It's the Resolution, Stupid! Part 2

Resolution Is More Important Than Most People Think. Read On to Find Out Why.

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By Cecil L. Smith, PE

From Part One: The traditional use of current loops as inputs to control systems is being replaced by measurement devices and/or input systems that provide the measured value in engineering units. In the era of digital technology, this is indeed appropriate. But unfortunately, the resolution of the digital values is often less than what became the norm for current loop inputs, specifically, a resolution of approximately 1 part in 4000.
Normally such a resolution is far beyond what is required on displays to the process operator, management reports, etc. The value chosen for the resolution is usually based on two factors:

1. How many digits after the decimal point do operators really need to see?
2. What is the accuracy of the measurement device itself?

This article examines this issue from the perspective of regulatory control, or more specifically, the impact of the resolution of the measured value on the performance of the proportional-integral-derivative (PID) controller. Control calculations often need a greater resolution than is required for data presented to humans. Furthermore, the performance of regulatory control actually depends on the repeatability of the measurement device, not its accuracy.

The impact of poor resolution on the three modes is as follows:

Proportional mode: Causes the output to change abruptly from one value to another.

Integral or reset mode: Not significantly affected by resolution.

Derivative mode: Causes pulses or "bumps" to appear in the controller output.

Part Two: When the input for the measured variable is the result of an analog-to-digital (A/D) conversion, the result (called the "raw value") is stored in a 16-bit integer format. As more "smarts" are incorporated into either the measurement device or into the input module, the "raw value" can be in engineering units. How does one incorporate this capability into systems whose original architecture contemplated the use of A/D converters?

A common answer: represent the engineering units value in a 16-bit integer word. Let's illustrate this "solution" for temperature inputs. For thermocouples and RTDs, input cards are available that perform the linearization and, for thermocouples, the cold junction compensation to give the temperature in either °C or °F (a configuration option). The result is typically the temperature to the nearest 0.1°, which can be stored in an integer word.

For example, the upper limit of the type J thermocouple is about 1320°F. This would be represented as 13200, which can be stored in a 16-bit integer word. The lower limit is typically -200°F. This would be represented as -2000, which can also be stored in a 16-bit integer word.

Unless one resorts to custom calibration or other methods, representing the temperature to 0.1°F is superior to the accuracy of thermocouples. With RTDs, the current technology provides an accuracy approaching 0.1°F. From an accuracy standpoint, this appears to be a perfectly satisfactory approach. In most applications, it is. However, there are a few exceptions.

As noted previously, the parameter of importance for control applications is repeatability, not accuracy. While 0.1°F is probably adequate for thermocouples in high temperature applications, it is not adequate for RTDs. In applications such as reactor temperature control, the sensor of choice is an RTD. Furthermore, in applications such as reactor temperature control, the derivative mode is frequently used. Today, product chemists expect the reactor temperature to be maintained within 0.5°C of set point, so control performance is of utmost importance.

If one considers the entire measurement range of the type J thermocouple, the input range is -2000 to +13200. The resolution over this input range is 1 part in 15200. For the A/D converters used in most industrial applications, the resolution is approximately 1 part in 4000 (some are slightly better; some are not quite this good). Over the entire input range, the integer representation of the engineering value is superior to what can be achieved with an A/D converter.

In control applications, the question is not the resolution over the entire possible input range; instead, the question is the resolution over the range required for control. For example, applications such as fermentation involve water under atmospheric pressure. The maximum possible input range is from 32°F or 0°C (the freezing point of water) to 212°F or 100°C (the boiling point of water). Over this range, the resolution is as follows:

• For °F, the input range is 320 (32.0°F) to 2120 (212°F), which gives a resolution of 1 part in 1800.
• For °C, the input range is 0 (0.0°C) to 1000 (100°C), which gives a resolution of 1 part in 1000.

If the field transmitter is set to output 4 mA at 32°F or 0°C and 20 mA at 212°F or 100°C, the resolution from the A/D converter would be superior. This issue is compounded by the fact that derivative is normally used in the temperature control loop in applications such as fermentation reactors.

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