Instrumentation Basics

Introduction:
                      You cannot control what you cannot measure. Sensors are the foundation of Feedback Control. Sensors measure the process variable and transmit a signal that represents the measurement to the Controller. The quality of performance of the system is directly related to the performance of the sensor.

                      The process variables we measure most often are temperature, pressure, level, flow and mass. No sensor measures a process variable directly. Each sensor measures the effect of the process variable by physical position, force, voltage or some other more easily measured property.


What are Sensors and Transducers?

Sensors: A sensor is a device that has a characteristic that changes in a predictable way when
exposed to the stimulus it was designed to detect.

               When making process measurements we are not really measuring the value of the process variable. We are inferring the value of the process variable by measuring the response of a sensor to the process. Sensors have a physical property that changes in a measurable and consistent fashion.

                For example, when measuring temperature we are not directly measuring the temperature of an
object, we are measuring a sensors change in resistance or the amount of voltage it produces from being exposed to a temperature.

Transducers: A transducer is a device that converts one form of energy into another.

                  Transducers are used to convert the output of a sensor into a signal that a controller can use. The
output of a sensor may be a mechanical movement, or a change in size or position, or a nonstandard electrical signal. The output of a sensor may even be nonlinear. A transducer will convert the output of the sensor into a standard signal that a controller can use.

A sensor and transducer may be packaged together as shown in bellow figure

Or the transducer may be part of the controller as shown in bellow Figure

For the sake of convenience we will refer to any device that measures a process variable as an instrument, understanding that some signal processing will take place

What are the Standard Instrumentation Signals

                              Standard instrument signals for controllers to accept as inputs from instrumentation and outputs to final control elements are pneumatic, current loop and 0 to 10 volt.

Pneumatic: 

                              Before 1960 pneumatic signals were used almost exclusively to transmit measurement  & control information. Today we still commonly find 3 to 15 psig used as the final signal to a modulating valve.

                             Where the final control element requires a pneumatic signal, in most cases the controller outputs a standard electrical signal and a transducer between the controller and the final control element

converts the signal to 3 to 15 psig.

                             Most often an I/P (I to P) transducer is used. This converts a 4-20 mA signal (I) into a pressure signal (P).

This conversion process is normally linear where the pneumatic signal is given by

                              Signal psig = (% Controller Output x 12 psig)+ 3psig .

If the controller output is 40%, then the pneumatic signal from the I/P transducer is

                              Signal psig = (40% x 12 psig)+ 3psig = 4.8psig + 3psig = 7.8psig .

Current Loop: 

                                4-20 milliamp current loops are the signal workhorses in many processes. A DC milliamp current is transmitted through a pair of wires from a sensor to a controller or from a controller to its final control element. Current loops are used because of their immunity to noise and the distances that the signal can be transmitted. Since the signal being transmitted is current the voltage drop that occurs across conductors does not affect the signal, it just limits the length of the signal cable; and induced voltages do not affect the signal.

Loop Scaling: 

                           The level of the current in the loop is related to the value of the process variable or the controller output. How the current level and process value are related is the loop scaling.

Output Scaling: 

                           Scale outputs for a one to one correspondence. That is the controller output is configured for 0% to correspond to a 4mA signal and 100% to correspond to a 20mA signal. The final control element is calibrated so that 4mA corresponds to its 0% position or speed and 20mA corresponds to its 100% position or speed.

Input Scaling: 

                          Scale inputs for a one to one correspondence as well. If we were using a pressure transducer with a required operating range of 0 psig to 100 psig we would calibrate the instrument such that 0 psig would correspond to 4mA output and 100 psig would correspond to a 20mA output. At the controller we would configure the input such that 4mA would correspond to an internal value of 0 psig and 10mA would correspond to an internal value of 100 psig.

0 - 10 V: 

                        0 to 10 volt is not commonly used in many control systems because this signal is susceptible to induced noise and the distance of the instrument or final control element is limited due to voltage drop. You may find 0-10 volt signals used in control systems providing the speed reference to variable speed drives. For this application the cabling from the controller to the drive is typically confined to a control panel, meaning the cabling distances are short and electrical noise is more easily controlled.

What are Smart Transmitters?

                        Pneumatic, current loop and 0-10 volt signals are all analog signals. They are capable of

transmitting a signal that is continuous over its range, but the signal that is transmitted can only

represent a single value and the communication is only one way.

                       A smart transmitter is a digital device that converts the analog information from a sensor into digital information, which allows the device to simultaneously send and receive information and transmit more than a single value.

Smart transmitters, in general, have the following common features:

1. Digital Communications

2. Configuration

3. Re-Ranging

4. Signal Conditioning

5. Self-Diagnosis

Digital Communications: 

                              Smart transmitters are capable of digital communications with both its configuration device and a process controller. Digital communications have the advantage of being free of bit errors, the ability to monitor multiple process values and diagnostic information and the ability to receive commands. Some smart transmitters use a shared channel for analog and digital data (Hart, Honeywell or Modbus over 4-20mA), others use a dedicated communication bus (Profibus, Foundation Fieldbus, DeviceNet, Ethernet). 

Most smart instruments wired to multi-channel input cards require isolated inputs for the digital communications to work.

Configuration

                 Smart transmitters can be configured with a handheld terminal and store the configuration settings in nonvolatile memory.

Signal Conditioning

                Smart transmitters can perform noise filtering and can provide different signal characterizations.

Self-Diagnosis

                Smart transmitters also have self-diagnostic capability and can report malfunctions that may indicate erroneous process values.

What Instrument Properties Affect a Process?

 Some instrument properties that can affect the performance of your control system include:

•  The instrument’s range and span.
•  The resolution of the measurement.
•  The instrument’s accuracy and precision.
•  The instrument’s dynamics.

Range and Span:

                 The range of a sensor is the lowest and highest values it can measure within its specification.

An RTD may have a specified range of -200oC to +560oC.

A temperature transducer with an RTD sensor may have a specified range of -10oC to +65oC.

                  The span of a sensor is the high end of the Range minus the low end of the Range.

The RTD with a range of -200oC to +560oC would have a span of 760oC.

The RTD transducer with a range of -10oC to +65oC would have a span of 75oC.

Match Range to Expected Conditions

                      Instruments should be selected with a range that includes all values a process will normally

encounter, including expected disturbances and possible failures. 

                      In Chapter Two we learned that an instrument with too wide of an operating span will lower the process gain, possibly hiding an oversized final control element and requiring higher controller gains. Also, for most instruments operating ranges larger than required reduce the accuracy of the measurement.

                      In the heat exchanger example we could reasonably expect that the water temperature would

always be between 0oC and 100oC (frozen water will not flow and the system is designed so that we cannot superheat the water). Matching a temperature transmitter closely to this range will give us the best measurement performance.

Measurement Resolution

                    Resolution is the smallest amount of input signal change that the instrument can detect reliably.

                 Resolution is really a function of the instrument span and the controller’s input capability. Most controllers convert their analog input signals into a digital equivalent. The resolution of the measurement is determined by the span of the measurement and the number of bits in the digital conversion process.

                 Most current controllers resolve their analog inputs into 16 bits of digital information. 16 bits of

information allows for 65,535 values with which to represent the input signal.

The resolution of a 16 bit conversion is Input Span / 65,535.

If we have a 4-20 mA signal that represents a 0 to 100 psig process value, the input resolution is  

 100 psig      / 65,535 = 0.0015 psig.

                     Some older control systems may have input processing that only resolves their inputs into 12 bits of digital information. 12 bits will only allow for 4095 values with which to represent the process signal which is 16 times less resolution than a 16 it conversion.

No matter how many bits are used for the conversion process, the larger your instrument span, the

lower the resolution of your measurement.

Accuracy and Precision

                       Accuracy of a measurement describes how close the measurement approaches the true value of the process variable.

Accuracy is often expressed as a % error over a range or an absolute error over a range.

% Error Over a Range

                      Accuracy may be specified as ± a percentage over a range, span or full scale of an instrument.

The uncertainty in your measurement will be the percentage times the range specified by the manufacturer.

For example, Manufacturer A specifies that their pressure instrument has an accuracy of ±0.4% of full scale. The full scale of their instrument is 500 psig. We can expect the measurement signal from this instrument to be accurate to 2 psig for all pressures in the instruments range.

                                          0.4% x 500 psig = 0.004 x 500 psig = 2 psig

Even if we span the instrument for the application to 0 to 100 psig the instrument is still only accurate to 2 psig.

Absolute Over a Range

Accuracy may also be specified as ± an absolute value over a range.

Manufacturer B specifies that their pressure instrument has an accuracy of ±1 psig over the full operating range. The full scale of their instrument is also 500 psig. We can expect the measurement signal from this instrument to be accurate to 1 psig for all pressures in the instruments range.

In any case, the sensors we select must be more accurate then the degree to which we want to control the process. There is no amount of control loop tuning you can do on a process to maintain 30 psig ± 1 psig pressure instrument is only accurate to ± 2 psig.

Precision is the reproducibility with which repeated measurements can be made under identical conditions.

Precision may also be referred to as stability or drift. Precision is always required for good control, even when accuracy is not required.

The distinction between accuracy and precision is illustrated in Figure 3-3. The dashed line represents the actual temperature being measured. The upper line represents a precise but inaccurate value from an instrument; the lower line represents an accurate but imprecise measurement from an instrument.

Precision is the more important characteristic of an instrument.

Instrumentation Dynamics

                   Instruments have dynamic properties just as process do. The dynamic properties instruments

posses are identical to process dynamics: gain, time constants and dead time. All of these instrument dynamics contribute to the process dynamics that the controller sees.

Instrument Gain

                  The gain of an instrument is often call sensitivity. The sensitivity of a sensor is the ratio of the output signal to the change in process variable.

                  For a thermocouple the typical sensitivity is 5 mV per °C. This means for every °C change in the

process variable the thermocouple will change its output by 5 mV.

Instrument Time Constants:

                   As for processes, one time constant for an instrument is the time it takes to provide a signal that

represents 63.2% of the value of variable it is measuring after a step change in the variable. Instrument manufacturers may sometimes specify the rise time instead of the time constant.

                   Rise time is the time it takes for an instrument to provide a signal that represents 100% of the value of the variable it is measuring after a step change in the variable. The rise time of an instrument is equal to 5 time constants

Instrument Dead Time

The dead time of an instrument is the time it takes for an instrument to start reacting to process change.

What is Input Aliasing?

                      Input aliasing is a phenomenon that occurs from digital processing of a signal. When a signal is

processed digitally it is sampled at discrete intervals of time. If the frequency at which a signal is sampled is not fast enough the digital representation of that signal will not be correct. Input aliasing is an important consideration in digital process control. Processor inputs that have configurable sample rates and PID loop update times must be set correctly.

Above figure shows a low frequency 2 Hz signal that was sampled every 0.4 seconds. The resulting

curve from the sampled points looks nothing like the original. If this was the signal for the process variable then we would be unable to achieve control.

Correct Sampling Frequency

                   Fortunately establishing the correct sampling rate for a signal is not a trial and error procedure.

There is a well established theorem (Nyquist Frequency Theorem) that tells us to correctly sample a waveform it is necessary to sample at least twice as fast has the highest frequency in the waveform. In the digital world this means sampling at 1/20th of the period of the waveform. The 2 Hz signal in Figure 3-4 has a period of 1/2Hz = 0.5 seconds per cycle. To sample this in the digital world the sampling interval would be 0.5/20 seconds = 0.025 seconds. bellow Figure shows the same waveform sampled at this interval. Notice the match between the real and sampled signal.

Determining the Correct Sampling Interval

                  While it’s nice to know there is guidance on how to set the sample interval for a waveform based

on its frequency, how does one know what the frequency of a process variable is?

                  When it comes to instrumentation, it’s not the frequency that’s important, it’s the time constant.

Figure 3-6 is a graph of the response of an instrument with a 5 second time constant (25 second rise time). The signal from the instrument was sampled at 1 second intervals.

One rule of thumb would be to set the sample interval for an instrument at 1/10th to 1/20th of the rise time (1/2 to 1/4th of the time constant).

Another rule of thumb would be to set the sample interval to 1/10th to 1/20th of the process time constant.

                 Temperature instrumentation (RTDs and thermocouples in thermowells) typically have time constants of several seconds or more. For these processes sampling intervals of 1 second are usually sufficient.

Pressure and flow instrumentation typically have time constants of ½ to 1 second. For these processes sampling intervals of 0.1 second are usually sufficient.