Feedback Resolution

Feedback Resolution specifies the smallest increment that can be measured by the feedback device (such as a position transducer or encoder). With analog feedback, the resolution can also be a function of the input circuit (Analog-to-Digital converter) on the controller. Sometimes resolution is referred to as granularity.

Why is Feedback Resolution Important?

There are two main reasons why feedback resolution is important:

1. Positioning Accuracy
   The controller cannot hold a position if it can’t accurately determine how close it is to the desired position. It is generally necessary to have resolution that is several times better than the desired accuracy. Notice, however, that high resolution is a requirement for, but is not equivalent to high accuracy.

2. Quantization Noise
   A less obvious, but equally important reason is quantization noise. Since velocity is the change in position per unit of time, the velocity resolution is dependent on the position resolution and the controller loop time. If the controller has a 1 millisecond loop time, the velocity resolution will be 1000 times worse than the position resolution. The acceleration measurement will be 1000 times worse than the velocity measurement. The differential gain and double differential gain use the actual velocity and actual acceleration respectively, to increase the system stability. Excessive quantizing noise severely limits the effectiveness of these gains.

Maximum Feedback Resolution for the RMC

The maximum resolution available on the RMC for various feedback types is listed below:

• MDT
  For MDT Start/Stop or PWM feedback with a typical transducer having a gradient (or calibration constant) of 9 µs/in, the resolution of obtained by the RMC is:

• RMC75 MA Module: 0.0005 inch with 1 recirculation

• RMC150 MDT Module: 0.001 inch with 1 recirculation

• RMC200 S8 and U14: 0.0005 inch with 1 recirculation

• SSI
  The SSI transducer sends the position information digitally, so the only limit is in the transducer or encoder. One micron resolution is common for linear SSI transducers, and 8192 counts per turn is common for rotary encoders. Other resolutions are readily available.
  The number of supported SSI bits is:

• RMC75 MA module: 8 to 32 SSI bits

• RMC150 Universal I/O module: 8 to 32 SSI bits

• RMC150 SSI module: 8 to 31 SSI bits

• RMC200 S8 and U14: 8 to 32 SSI bits

Delta recommends that the SSI Counts value should not exceed 24 bits (16,777,216). See the Exceeding 24 Bits section below.

• Load Cell

The analog-to-digital converter on the LC8 load cell input is 24 bits. The effective resolution is lower, at approximately 17 bits, depending on the LC8 module filter settings and external noise. Given that the input range is ±34.5 mV, and an approximate resolution is 17 bits, the effective resolution is 540 nanovolts.

Note:
Typically, noise on the load cell wires will exceed these small resolution values, and will have a larger impact on system performance.

• Analog
  The RMC Analog-to-Digital converter support the following number of bits:

• RMC75 AA, A2, and AP2: 16 bits

• RMC150 H, G, and Universal I/O: 16 bits

• RMC150 A: 12 bits

• RMC200 A8 and U14: 18 bits

The effective resolution of the Analog-to-Digital converted signal is increased by the following items:

1. Oversampling
   The analog-to-digital converters are read multiple times per sample, increasing the effective resolution of the Analog-to-Digital converted signal:

1. AA, A2, AP2, H, and G: eight times oversampling per sample, increasing the effective resolution of the Analog-to-Digital converted signal. For example, the eight times oversampling causes a 16-bit input's effective resolution to be 19 bits (one part in 524,288) over the full ±10V range.

2. RMC150 Universal I/O Module: sampled at 60kHz, which is a minimum of 15 times oversampling.

3. RMC200 A8 and U14 module: sampled internally at 200 kHz. The A8 is effectively 20 bits, and the U14 is effectively 21 bits.

2. Input Range Gain
   Choosing the ±5V or 4-20mA ranges on the RMC150 H or G modules or the 4-20 mA range on the U14 module changes the gain of the analog input, increasing the resolution over the requested range.
    

Due to the factors listed above, the effective resolution of the RMC analog inputs is as shown in the table below.

Note:
Typically, noise on the analog signals will exceed these small resolution values, and will have a larger impact on system performance. This is especially true on 18-bit inputs such as the A8 and U14 modules.

• Quadrature
  Quadrature encoder resolution is specified in pulses (also called lines) per revolution on rotary encoders or pulses per inch (or meter) on linear encoders. The RMC quadrature input will decode the pulses to generate four counts per pulse. So the internal resolution on the RMC will be four times the resolution of the encoder given in pulses. For example, encoders with 2000 pulses will have 8000 counts.

The maximum quadrature encoder frequency is limited:

Delta recommends that the quadrature Counts value should not exceed 24 bits (16,777,216). See the Exceeding 24 Bits section below.

• Resolver
  The RMC150 Resolver module can be configured for 14 or 16 bits per revolution. One revolution of the resolver will always consist of 65,536 counts on the RMC, regardless of the resolver resolution parameter. With 16-bit resolution, the counts will increment by one; with 14-bit resolution the counts will increment by four.

Exceeding 24 Bits

The quadrature and SSI inputs can handle Counts values up to 32 bits. However, Delta recommends that you design your system and programming such that the quadrature and SSI Counts value do not exceed 24 bits (16,777,216). The RMC can still interface with SSI devices that have more than 24 bits, but you should make sure the counts will not exceed 16,777,216. These limitations do not apply to voltage, current, or MDT feedback types, since their values never exceed 24 bits.

Delta recommends that the Counts value not be allowed to exceed 24 bits (16,777,216) because this causes the Actual Position to lose resolution. This occurs because the Actual Position is stored as a 32-bit floating point number, which is limited to 24 bits of precision. The resolution of a floating-point number depends on how large the number is. For example, a floating point number can precisely represent any integer that fits in 24 bits (-16,777,216 to +16,777,216) or it can represent numbers at a 0.001 resolution in the range of -16,777.216 to +16,777.216.

To determine when an axis’ Actual Position will lose resolution, look at the Counts register. As long as the Counts register stays within 24 bits (-16,777,216 to +16,777,216), then the Actual Position register will approximately match the resolution of the transducer. However, as the Counts move outside that range, the Counts register and the Actual Position register will lose resolution.

For example, if the Counts are 16,777,220 (slightly larger than 24 bits), and the transducer counts (the counts directly from the transducer are represented exactly in the Raw Counts register, which may be different from the Counts register, but it does indicate the change in counts exactly) change by one to 16,777,221, the Counts value will still read 16,777,220. It will not change until the counts have changed by 2, to 16,777,222. This will cause the Actual Position to become "jerky" and will affect the control. This problem is doubled for each power-of-two increase in the Counts value. Notice that the Counts and Actual Position registers are still accurately keeping track of the position change, but they are losing resolution.

Notice that in order to preserve accuracy on incremental feedback types, the RMC internally maintains a 32-bit integer accumulator. This ensures that the position does not drift due to loss of resolution.

Rotary axes use the Count Unwind value, which will keep the Counts within a defined range. Therefore, as long as the Count Unwind is kept below 16,777,216, this additional loss in resolution will not occur.

For linear axes, you can keep the Counts register from exceeding 24 bits by homing the axis, or using the Set Actual Position (49) or Offset Position (47) commands. With quadrature encoder inputs, the usable range with full resolution can be doubled by setting the zero value of the Actual Position to the middle of travel. For absolute linear SSI feedback, you can also use the Count Offset parameter to move the usable Counts range closer to zero.

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