1. PLC Programming: Instrumentation and Process Control
Juan David Bastidas Rodríguez
Escuela de Ingenierías Eléctrica, Electrónica y de Telecomunicaciones
Universidad Industrial de Santander

2. Objectives: Understand instrumentation basics, digital and analog.
Identify process-control elements and associated uses.
Understand signal-conversion and quantification errors.

3. Instrumentation Basics
Sensors translate between the physical real-time world and the standardized world of PLCs.
2 categories:
Analog sensors: a signal range (e.g. 0 to 10 V) and a resolution
Digital sensors: 1 or 0
Digital sensors not binary: stair-step shape (e.g. encoder)

4. Instrumentation Basics
Analog Sensors:
Signals must be converted to a digital format (A/D converter)
Usually built-in A/D ports in the I/O module interface.
E.g. potentiometer
The potentiometer must be carefully selected to ensure adequate current limitation (R3)
Audio (logaritmic) and linear.
VCC = 10 V => Maximum V see by A/D? Value read by the PLC with A/D resolution of 0.01 V? How can Vmax be incremented?

5. Instrumentation Basics
Analog Sensors:
VR2 = VCC × [R2/(R2 + R3)] = 10.0 × [10 kΩ/(10 kΩ )] = 9.68 V
A/D converter value = 9.68/0.01 = 968
For R2 = 100 kΩ:
VR2 = 10.0 × [100 kΩ/(100 kΩ + 330)] = 9.94 V
A/D converter value = 9.94/0.01 = 994

6. Instrumentation Basics
Digital Sensors:
Many different types of digital input sensors
Many of them are wired in the same form (pull-up resistor)
2 types:
Normally open (NO)
Normally closed (NC)
Many microswitch designs: one common terminal, and both an NO and NC.

7. Process-Control Elements
A simple process-control loop consists of three elements:
The measurement (one of the most important): take information from the physic world to the PLC or control system
The controller: determine the actions to perform in the process
Final control element: take information from the PLC or control system to modify something in the physic world

8. Process-Control Elements
Process-Control Variables:
Some examples: temperature, pressure, speed, flow rate, force, movement, velocity, acceleration, stress, strain, level, depth, mass, weight, density, size, volume, acidity, etc, etc, etc.
Sensors may operate simple ON/OFF switches to indicate certain events or detect objects
The final control element is the part of the control system that acts to physically change the process behavior.
E.g. a valve used to restrict or cut off fluid flow, pump motors, louvers used to regulate airflow, solenoids, or other devices.

9. Process-Control Elements
Basic Measurement System:
Transducer/sensor: converts the controlled variable into another form suitable for the next stage
Signal conditioning: adjusts the measurement signal to interface properly with the A/D conversion system
Transmitter: propagates measurement information from the site of measurement to the control room

10. Process-Control Elements
Basic Measurement System:
Standard signal ranges:
Electric current of 4 to 20 mA
Electric voltage of 0 to 10 V
Pneumatic pressure of 0.2 to 1.0 bars (1 bar = 100 kPa ≈ 1 atmosphere)
Digital with a built-in binary digital encoder
Advantages of standard instruments:
All instruments can be easily calibrated
The signal produced is independent of the physical measurement
The same PLC hardware-interface modules are used for all measurements
Users can select instruments from a large number of competing vendors

11. Process-Control Elements
Transducers:

12. Process-Control Elements
Signal Conditioning: Changes the characteristic of the sensor/ transducer-measured signal. E.g. square-root extractor Differential-pressure flowmeters/sensors produce an output that is directly proportional to the square of the flow. A signal conditioner/processor extracts the square root => the resulting signal delivered to the transmitter element is directly proportional to the actual flow rate.

13. Process-Control Elements
Signal Conditioning:
Changes the characteristic of the sensor/ transducer-measured signal.
Include different applications:
Integrators
Differentiators
Signal filters (to remove unwanted parts, noise, or interferences)
Arithmetic operations

14. Process-Control Elements
Signal Transmitters: Transmitters are used to send the measured and conditioned signals to the controller using a communication link (wired or wireless).
They use, among others:
“Handshaking”
Time-division multiplexing (TDM): digital signals
frequency-division multiplexing (FDM): analog signals

15. Signal Conversion Analog-to-Digital Conversion:
Analog-to-digital (A/D) conversion can be achieved in different ways.
One type uses a synchronous counter
Result is a discrete/digital value.
It is typical for the range of an A/D converter to be 0 to +10 V or 4 to 20 mA.

16. Signal Conversion Analog-to-Digital Conversion:
The range of the analog signal: 0 to V.
It is a 10-bit A/D converter: discrete values.
A/D converter divides V by to yield approximately 0.01 V per step.
Table would continue up to the conversion value of 1023.
12- and 16-bit A/D converters are common in PLCs

17. Signal Conversion Analog-to-Digital Conversion:
Example: A 10-bit A/D converter has a 10-V reference Vr and a digital output count of
What is the A/D resolution R in volts per bit?
What is the digital output count N in hex for an analog input of 6 V?
What is the average quantization error?

18. Signal Conversion Analog-to-Digital Conversion:
Example: A 10-bit A/D converter has a 10-V reference Vr and a digital output count of
What is the A/D resolution R in volts per bit?
R = Vr/2n = 10/1024 = V/bit
What is the digital output count N in hex for an analog input of 6 V?
N = 2n × Vin/Vr = 1024 × 6/10 = 614 = 266 H = B
What is the average quantization error?
R/2 = /2 = V/bit

19. Signal Conversion Digital-to-Analog Conversion:
Opposite function of the D/A conversion
There are many D/A converter architectures
The suitability of a particular D/A converter is determined by a variety of measurements (principally speed and resolution).
A typical analog I/O module uses 12-bit resolution with signed or unsigned integer representation
The internal operation of the PLC analog modules is independent of the type of physical sensors/actuators interfaced.

20. Signal Conversion Digital-to-Analog Conversion:
Example: For a 12-bit D/A converter with a 10-V reference voltage that is used to convert digital counts to analog output voltage, answer the following questions:
What is the analog output voltage for a digital input = 0A3h H?
What is the input digital count N for an analog output voltage of 8 V?

21. Signal Conversion Digital-to-Analog Conversion:
Example: For a 12-bit D/A converter with a 10-V reference voltage that is used to convert digital counts to analog output voltage, answer the following questions:
What is the analog output voltage for a digital input = 0A3h H?
Vout = (N/2n) × Vr = (163/4096) × 10 = V
What is the input digital count N for an analog output voltage of 8 V?
N = (2n × Vin)/Vr = (4096 × 8)/10 = 3276

22. Signal Conversion Quantification Errors and Resolution:
The resolution of an A/D or a D/A converter indicates the number of discrete values it can produce over the range of analog values.
The values are usually stored electronically in fixed-length binary form => resolution expressed in bits
Example: 8 bits A/D converter can encode an analog input to one in 256 different levels: 28 = 256.
There are 2 options (depending on the application)
Values from 0 to 255 (unsigned integers)
Values from −128 to 127 (signed integer)

23. Signal Conversion Quantification Errors and Resolution:
Example: D/A conversion for a 3-bit resolution and a normalized 1-V range.
The binary count ranges from 000 to 111: 8 levels equivalent to the analog range from 0 to 1 V.
The least significant bit (LSB) is (in this example) equivalent to a D/A converter resolution of V
Worst-case quantization error (LSB) V
The average quantization error in this case is V (0.125 V/2).

24. Signal Conversion Quantification Errors and Resolution:
Resolution also can be defined electrically and expressed in volts or current
The minimum change in voltage required to guarantee a change in the output code level is called the least-significant-bit (LSB) voltage
The resolution R of the A/D converter is equal to the LSB voltage
N is the number of voltage intervals, full-scale range is the difference between the upper and lower extremes, and M is resolution in bits.

25. Signal Conversion Quantification Errors and Resolution:
Quantization error (or quantization noise), is the difference between the original analog signal and the digitized binary count.
The magnitude of the average quantization error at the sampling instant is equal to half of one LSB voltage.
Quantization error is an unavoidable imperfection in all types of A/D converters.

26. Signal Conversion Quantification Errors and Resolution:
Example: An 8-bit A/D converter with a 10-V reference converts a temperature of 0°C into digital outputs. If the temperature transducer outputs 20 mV/°C, answer the following questions:
What is the maximum temperature that the converter can measure?
What is the resolution of the A/D converter in millivolts per bit?
What is the worst-case quantization error in degrees Celsius?

27. Signal Conversion Quantification Errors and Resolution:
Example: An 8-bit A/D converter with a 10-V reference converts a temperature of 0°C into digital outputs. If the temperature transducer outputs 20 mV/°C, answer the following questions:
What is the maximum temperature that the converter can measure?
Maximum temperature = 10,00 [V]/20 [mV/°C] = 500°C
What is the resolution of the A/D converter in millivolts per bit?
Resolution = 10,00/256 = mV/bit
What is the worst-case quantization error in degrees Celsius?
Worst-case quantization error = 500/256 = 1.952°C/bit

28. Process-Control System
In a process-control system
The controller links the measurement and final control element.
Traditionally, closed-loop proportional-integral-derivative (PID).
PIDs are designed to execute Proportional, Integral and Derivative control functions.
Other types of control are Oroller is the elementN/OFF and fuzzy logic.

29. Process-Control System
Two types of controllers:
Analog controllers: use mechanical, electrical, pneumatic, or other type devices that cause changes in the process through the final control element continuously.
Digital controllers: they use processors to calculate the output based on the measured values.

30. Process-Control System
Control Process:
Process refers to an interacting set of operations that lead to the manufacture or development of some products.
E.g.
Chemical industry process: operations necessary to take raw materials and cause them to react to produce a desired end product (gasoline)
Food industry process: to take raw materials and operate on them in such a manner that an edible product results
Products MUST have certain specified properties.
Control refers to steps and procedures to obtain such properties.

31. Process-Control System
Control Process:

32. Process-Control System
Controlled and Manipulated Variables:
Controlled variable (e.g. level) are necessary to maintain product’s properties.
A manipulating variable variable can be used to exert control over the tank process.
Flow rate in or flow rate out of the tank.
Controlled variable must be accessible and easy to change.

33. Process-Control System
Control Strategy and Types:
The value of a variable (vi) depends on other variables in the process and time.
Typically, one or a few variables dominate and define the dependency relationship.
Two types of control are common: mainly the single-variable control and multivariable control.

34. Process-Control System
Control Strategy and Types: single- variable control The level in the tank is the control variable. Only one of the two valves available in this mode can be selected as a controlling variable to regulate the tank level.

35. Process-Control System
Control Strategy and Types: multivariable control
The control variables include:
the feed rate
conveyor speed
oven temperature
cracker color
cracker size.
Multivariable control is more complex because of the strong and nonlinear interactions between variables

36. Process-Control System
Process-Control Loop:
Typical control loop:
Process
measuring elements
final control element

37. Process-Control System
Control-System Error Quantification:
Perfect regulation of a process variable is not possible => ERRORS
Errors can be measured in three ways:
Variable value: Set point = 230°C; measured value = 220°C; range = 200 to 250°C; and Error = 10°C
Percent of set point: The error is expressed as a percent of the controlled variable SP. Error = (10/230) × 100 = 4.4%.
Percent of range: The error is expressed as a percent of the controlled variable range. Error = [10/(250 – 200)] × 100 = 20%.

38. Process-Control System
Control-System Error Quantification:
Two types of errors are of great importance:
steady-state residual errors
transient dynamic of such errors
Those errors are used to to evaluate a control-system implementation and design.

39. Process-Control System
Control-System Transient and Performance Evaluation:
The objective of a control system is:
to minimize (not to eliminate) the error without affecting the overall system stability and performance.
Control strategy and adequate tuning of existing control loops are very critical to the performance of the whole system
The quality of a control-system is based on: transient response, steady- state errors, stability, scalability, user interface, continuous quality improvements, and ease of maintenance.

40. Process-Control System
Control-System Transient and Performance Evaluation: Oscillatory instability

41. Process-Control System
Control-System Transient and Performance Evaluation: Overdamped process Underdamped process

42. Closed-Loop Process-Control Types
Closed-loop process control can be implemented using a wide variety of techniques and strategies.
Four commonly used techniques are:
ON/OFF
Proportional
PID
Supervisory control.

43. Closed-Loop Process-Control Types
ON/OFF Control Mode:
A Dead Band (DB) is defined
The controller output is
ON: error > +ɛ
OFF: error > – ɛ
|ɛ| = |DB|

44. Closed-Loop Process-Control Types
ON/OFF Control Mode:
Example: Assume a temperature cooling control process with a set point of 80°C and a dead band of 6°C.
The system cools at -2°C/min once the controller output is ON.
Thesystem heats at+4°C/min when the output is OFF

45. Closed-Loop Process-Control Types
Proportional Control Mode: Cp = controller output in percent Kp = proportional gain in percent of output/percent of error Ep = error in percent of range Co = controller output with zero error

46. Closed-Loop Process-Control Types
Proportional Control Mode: Example: A control system is to control pressure in a range from 120 to 240 lb/in2 with a 180 lb/in2 set point. The proportional gain is 2.5 percent and the zero-error output is 65 percent.

47. Closed-Loop Process-Control Types
Composite Control Mode:
Closed-loop process controllers can be designed to respond to:
the history of error during a prespecified time period (integral mode)
the forecast of the error behavior in the near future (derivative mode)
the current instantaneous value of errors (proportional mode)
Therefore, 3 types of controllers:
Proportional-integral (PI) mode
Proportional-derivative (PD) mode
Proportional-integral-derivative (PID) mode

48. Closed-Loop Process-Control Types
Composite Control Mode: General structure of a PID controller

49. Closed-Loop Process-Control Types
PLC/Distributed Computer Supervisory Control: A mix of technologies: Universal standards, digital hardware, real-time operating systems, communication and networking, human-machine interfaces (HMIs), remote sensing, redundancy and safety tools, and the widespread use of open- system architectures.

50. Closed-Loop Process-Control Types
PLC/Distributed Computer Supervisory Control:
Modular: design, development, implementation, enhancement, expansion, maintenance, etc.
Large systems are composed of several highly interactive and connected subsystems.
High initial cost but more effective and less expesive in long term.