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This section covers PLC process-control and associated instrumentation fundamentals. Process-control strategies, control modes, and common types of control are covered. Instrumentation and system performance are examined.
A programmable logic controller (PLC) is designed to regulate real-time processes having both discrete and analog variables. So far we have covered the discrete/digital programming side; we will do the same for analog programming in this section. Analog signals are brought to a PLC from sensors through an analog to-digital (A/D) converter interface, whereas analog output signals are produced by a PLC through a digital-to-analog (D/A) converter interface. All analog signals are connected to the PLC through standard input-output (I/O) modules, which incorporate the A/D and D/A conversions, signal conditioning/scaling, and electronic isolation.
Sensors measure and provide small-current or small-voltage signals to the analog input module, whereas actuators receive the output analog signal from the PLC output module. Sensors, actuators, and analog I/O modules are available in different standard formats and can meet the requirement of any process.
1 Instrumentation Basics
An important part of a control system is the incorporation of sensors. Sensors translate between the physical real-time world and the standardized world of PLCs. This section will explain the common types of sensors used in process control and the basic operation fundamentals of sensors. It will briefly cover common analog and digital sensors.
1.1 Sensors Basics
Sensors translate physical process attributes into values that the I/O modules can accommodate. The translation produces sensor standard output that interfaces with the PLC. In general, most sensors fall into one of the two categories: analog sensors and digital sensors. An analog sensor, such as a thermostat, might be wired into a circuit and calibrated to produce an output that ranges from 0 to 10 V. The analog signal can assume any value within the available range, 0 to 10 V in this case, as defined by the sensor resolution. In order for the PLC to deal with analog signals, those signals must be converted to a digital format in a simple and transparent way. The transformation from analog to digital and digital to analog also must follow predefined universal standards.
Digital sensors generate discrete signals that typically have a stair-step shape in which every signal has a predefined relation with the values preceding and following it. A push-button switch is one of the simplest sensors with two discrete signal values: ON or OFF. Other discrete sensors might provide a binary value in a given range. A stepper-motor position encoder, for example, may provide the motor's current position by sending a 10-bit value with a range from 0 to 1023. In this case, the discrete signal has 1024 possibilities. Much of our discussion assumes a digital/discrete signal to be binary.
1.2 Analog Sensors
Analog sensor signals must be converted to a digital format. Sensor output circuits are designed to be connected to an A/D converter port. Most standard microcontrollers and PLCs, such as the Siemens S7-1200 system, have built-in A/D ports in the I/O module interface.
An often overlooked but extremely popular sensor is the potentiometer. A potentiometer is a resistive sensor. Almost all resistive sensors are wired in a similar fashion as part of a voltage divider. FIG. 1 shows an example of a potentiometer that is connected to the VCC (assumed to be +10 V in this section) and the GND (assumed to be 0 V). The potentiometer must be carefully selected to ensure adequate current limitation. Notice in this circuit that the current-limiting resistor R3 is connected to limit the output current when the sweep on the potentiometer is turned all the way to the top position. There are two types of potentiometers on the market: audio and linear. A linear potentiometer changes its value at a linear rate. An audio potentiometer changes its value on a logarithmic scale.
Using the resistor values shown in the figure, the voltage ranges the potentiometer will provide can be calculated. With the sweep all the way to the top position, the value for R2 at the top sweep is 10 k-ohm. The voltage drop across R2 = VCC × [R2/(R2 + R3)] = 10.0 × [10 k-ohm/(10 kO + 330)] = 9.68 V.
Assuming an A/D converter resolution of 0.01 V, the highest digital value will be 9.68/0.01 = 968. The lowest value should be zero because with the sweep all the way to the bottom, the A/D port will be connected to GND. Thus the limiting resistor has reduced the useful range of the potentiometer to 9.68 V instead of 10 V. The range can be increased by selecting a larger R2. For example, using a 100-k? potentiometer means a top sweep voltage across R2 of 10.0 × [100 k-O/(100 k-O + 330)] = 9.94 V. Thus the highest digital count value is 9.94/0.01 = 994.
1.3 Digital Sensors
There are many different types of digital input sensors. Many of them are wired in the same form, which uses a pull-up resistor to force the line voltage high and to limit the amount of current that can flow to the A/D converter circuit. One of the most basic of all sensors is a simple switch. Switches are used to detect limits of motion, proximity to an object, user input, and a whole host of other things.
Switches come in two types: normally open (NO) and normally closed (NC). Many microswitch designs actually have one common terminal, and both an NO and an NC terminal. The PLC wiring diagram for a switch is simple, as discussed in Section 2. NO switches are recommended to limit the amount of power consumed ( FIG. 2). With a 10-k-O pull-up resistor, the amount of current is small, but many switches can add up to some noticeable power.
2 Process-Control Elements
A simple process-control loop consists of three elements: the measurement, the controller, and the final control element. Measurement is one of the most important elements in any process-control plant. Decisions made by the controller are based on the real-time measurements information received. Regardless of system type, all controller decisions are similarly based on measurements, control strategy, and the desired process response/performance. Final control elements can refer to actuators such as control valves, heaters, variable-speed drives, solenoids, and dampers. In most chemical process plants, a final control element is often a control valve. In manufacturing assembly lines, final control elements mostly will include variable-speed drives, solenoids, and dampers. Final control elements receive command signals from the controller/PLC in real time to bring about the desired changes in the controlled process. As with sensors/measurement elements, final control devices interface with the PLC output modules in a similar way. The PLC digital-signal outputs are transformed to the actuator required digital- or analog-signal format, which might require a D/A conversion or coupling isolation.
2.1 Basic Measurement System
A basic instrument/measurement system consists of three elements:
• Transducer/sensor. The transducer is the part of the measurement system that initially converts the controlled variable into another form suitable for the next stage. In most cases, conversion will be from the actual variable into some form of electrical signal, although there is often an intermediate form, such as pneumatic.
• Signal conditioning. In computer process control, signal conditioning is used to adjust the measurement signal to interface properly with the A/D conversion system.
• Transmitter. The transmitter has the function of propagating measurement information from the site of measurement to the control room where the control function is to occur. Usually pneumatic or electronic signals are used.
A simplified block diagram of a basic measurement system is shown in FIG. 3.
Input -- Signal Conditioning -- Transmitter Sensor -- Output
Most modern analog instruments use the following 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 (The bar is a unit of pressure equal to 100 kPa and roughly equal to the atmospheric pressure on earth at sea level.)
• Digital with a built-in binary digital encoder so as to provide a binary digital output Having a standard instrument range or using digital signals greatly contributed to the advancement of digital process control and the evolution of modern PLCs.
The following are a few of the primary advantages of such instruments:
• All instruments can be easily calibrated.
• The signal produced is independent of the physical measurement. For example, the minimum signal (e.g., temperature, speed, force, pressure, acidity, and many other measurements) is represented by 4 mA or 0.2 bars, and the maxi mum signal is represented by 20 mA or 1.0 bar.
• The same PLC hardware-interface modules are used for all measurements.
• Users can select instruments from a large number of competing vendors; all must comply with universal standards.
2.2 Process-Control Variables
Process-control variables that are commonly either measured by sensors or regulated through actuators (final control elements) include temperature, pressure, speed, flow rate, force, movement, velocity, acceleration, stress, strain, level, depth, mass, weight, density, size, volume, and acidity. Sensors may operate simple ON/OFF switches to indicate certain events or detect objects (proximity switch), empty or full (level switch), hot or cold (thermostat), high or low pressure (pressure switch), and other overload conditions.
German physicist Thomas Johann Seebeck discovered the conversion of temperature differences directly into electricity in 1821. The block diagram of a temperature sensor is shown in FIG. 4. This phenomenon takes place when two wires with dissimilar electrical properties (A and B wires) are joined at both ends, and one junction is made hot (T1) and the other cold (T2). A small electrical voltage is produced proportional to the difference in temperature between the two junctions. This voltage can be calibrated to indicate the measured temperature value, as shown in the figure. A typical industrial temperature probe with a flexible extension and standard plug is shown in FIG. 5.
The final or correcting control element is the part of the control system that acts to physically change the process behavior. In most processes, the final control element is a valve used to restrict or cut off fluid flow, pump motors, louvers used to regulate airflow, solenoids, or other devices. Final control elements are typically used to increase or decrease fluid flow. For example, a final control element may regulate the flow of fuel to a burner to control temperature, the flow of a catalyst into a reactor to control a chemical reaction, or the flow of air into a boiler to control boiler combustion. In any control loop, the speed with which a final control element reacts to correct a variable that is out of set point is very important.
Many of the technological improvements in final control elements are related to improving their response time.
2.3 Signal Conditioning
The signal-conditioning element changes the characteristic of the sensor/ transducer-measured signal. One example is the square-root extractor. For example, differential-pressure flowmeters/sensors produce an output that is directly proportional to the square of the flow. A signal conditioner/processor is used to extract the square root so that the resulting signal delivered to the transmitter element is directly proportional to the actual flow rate. Other signal-conditioning elements include integrators, differentiators, and a wide variety of signal filters.
Filters are used with electrical signals to remove unwanted parts, noise, or interferences. For example, a signal may contain unwanted frequencies or undesired direct-current (dc) components as a result of external sources or the inherent characteristic of the sensor technology. Some signal conditioning is performed to pre pare for successful transmission.
2.4 Signal Transmitters
Industrial sensory information needs to be sent from one place to another using either a wireless or wired transmission medium. Transmitters are used to send the measured and conditioned signals to the controller using a single frequency of transmission or a single pair of wires such as the twisted pair used in wired telephone lines. Modems are simple devices that can receive and transmit information through direct connection or the telephone network. They require a marker signal to let each other know when to receive or transmit. They use "handshaking" to regulate and enforce the predefined communication protocol. A time-division multiplexing (TDM) for digital signals or frequency-division multiplexing (FDM) for analog signals can be used to accommodate four sensory communication channels, as shown in FIG. 6.
Squeezer Transmitter Expander Receiver Expander Receiver Modem; Modem Squeezer Transmitter
3 Signal Conversion
The real word is a mix of analog and digital variables combining to describe a process or a system behavior in time. The PLC side uses digital format in both variables measurements and control. This section will cover simplified A/D and D/A converters. It will also briefly discuss issues associated with these converters, including resolution, sampling rate, and quantification errors.
3.1 Analog-to-Digital Conversion
Analog-to-digital (A/D) conversion can be achieved in different ways. One type of converter uses a synchronous counter, as shown in FIG. 7. The output of the counter, which is driven by a clock of a fixed frequency, is a digital pattern. This count is converted back into an analog signal by the D/A converter and compared with the input analog signal. Once the two signals match, the counter is disabled by the end-of-conversion signal, and the digital count is latched. The counter stops, and the digital value of the counter output, which is equivalent to the analog signal, is acquired by the PLC/computer-input interface. The higher the number of counter bits, the higher is the resolution/accuracy of the A/D converter and the longer is the average conversion time.
The PLC always deals with discrete/digital values. An important part of using an analog signal is being able to convert it to a discrete signal, such as a 10-bit digital value. This allows the PLC to do things like compute values, perform comparisons, and execute logic operations. Fortunately, most modern PLCs/controllers have a resource called an A/D converter. The function of the A/D converter is to convert an analog signal into a digital value. It does this with a mapping function that assigns discrete values to the entire range of voltages or currents. It’s typical for the range of an A/D converter to be 0 to +10 V or 4 to 20 mA. The A/D converter will divide the range of values by the number of discrete combinations. For example, Table 7.1 shows eight samples of an analog signal that have been converted into digital values. The range of the analog signal is 0 to +10.24 V. It’s a 10-bit A/D converter, which has 1024 discrete values. Therefore, the A/D converter divides 10.24 V by 1024 to yield approximately 0.01 V per step.
The table shows how voltages map to specific conversion values. The values shown only included the first six samples, but the table would continue up to the conversion value of 1023.
Table 1 10-Bit A/D Conversion Pattern From (V) To (V) Conversion (decimal) Conversion (binary)
There are many types of A/D converters on the market. An important feature of A/D converters is their resolution, which is proportionate to the number of bits used by the A/D converter to quantify and store the analog signal samples. An 8-bit converter is used widely on microcontrollers, whereas 12- and 16-bit A/D converters are common in PLCs. A 16-bit A/D converter will use 65,356 discrete values. The resolution required for an application depends on the accuracy the sensor requires and the transient nature of the process. The higher the resolution, the greater is the accuracy of the signal representation in digital format and the lower the quantization error. In this example, the worst-case quantization error is 0.01 V, whereas the average value is 0.005 V.
A 10-bit A/D converter has a 10-V reference Vr and a digital output count of 0010100111.
a. What is the A/D resolution R in volts per bit?
b. What is the digital output count N in hex for an analog input of 6 V?
c. What is the average quantization error?
3.2 Digital-to-Analog Conversion
Wikipedia states that a digital-to-analog (D/A) converter is a device that converts a binary digital code to an analog signal (current or voltage). An A/D converter performs the reverse operation. Signals are easily stored and transmitted in digital form, but a D/A converter is needed for the signal to be recognized by human senses or other non-digital systems. A common use of D/A converters is generation of audio signals from digital information in music players. Digital video signals are converted to analog in televisions and cell phones to display colors and shades. D/A conversion can degrade a signal, so conversion details are normally chosen so that the errors are negligible.
Given the cost and need for matched components, D/A converters are almost exclusively manufactured on integrated circuits (ICs). There are many D/A converter architectures that have different advantages and disadvantages. The suit ability of a particular D/A converter for an application is determined by a variety of measurements, including speed and resolution. As documented in the Nyquist and Shannon sampling theorems, a D/A converter can accurately reconstruct the original signal from the sampled data provided that its bandwidth meets certain requirements. Digital sampling introduces quantization error that manifests as low-level noise added to the reconstructed signal. FIG. 8 shows a simplified functional diagram of an 8-bit D/A converter.
PLCs use a wide variety of analog input and output modules that accommodate different current, voltage, and high-speed pulse signals. These modules come in different sizes (the number of I/O points per module) and also A/D versus D/A resolutions. 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. This simplifies the analog module configuration and its associated application programming/deployment.
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:
a. What is the analog output voltage for a digital input = 0A3h H?
b. What is the input digital count N for an analog output voltage of 8 V?
3.3 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, so the resolution is usually expressed in bits. The number of discrete values or levels available is a power of 2. For example, an A/D converter with a resolution of 8 bits can encode an analog input to one in 256 different levels because 2^8 = 256. The values can represent the ranges from 0 to 255 (unsigned integers) or from -128 to 127 (signed integer) depending on the application. FIG. 9 illustrates the D/A conversion for a 3-bit resolution and a normalized 1-V range. The binary count ranges from 000 to 111, which represents 23 , or 8, different levels equivalent to the analog range from 0 to 1 V. The least significant bit (LSB) in this example is equivalent to a D/A converter resolution of 0.125 V, which is equal to the worst-case quantization error. The average quantization error in this case is 0.0625 V.
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. The voltage resolution of an A/D converter is equal to its overall voltage measurement range divided by the number of discrete voltage intervals, as shown below:
R = full-scale range/N
... where N is the number of voltage intervals, and full-scale range is the difference between the upper and lower extremes, respectively, of the voltages that can be coded.
The number of voltage intervals is given by N = 2M where M is the A/D converter's resolution in bits.
Quantization error, also known as 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 volt age. Quantization error is due to the finite resolution of the digital representation of the signal and is an unavoidable imperfection in all types of A/D converters.
An 8-bit A/D converter with a 10-V reference converts a temperature of 0°C into 00000000 digital outputs. If the temperature transducer outputs 20 mV/degree, answer the following questions:
a. What is the maximum temperature that the converter can measure?
b. What is the resolution of the A/D converter in millivolts per bit?
c. What is the worst-case quantization error in degrees Celsius? Solution
a. Maximum temperature = 10,000/20 = 500°C
b. Resolution = 10,000/256 = 39.06 mV/bit
c. Worst-case quantization error = 500/256 = 1.952°C/bit
4 Process-Control System
In a process-control system, the controller is the element linking the measurement and final control element. Traditionally, closed-loop proportional-integral-derivative (PID) controllers are used. These controllers are designed to execute PID control functions. Other types of control are also common, including ON/OFF and fuzzy logic.
Advancement in computer hardware and software has a led to a wide deployment of PLCs and distributed digital control systems as a replacement of the hardwired analog relay controllers. This section focuses on controller types typically implemented using PLCs.
Analog controllers use mechanical, electrical, pneumatic, or other type devices that cause changes in the process through the final control element. The controller moving mechanical parts are subject to wear and tear over time that affect the response/performance of the process. Also, analog controllers regulate the process by continuously providing signals to the final control element. Digital controllers don’t have mechanical moving parts. Instead, they use processors to calculate the output based on the measured values. Because they don’t have moving parts, they are not susceptible to deterioration with time. Digital controllers don’t regulate continuously, but they execute at very high rate, usually several times every second. Pneumatic controllers use instrument air to pass measurement and controller signals instead of electronic signals. These controllers have the disadvantage of longer dead time and lag owing to the compressibility of the instrument air.
4.1 Control Process
In the industrial world, the word process refers to an interacting set of operations that lead to the manufacture or development of some products. In the chemical industry, process means the operations necessary to take an assemblage of raw materials and cause them to react in some prescribed fashion to produce a desired end product, such as gasoline. In the food industry, process means to take raw materials and operate on them in such a manner that an edible product results. In each use, and in all other cases in the process industries, the end product must have certain specified properties that depend on the conditions of the reactions and operations that produce them. The word control is used to describe the steps necessary to ensure that the conditions produce the correct properties in the product.
A process, as shown in FIG. 10, can be described by an equation. The process has m variables v1 to vm. Suppose that we let a product be defined by a set of properties P1 , P2 , . . . , Pn. Each of these properties must have a certain value for the product to be correct. Examples of properties are things such as color, density, chemical composition, and size.
Pi = f (v1 , v2 , . . . , vm, t) where Pi is the ith property and t is time.
Process Inputs Outputs
4.2 Controlled Variables
To produce a product with the specified properties, some or all the variables must be maintained at specific values. FIG. 11 shows an unregulated tank with open flow coming in and out. Fluid level in the tank is expected to vary as long as a difference in flow in and out exists. A controlled/controlling variable can be used to exert control over this simple tank process. Choices of such a variable can include the flow rate in or flow rate out of the tank. The controlled variable must be accessible and easy to change. It also must have adequate influence on the regulation of the selected control variable, the tank level in this case.
Some of the variables in a process may exhibit the property of self-regulation, whereby they will naturally maintain a certain value under normal conditions and very small disturbances. Control of variables is necessary to maintain the proper ties of the product within specification.
4.3 Control Strategy and Types
The value of a variable vi actually depends on other variables in the process, as well as on time. Typically, one or a few variables dominate and define the dependency relationship. This relation can be expressed as shown in the following equation:
vj = g(v1 , v2 , . . . , vc , . . . , vm, t)
Two types of control are common: mainly the single-variable control and multi variable control. These two types are briefly defined below.
We will demonstrate single-variable control using the tank process with minor modification. Two valves are added, one at the inlet flow to the tank and one at the output. The level in the tank varies as a function of the flow rate through the input valve and the flow rate through the output valve. The level in the tank is the control variable, which can be measured and regulated through either inlet- or output valve control and adjustment. FIG. 12 illustrates the modified tank process, which can accommodate the implementation of single-variable control. Only one of the two valves available in this mode can be selected as a controlling variable to regulate the tank level, the control variable. The next mode of control, multi variable control, is more complex and can use more than one controlling variable to regulate the control variable, the tank level in our process. For example, regulation of the two valves can be used to control the tank level at a desired set of values at different times.
FIG. 13 shows a schematic diagram of an oven used to bake crackers in a system under multivariable control. The control variables that may be used include the feed rate, conveyor speed, oven temperature, cracker color, and cracker size.
Other variables such as the temperature outside the oven are difficult to measure, control, and use in the control-system strategy. Multivariable control is more complex because of the strong and nonlinear interactions between variables.
FIG. 13 Multivariable oven control.
4.4 Process-Control Loop
Process-control loops are the core of all control systems and process-automation tasks. A schematic of a typical control loop is shown in FIG. 14. The loop consists of three blocks: process, measuring elements, and final control element.
What comes from the process is what we referred to as the control variable, the tank level in the preceding example, which can be easily measured and quantified in time. What goes as input to the process is the controlling variable, the inlet valve opening or flow rate in the tank process. The valve opening can be changed manually or automatically using an available final control element. Load disturbances refer to external process influences that affect the behavior of the process.
The setpoint (SP) refers to the desired control-variable value as defined by the system end user. Actuation of the final control element is based on the SP, control variable measurements characteristic of the process, type of final control element, and the implemented control strategy. The man shown in the loop represents two primary loop functions, mainly error detection and the control tasks. Most of the human involvement in the control loop can be replaced by automated means including the deployment of PLCs, PCs, and other types of automated control.
In manual control, the operator is expected to perform the task of error detection and control. Observations and actions taken by operators can lack consistency and reliability. In automated systems, the operator is removed and replaced by electronic controllers, as in the wide use of PLCs and specialized digital computers. The operator still plays an important role in the automated system, including input of control-variable set points and required human interactions with the control system. Automated systems such as the one shown in FIG. 15 allow for greater flexibility and higher degrees of process control, quality, and consistency.
The following are the steps used in implementing single-variable closed-loop control:
1. Select one variable to be a controlled variable (the controlled variable in this case is labeled vc ).
2. Make a measurement of the controlled variable vc to determine its present value. The desired value is called the setpoint of the controlled variable.
3. Compare the measured value of the controlled variable with the desired value (set point).
4. Determine a change in the controlling variable that will correct any deviation or error in the controlled variable.
5. Feed back this changed value of the controlling variable to the process through the final control element to create the desired correction in the controlled variable.
6. Go to step 2 and repeat.
4.5 Control-System Error Quantification
Perfect regulation of a process variable by any control system is not possible.
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 setpoint. The error is expressed as a fraction or percent of the con trolled variable SP. Error = (10/230) × 100 = 4.4%.
• Percent of range. The error is expressed as a fraction or percent of the con trolled variable range. Error = [10/(250 - 200)] × 100 = 20%.
Two types of errors are of great importance in system performance, as observed in all selected control variables: mainly the steady-state residual errors and the transient dynamic of such errors. Both residual (the steady-state error) and dynamic errors (errors during transient behavior) are used to evaluate a control-system implementation and design. In most control applications, the steady-state error is the primary goal. It’s desired that this error would be small or show a rapid decay in magnitude with time. The residual error is expected to be reached after a small transient time from a load change or when a system offset takes place. Quantification of the value of the error is always subject to a small tolerance.
The transient response of a process includes the time interval prior to and leading to a steady-state condition from the time of a load change or an offset (a change in the set point). Primary interest during the transient time includes error values, frequency of oscillation, and duration of oscillation for the controlled vari able under consideration. Oscillations in controlled variables are expected but can lead to oscillatory instability, which is often caused by an ill-designed controller or control strategy. Hardware failure can cause monotonic instability, which is materialized in the continuous increase or decrease in the value of the controlled variable resulting in an overall system failure. For example, if the transmitter for the tank-level signal fails, it can cause the level to increase and eventually over flow the tank. The tank can run dry if the last correct measurement before the transmitter failure required a decrease in tank level. This type of failure can be detected and prevented by using backup hardware such as limit switches and redundant sensors.
4.6 Control-System Transient and Performance Evaluation
The quality of a control-system performance is based on many factors, including transient response, steady-state errors, stability, scalability, user interface, continuous quality improvements, and ease of maintenance. Controller response to errors depends on the control-system strategy. The objective of a control system is to minimize, not to eliminate, the error without affecting the overall system stability and performance.
As stated in Sec. 7.4.5, perfect regulation of a process variable by any control system is not possible, which means that we have to live with some errors, hope fully small. Control strategy and adequate tuning of existing control loops are very critical to the performance of the whole system. This task is one of the most challenging, and it can be easier to perform if the error behavior is well understood.
FIG. 16 shows an ill-designed control-system behavior or one completely out of tuning. As shown in the figure, the controlled variable has gone wild, with increasing amplitude oscillations ultimately leading to instability and system shutdown. This type of behavior is called oscillatory instability and can be eliminated during implementation of the controller and overall strategy.
As stated in Sec. 5.1, a tolerance around the set point where no controller action is needed is essential to protect the final control element (actuator) from failure owing to excessive control actions. This is true in all kinds of process regulations: manual, PID, or ON/OFF control. FIG. 17 shows the transient behavior of an overdamped process where TD is the total delay/transient time. There are no overshoots or oscillation in this case, but the controller action is slow. FIG. 18 shows a faster controller for an underdamped process resulting in controlled variable oscillations and shorter transient/delay time TD. Configuring the controller to be very aggressive in reacting to real time controlled-variable errors can lead to instability and the situation shown in FIG. 16. The most desired controlled-variable response is known as quarter decay, which means that the ratio of consecutive overshoots is approximately 4, which represents a 0.25 decay ratio. Guidelines and techniques for tuning PID controllers for such responses exist in the literature and in most PLC technical manuals.
5 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 covered briefly in this section: ON/OFF, proportional, PID, and supervisory control.
Each type of process control has unique characteristics and can be the best strategy for the correct application. Depending on the process and the associated control requirements, the most appropriate and simple technique possible is selected.
5.1 ON/OFF Control Mode
ON/OFF control is the simplest mode of closed-loop control, but it’s a good match for many applications. The final control element is either ON or OFF depending on the controlled-variable measured value. A deadband (a tolerance around the set point where no control action is needed) is used to prevent the final control element from being switched ON/OFF excessively. The controller output is ON if the error value is greater than the set point + e and is OFF if the error value drops below the set point - e, where e is one-half the dead band. No control action is needed while the controlled-variable measurement lies within the implemented dead band (DB). FIG. 19 illustrates the general behavior of an ON/OFF control action.
Example 4 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. The system heats at +4°C/min when the output is OFF. The ON/OFF controller response is shown in FIG. 20. Control action is ON while the temperature is higher than the upper threshold of the dead band (83°C) and turns OFF once the temperature dips below the low threshold of the dead band (77°C). The figure shows two functions of time: the measured temperature variation and the controller output. The first function is continuous in time, whereas the second is discrete-the controller is either ON or OFF. Notice that the control action only takes place while measured temperature is outside the specified dead band. More precise control can be achieved, if needed, using other, more sophisticated techniques.
5.2 Proportional Control Mode
Proportional control mode assumes a correction strategy based on the calculated error, the difference between the measured controlled variable and the set point.
The controller output (controlling variable) is proportional to the amount of error in addition to the fixed amount needed to support the process during the time the control variable stays within the defined dead band. This amount is known as the controller output with zero error. The following is the mathematical formulation for the proportional control mode:
Cp = Kp × Ep + Co
where 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
Example 5: A control system is to control pressure in a range from 120 to 240 lb/in^2
...with a 180 lb/in^2 set point. If the proportional gain is 2.5 percent and the zero-error output is 65 percent, the error as a percentage of range is given by the following formulation:
Ep = (P - 180)/(240 - 120) × 100 = 0.833 × (P - 180)
where P is the measured pressure. The controller output is given by the following formulation:
Cp = 2.5 × Ep + 65
= 2.5 × 0.833 × (P - 180) + 65
= 2.0825 × (P - 180) + 65
The controller output varies from 0 to 100 percent, which corresponds to an error range defined as in the following formulation:
Ep (at Cp = 0) = -26% and Ep (at Cp = 100%) = 14%
The range of errors covering the entire available controller output is known as the controller proportional band, which is calculated in this example as follows:
Proportional band = 14% - (-26%) = 40%
Notice that the higher the proportional band, the lower is the controller proportional gain because the following relation is true at all times:
Proportional band × proportional gain = 1 This type of control is more complex than ON/OFF control because it requires experience in implementing and tuning both the proportional gain and the controller zero-error output.
5.3 Composite Control Mode
Closed-loop process controllers can be designed to respond to the history of error during a pre-specified time period (integral mode), the forecast of the error behavior in the near future (derivative mode), and the current instantaneous value of errors (proportional mode). These controllers are commonly labeled in the following three types:
• Proportional-integral (PI) mode
• Proportional-derivative (PD) mode
• Proportional-integral-derivative (PID) mode
FIG. 21 shows a simplified schematic of PID control while the AUTO/MANUAL mode switch is placed on AUTO, which is the universal format for the composite controller. All composite controllers must include the proportional mode.
5.4 PLC/Distributed Computer Supervisory Control
The initial use of computers in process control was in support of the traditional analog-system process control. This type of application of computers still exists because many industries use analog control systems and will no doubt continue to do so. Generally, large- or medium-scale computers provide the support activities, including data acquisition, human interface, simulation/modeling, communication, and digital control. A simplified block diagram for a supervisory control system is shown in FIG. 22.
Distributed computer control/supervisory control has evolved as the choice for automation and process-control implementation in the past 20 years. This revolution greatly benefited from and made use of huge advancements in technology, including universal standards, digital hardware, real-time operating systems, communication and networking, human-machine interfaces (HMIs), remote sensing, sensory fusion, redundancy and safety tools, and the widespread use of open-system architectures.
Some of the world's largest international chemical and petroleum corporations own and operate the largest global computer networks. Every process controller, data acquisition system, HMI, actuator, sensor, and communication device has to be accessible from any location in the world with proper authorization.
Supervisory distributed control allows for a more efficient modular design and far easier overall system cost in all phases of system development, implementation, deployment, enhancement, expansion/scalability, and maintainability. It also allows for greater operator, designer, and user interactions, leading to the realization of an overall system of continuous quality improvement. Most large systems are composed of several highly interactive and connected subsystems. The set point for a given single-variable closed-loop control might be a function of other variables belonging to different subsystems. Distributed control systems demand larger and more complex development with higher cost, but they are more effective and less expensive in the long term.
QUIZ and Lab Project
1 Define the following terms:
a. Signal conditioner
e. Quantization error
2 What is the difference between the following?
a. Digital sensors and analog sensors
b. Sensors and actuators
3 Which statement is true about instruments?
a. All instruments can be easily calibrated.
b. All instruments produce a signal that is independent of the physical measure.
c. Users can select instruments from a large number of competing vendors; all must comply with universal standards.
d. All of the above.
4 What are the elements of a basic measurement system?
5 What does the term Seebeck effect refer to?
6 Draw the basic elements of a process-control loop, and describe the function of each element.
7 List two standard analog signals.
8 For an 8-bit analog input module (A/D), what is the range of values it can represent (signed/unsigned)?
9 What does multivariable control mean?
10 What methods are used in the process-control loop to provide optimal control to a process control system?
11 Define the following terms:
a. Data logging
b. Digital process control
c. Supervisory control
d. A/D converter
e. D/A converter
12 For which mode of control is the rate of change of the controller output determined by the amount of error, ON/OFF, proportional, derivative, or integral control?
13 For which mode of control is the number of outputs determined by the rate of change of the error, ON/OFF, proportional, derivative, or integral?
14 Explain what the word process load means, and give an example.
15 Which of the following statements is true in proportional control?
a. Proportional control usually produces zero error when stability is reached after a change in the load.
b. Proportional control usually produces an offset when stability is reached after a change in the load.
16 Define the following terms:
a. Process transient time
b. Process load time
c. Process regulation time
d. Process lag time
17 A temperature sensor is used to measure an oven temperature between 50 and 300°F. The output of the sensor is converted to a signal in the range of 0 to 5 V. The signal is connected to a 12-bit A/D converter of a PLC system. Answer the following questions:
a. What is the sensor resolution in °F/volt?
b. What is the A/D converter resolution in °F/bit?
c. What A/D converter digital count corresponds to 100°F?
d. What is the resolution of the A/D converter?
e. Calculate the average quantization error of the A/D converter.
18 A sensor provides real-time temperature measurements of an oven in the range of 0 to 10 V, which represents engineering unit values of 50 to 400°F. The oven temperature is desired to maintain a 200°F set point by sending an ON/OFF signal to the oven heater. The dead band allowed for the ON/OFF oven control is 2°F. Calculate the high and low thresholds around the dead band.
19 In a home heating system, what is the effect of increasing or decreasing the dead band?
20 What is the advantage of set-point automatic generation in supervisory control systems?
21 What is the proportional band of a temperature controller having a 0.75 proportional gain and a set point of 300°F?
22 A 12-bit A/D converter with 10 V reference has an input signal of 2.69 V. What is the digital count for this input signal? What is the equivalent analog input signal to a 3A5 hex digital count?
23 A sensor provides real-time temperature measurements of an oven in the range of 4 to 20 mA, which represents engineering unit values of 40 to 350°C. An analog input module is interfaced with the sensor output. The oven temperature is desired to maintain a 250°C set point using ON/OFF control and an oven heater. The dead band allowed for the ON/OFF oven control is 4°C. Answer the following questions:
a. What is the sensor resolution in °C/mA?
b. What is the A/D converter resolution in °C/bit?
c. What is the digital count of the A/D converter for a 159°C measurement?
d. What is the resolution of the A/D converter?
e. Calculate the maximum quantization error of the A/D converter.
24 A sensor provides real-time measurement of a tank level in the range of 4 to 20 mA, which represents engineering unit values of 20 to 500 m. An analog input module with 12-bit resolution is used to acquire this signal. What range of level does a (256) 10 count represent?
Lab 1: ON/OFF Temperature Control:
The objective of this laboratory is to get hands-on knowledge of the ON-OFF process control in commercial and industrial application.
A sensor provides real-time temperature measurement of an oven in the range of 0 to 10 V, which represents engineering unit values of 50 to 400°F. The oven temperature is desired to maintain a 300°F set point by sending an ON/OFF signal to the oven heater. The dead band allowed for the ON/OFF oven control is 1°F. Implementation Specifications
• Configure the PLC analog module attached to the CPU for a 0- to 10-V input signal range.
• Use a 10-V potentiometer to supply the analog input signal (0 to 10 V). Apply the signal to the analog input module connected to the main CPU of the training unit.
• Change the potentiometer setting in the range from 0 to 10 V to represent an oven temperature in engineering units in the range of 50 to 400°F.
• Configure a new HMI Function Keys page. This page will allow the operator to access two other pages: Status and Control pages. Define this page as the HMI start page.
• Configure a Status page in the HMI to display the oven temperature (in °F) as you change the potentiometer from the minimum to the maximum voltage (0 to 10 V), representing the engineering units (50 to 400°F). Also, define two text objects: Heater ON and Heater OFF. The function key F1 should allow users to go back to the Function Keys page.
• Configure a Control page in the HMI to allow an operator to enter the oven set point in the range of 50 to 400°F.
• Assign the system inputs.
• Assign the system outputs.
• Program the required networks.
• Download the program, and go online.
• Simulate the program using the training units or the Siemens simulator. Configure the Watch table to display the raw input digital count (0 to 27,648), tempera ture in engineering units (50 to 400°F), and the 12-bit analog input/digital count (0 to 4095) as the potentiometer setting is adjusted from 0 to 10 V.
• Simulate the program using the HMI. Verify that the program is running according to the process description.
Laboratory Modifications Document all the networks shown in FIG. 23. Add the network needed to validate that the operator-entered set point is within limits (50 to 400°F). If the set point is outside the limit, send a message to the HMI: "Invalid Set Point! Re-Enter." Implement the HMI requirements, and make the needed modifications to the S7-1200 PLC ladder program.
Updated: Monday, March 9, 2015 18:52 PST