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:

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.
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. On many systems the velocity measurement is used (with the differential gain) to increase the system stability. Excessive quantizing noise on the velocity measurement limits its effectiveness.

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 obtained by the RMC70 MA Module is 0.0005 inch with 1 recirculation. The resolution obtained by the RMC150 MDT Module is 0.001 inch with 1 recirculation.
SSI
The SSI transducer sends the position information digitally, so the only limit is in the transducer or encoder. Five micron resolution is common for linear SSI transducers, and 8192 counts per turn is common for rotary encoders. Other resolutions are readily available.

The RMC70 MA Module and RMC150 Universal I/O Module support 8 to 32 SSI bits. The RMC150 SSI Module supports 8 to 31 bits. However, Delta recommends that the SSI Counts value should not exceed 24 bits (16,777,216). See the Exceeding 24 Bits section below.

Analog
The RMC70 AA, A2, and AP2 modules and the RMC150 H, G, and Universal I/O modules use 16-bit Analog-to-Digital converters. The RMC150 A module uses 12-bit Analog-to-Digital converters.

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

Oversampling
The AA, A2, AP2, H, and G analog-to-digital converters are read eight times 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.
The Universal I/O module's analog inputs are sampled at 60kHz, which is a minimum of 15 times oversampling.
Input Range Gain
Choosing the ±5V or 4-20mA ranges on the RMC150 H or G modules 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.

Module	±10V	±5V	4-20mA
AA, A2, AP2	38.1µV		0	.15µA
Analog (H)	38.1µV	19.1µV	0	.076µA
Analog (G)	38.1µV		0	.15µA
Analog (A)	610µV	305µV	1	.221µA
Universal I/O	38.1µV		0	.15µA

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

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. Encoders with 2000 pulses (or 8000 counts) per turn are common. The maximum quadrature encoder frequency is limited to 8,000,000 counts per second for the RMC70 and 4,000,000 counts per second for the RMC150.

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). 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.