-optical and electro-mechanical project that really tested my developing electronics technician skills. The stepper motor was a large Superior Electric motor that was usually driven with 60 Hz AC, using a phase-shift capacitor to produce quadrature excitation currents for the two windings. We needed to drive it with variable-frequency DC square waves in discrete rotational increments. Easy peasy today with switch-mode MOSFETs and PWM control of the motor winding currents.
A real PITA back then was the huge power-wasting, forced-air cooled, wire-wound, ceramic-insulated, current-limiting resistors in series with each motor winding. We drove the windings from a large DC power supply through several (I forget how many) 2N3055 NPN power transistors operating as saturated switches. The whole electronics package looked like a kluge. The heat given off was huge. Plus, in retrospect, I think the mechanical engineer who specified the Superior Electric stepping motor went a little overboard on the size. I now know enough mechanical engineering today (but not then) to specify a better motor solution.
Anyhoo, we spent a few months getting it all wired up and tested to make sure the stepper motor would rotate the diffraction grating. I also had to come up with an easy method to download the 256 values for the 12-bit LUT. Back then, we had no flash memory to store data so the LUT had to be re-loaded after every power interruption. Could have used battery backup, but the static random access memory (SRAM) was a relative power hog. The LUT values were also subject to change for a number of reasons, so the load mechanism had to be simple.
We toyed around with the idea of using ASR-33 teletype terminals to punch and read a "LUT tape" but the end user didn't want to tie their monochromator down to a huge, noisy, teletype terminal. The final solution was a program, written in interpreted BASIC, that accepted user input at the teletype terminal (connected to a time-sharing computer located elsewhere) and produced a punched tape output. Of course the output was 7-bit ASCII characters, which then had to be converted to 8-bit binary values after reading the tape. But this was all transparent to the end user. All they had to do was type in 256 decimal values, each representing a 12-bit binary number, and the software would output, and punch onto paper tape, two ASCII characters for each of those input values. A tape reader on the kluge would then read the tape, strip off the bits in the two characters representing the 12-bit LUT data value, and sequentially load the LUT. Entire read and load process took about ten seconds IIRC. The ASR-33 was only needed when a new "program" tape for the LUT needed to be generated.
I thought we were done, but sadly several months of troubleshooting lay ahead. Turns out the differential rotary transducer was somehow "losing" some pulses and a cumulative position error would occur as a result. Thankfully, we had left the mechanical wavelength counter intact, so it was easy to manually drive the grating to a known position and then reset the counter. But it took weeks to find out what was causing the problem. I won't go into any detail about how we eventually solved this, but if
@Cliff T. experiences similar difficulties, perhaps we can start another thread on how to troubleshoot and permanently "fix" the problem.