Bryan L. Programmable controllers. Theory and implementation

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PLC System

Documentation

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Programming

12-4 CONCLUSION

Much can be said about documentation and its relevance to the total system

package. We cannot overemphasize the importance of establishing—from

the outset—complete, accurate documentation of the control problem and its

solution. If the system documentation is created during the system design

phase, as it should be, it will not become an unwelcome burden imposed on

designers as the project nears completion.

Documentation may seem trivial to some or too much work to others.

Whether designing their own control system or subcontracting the design,

users should ensure that a good documentation package is delivered with the

equipment. A well-designed system is one that is not just put to work during

start-up, but can also be maintained, expanded, modified, and kept running

without difficulty. Good documentation will definitely help both the design-

ers and the end users in these tasks. Remember that, regardless of the

application, a design is not good unless its documentation is also good.

control program printout

documentation

internal storage address assignment document

I/O address assignment document

I/O wiring connection diagram

storage register assignment document

system abstract

system configuration diagram

Besides the ladder printout, documentation systems also provide input and

output usage (assignment) reports. These reports list the controller’s I/O

addresses, illustrating how each point is used. These systems can also

generate construction mnemonics documentation (e.g., contacts, limit

switches, etc.), as well as a complete report of all instructions available for

use in the PLC. Moreover, full cross-referenced reports provide direct

information about all register contents and where each element is used in the

program. An important advantage of the program listings produced by

documentation systems is that they show, on a single document, all of the vital

information about the control program.

Documentation systems are capable of uploading, verifying, and storing the

PLC program directly from the controller or from a cassette, floppy disk,

micro disk, or other storage media. Even though many third-party documen-

tation and software programming systems exist, many PLC manufacturers

now incorporate this capability into their own systems. In addition to

documentation and programming capabilities, some of these systems also

provide graphic user interfaces, or GUIs, which create user-friendly graph-

ics that visually depict the control process.

KEY

TERMS

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PLC PROCESS

APPLICATIONS

SECTION FOUR

• Data Measurements and Transducers

• Process Responses and Transfer Functions

• Process Controllers and Loop Tuning

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DATA MEASUREMENTS

AND TRANSDUCERS

CHAPTER

THIRTEEN

When you measure what you are speaking about

and express it in numbers, you know something

about it; but when you cannot measure it, when

you cannot express it in numbers, your knowl-

edge is of a meager and unsatisfactory kind.

—William Thomson, Lord Kelvin

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Data Measurements

and Transducers

CHAPTER

HIGHLIGHTS

As in any technical discipline, PLC users must know how to use and apply

the measurement instruments and equipment that are connected to different

field devices. In this chapter, we will explain how to interpret the data

produced by measurement equipment, as well as how to deal with unex-

pected, erroneous measurements. We will also discuss transducers, a type of

measurement device. This discussion, which will include displacement,

pressure, flow, and vibration transducers, will explain how these devices turn

measurement data into electrical signals. In the next chapter, you will apply

this knowledge to process control applications.

13-1 BASIC MEASUREMENT CONCEPTS

DATA INTERPRETATION

Data interpretation and representation are very important when working

with on-line process control operations. Measurement devices provide the

control system with important information about the inner workings of the

process. Therefore, every user must clearly understand what data is being

collected by the measurement devices and how it should be interpreted. This

will help the user to apply the control program correctly, so that the process

will behave in a predictable manner.

To understand the data-gathering process, you must first understand how

instrumentation and data-collecting devices interpret data readings. These

devices can interpret data sampling readings four different ways, each with

a different meaning. These methods for interpreting information include:

• mean

• median

• mode

• standard deviation

Mean. The mean is the average value of a set of readings. This value is useful

in applications that require an estimation of future or expected readings. To

illustrate the mean, let’s use an instrument that emits a signal at set time

intervals (every 10 seconds). This signal ranges from 2 to 20 mV and

represents the mean value of the measurements taken during the 10-second

time interval. That is, each signal’s value is the average of the readings taken

since the last signal. Let’s suppose that the instrument last emitted a 13 mV

signal and that it will send another signal in 10 seconds. Meanwhile, the

instrument collects data every two seconds, resulting in values of 14 mV, 14.5

mV, 15 mV, 14.7 mV, and 14.8 mV. The mean of these readings, expressed

, is defined as:

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Data Measurements

and Transducers

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XXX X

+++…

∑

123

Therefore, at the new reporting time, the instrument will emit a 14.6 mV

signal—the mean value of the five readings (i.e., n = 5):

X =

mV + 14.5 mV + 15 mV + 14.7 mV + 14.8 mV

=14.6 mV

Median. The median is the middle value of a set of readings that are organized

in ascending order. The following equations define the median:

()

for an odd number of samples

for an even number of samples

where:

the median

the total number of readings

a reading value

The readings from the previous example placed in ascending order are 14 mV,

14.5 mV, 14.7 mV, 14.8 mV, and 15 mV. This is an odd number of values

(i.e., m = 5). Therefore:

()

The value X

is the third value in ascending order, so the median is 14.7 mV.

Note that for an even number of samples the median is the mean of the two

center values.

The median calculation provides statistical information about the data

measurements taken and is more tolerant of errors than the mean calculations.

Referencing the previous example, if the 14 mV reading had been erroneously

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CHAPTER

Data Measurements

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read as 20 mV due to noise in the system, the mean would have increased to

15.8 mV, whereas the median would have remained 14.7 mV. Thus, the

median value is not greatly affected by extreme deviations caused by

measurement errors.

Mode. The mode is the most frequent value or values in a set of data. The

mode value for the following set of instrumentation readings—14 mV, 14.5

mV, 14 mV, 14.5 mV and 14.5mV—is 14.5 mV, because it is the most

frequent value. If six readings had been taken and the sixth one was 14 mV,

two mode values would have existed, 14.5 mV and 14 mV (three occurrences

of each).

Mode values occur mostly in discrete processes, where events are not broken

down into infinitesimal readings, as in analog processes. PLC count readings

from analog input modules rarely contain a significant mode value, since

the continuous nature of the signal constantly introduces changes into the

readings. Therefore, the mode is not as valuable as the mean and median in

determining measurement errors.

Standard Deviation. Often, an application requires information not only

about the mean value of a set of process readings, but also about how these

readings are distributed in relation to the mean. The standard deviation

provides valuable information about a group of data, thus aiding in the

quantitative evaluation of the sample measurements.

To demonstrate standard deviation, let’s examine a set of five instrument

readings: 9 mV, 9.5 mV, 15 mV, 19.7 mV, and 19.8 mV. The mean of

this sample is 14.6 mV, yet the readings are very dispersed. Standard

deviation measures the spread of these values in relation to the mean and is

expressed as:

−

()

−

∑

where:

the standard deviation

the calculated mean

the number corresponding to each reading,

starting at 1 and ending at the last reading,

This formula computes the deviation of each sample from the mean. The

larger the standard deviation value, the more spread out the values (samples)

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are from the mean. For our instrument readings, the standard deviation will

have a value of σ = 5.26:

++++

−

31 36 26 01 0 16 26 01 27 04

110 58

526

.....

When the data values are evenly distributed around the mean in a bell form,

they are said to have a normal distribution or Gaussian distribution (see

Figure 13-1). The standard deviation in a Gaussian (normal) distribution

measurement provides information that allows for a quantitative determina-

tion about how the data is spread. In a normal distribution, several conclu-

sions can be obtained:

• 68% of all readings lie within ±1σ (see Figure 13-2a)

• 95% of all readings lie within ±2σ (see Figure 13-2b)

• 99% of all readings lie within ±3σ (see Figure 13-2c)

Figure 13-1. Normal distribution curve.

For example, if a set of reactor vessels in a continuous process has two

temperature control loops, one that maintains a 358°C temperature with a

standard deviation of 40°C and another that maintains a 358°C temperature

with a standard deviation of 20°C, we know that the latter provides us with

a more peaked graph about the mean. In fact, 68% of the temperature readings

in the second loop lie between 338°C and 378°C, while in the first loop, 68%

of the readings lie between 318°C and 398°C.

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Data Measurements

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Figure 13-2. Distribution of data values as a function of standard deviation.

MEASUREMENT ERRORS

The possibility of measurement errors is present in any system that produces

a finished good. Equipment malfunctions or misreadings of process variables

can cause these errors, which are variations or deviations from the true or

expected reading. Errors can be classified in three categories:

• gross errors

• system errors

• random errors

Gross errors are the result of human miscalculation, system errors are the

result of the instrument itself or the environment, and random errors are the

result of unexpected actions in the process line. Table 13-1 shows some

examples of these types of errors, along with ways to predict and prevent them.

– 1σ

+ 1σ

– 2σ

+ 2σ

– 3σ

+ 3σ

95%

68%

99%

(a)

(b)

(c)