9.1 Overview
The key characteristic of control is to interfere, to influence or to modify the process. This control function or the interference to the process is introduced by an organization of parts (including operators in manual control) that, when connected together is called the control system. Depending on whether a human body (the operator) is physically involved in the control system, they are divided into manual control and automatic control. Due to its efficiency, accuracy and reliability, automatic control is widely used in chemical processed.
9.2 Control system
9.2.1 Functions of a control system
Control system, completed by the operator, possesses the following functions:
Measurement
This is essentially an estimate or appraisal of the process being controlled by the system. In this example, this is achieved by the right hand of the operator.
Comparison
This is an examination of the likeness of the measured values and the desired values and is carried out in the brain of the operator.
Computation
This is a calculated judgment that indicates how much the measured value and the desired values differ and what action and how much should be taken. In this example, the operator will calculate the difference between the desired temperature and the actual one.
Accordingly the direction and amount of the adjustment of the valve are worked out and the order for this adjustment is sent to the left hand from the brain of the operator.
If the outlet water temperature is lower, then the brain of the operator will tell the left hand to open the steam valve wider. If there is any disturbance, or variation of flow rate in water to the shower inlet, some adjustment must be made to keep the outlet water temperature at a desired value.
Correction
This is ultimately the materialization of the order for the adjustment. The left hand of the operator takes the necessary actions following the order from brain.
Therefore, for a control system to operate satisfactorily, it must have the abilities of measurement, comparison, computation and correction.
Of course, the manual operation has obvious disadvantages e.g. the accuracy and the continuous involvement of operators. Although accuracy of the measurement could be improved by using an indicator, automatic control must be used to replace the operator. In industry, it is automatic control that is widely used.
9.2.2 Manual control system
A diagram of the manual control system is shown in the figure 9.1.
Simple manual control system
To begin with, the shower is cold. To start the heating process the valve in the hot water line is opened. The operator can then determine the effectiveness of the control process by standing in the shower. If the water is too hot, the valve should be closed a little or even turned off. If the water is not hot enough then the valve is left open or opened wider.
9.2.3 Automatic control system
Based on the above process an automatic control system can be easily set up as shown in the figure 9.2.
Automatic control system
First, we can use a temperature measurement device to measure the water temperature, which replaces the right hand of the operator. This addition to the system would have improved accuracy.
Instead of manual valves, we use a special kind of valve, called a control valve, which is driven by compressed air or electricity. This will replace the left hand of the operator.
We put a device called a controller, in this case a temperature controller, to replace the brain of the operator. This has the functions of comparison and computation and can give orders to the control valve.
The signal and order connections between the measurement device, control valve and controller are transferred through cables and wires, which replace the nerve system in the operator.
9.2.4 Hardware of a control system
Examining the automatic control system, it is found that it contains the following hardware:
Sensor - a piece of equipment to measure system variables. It serves as the signal source in automatic control.
Controller - a piece of equipment to perform the functions of comparison and computation.
Control element - a piece of equipment to perform the control action or to exert direct influence on the process. This element receives signals from the controller and performs some type of operation on the process. Generally the control element is simply a control valve.
9.2.5 Software of a control system
Associated with a control system are a number of different types of variables:
Controlled variable: This is the basic process value being regulated by the system. An important concept related to the controlled variable is the Set point. This is the predetermined desired value for the controlled variable. The objective of the control system is to regulate the controlled variable at its set point.
To achieve the control objective there must be one or more variables we can alter or adjust. These are called the Manipulated Variables. In the above example this was the input hot water flow rate.
Conclusively, in the control system we adjust the manipulated variable to maintain the controlled variable at its set point. This meets the requirement of keeping the stability of the process and suppressing the influence of disturbances.
9.3 Practical control examples
Many different operations take place in a chemical plant. The classical approach of Unit Operations might thus be extended to process control, and we could consider in turn the control of heat exchangers, chemical reactors, distillation columns etc.
This turns out not to be a useful approach in most cases. The reason for this is that we are in the end concerned with the control of processes, which consist of several operations, and these cannot be considered in isolation. This makes the engineer’s task of designing a control system a difficult one, since it is hard to find just where to start! The starting point is to regulate each of the basic quantities we may wish to keep constant in a process.
These quantities are:
- Flow
- Inventory – level or pressure
- Temperature
- Composition
- Pressure – two phases
The following sections discuss simple, but real, examples of how feedback control is applied to these basic quantities in a chemical plant. They are primarily examples of control for operability, and most of them will refer to single items of equipment or simple combinations. A number of safety issues will also be identified.
Strategic control for profitability will be dealt with in a later section in the context of control of complete plants and processes.
A number of fundamental concepts will be illustrated in the course of these examples. They are ‘graded’ in the sense that the simplest examples come first; the reader is advised to follow the sequence we have presented. Even apparently trivial examples may be used to introduce important ideas.
9.3.1 Flow control systems
The most basic requirement in any chemical plant is to be able to make the flow through a pipe take a particular value. Consider the simplest item of plant equipment, namely a pipe, as shown in the figure 9.3.
Flow through a pipe
The basic pipe has had the following parts added to it, to make a control system:
- A flow measuring device or Flow meter. This consists of two parts:
- Orifice Meter: This is shown in the diagram by two parallel lines, and is connected to a sensor or Flow Transducer labelled FT in the figure
- Control Valve or an adjustable valve, which alters the flow rate. This is shown by its conventional flow sheet symbol
- Controller, identified by the element FC, connects the Orifice Meter and the Control Valve
This completes a control system to regulate the measured quantity, here the flow, by adjustment of the valve position.
Positioning of elements
One of the problems with designing control systems is that, as in any design problem, we are faced with alternatives. We have an alternative here in the positioning of the elements.
The measurement element should either be placed upstream of the valve as shown in the figure 9.3 or be placed downstream.
Consideration of the properties of flow meters and valves suggests that the measurement element be placed upstream. If the valve were upstream of the flow meter then there are a number of ways in which it might affect the flow meter calibration.
Control algorithms
In the simple illustrative example of the water heater the rule for making the adjustment was:
If the temperature is too high then turn the heater off.
If it is too low then turn the heater on.
This is an example of an on-off control algorithm. The heater is either on (full) or off (completely).
If the flow is too high then shut the valve off.
If it is too low then open it.
Clearly, this is unlikely to serve, as rather than maintaining a specified flow the conditions will switch between zero and some maximum value. To achieve a specified steady flow we require something like:
If the flow is too high then shut the valve some more.
If it is too low then open it more.
This is a proportional control algorithm; the larger the error in the measured quantity, the larger will be the adjustment. This arrangement should result in the system settling at or near the required flow.
In practice, on-off control is seldom used. Most adjustment elements are valves, or occasionally other mechanical elements. These do not take kindly to being regularly or rapidly swung across their full range of adjustment; they very quickly wear out or break down.
In most cases, therefore, proportional control or some variant is used. More detailed investigation of control algorithms requires quantitative information about the process. This aspect will be dealt with in a later section.
9.3.2 Inventory control systems
The next most basic requirement in a plant is a control system to regulate the amount of material or inventory in an item of equipment or over part of the process.
Inventory may be measured in a number of ways. Mass holdup may sometimes be determined directly, but usually volume is measured. In liquid systems volume is measured by level. In gas or vapour systems pressure is used as a measure of inventory.
Level control systems
Here we will consider simple feedback control of the level in a tank. This being the case it is necessary to measure the level directly and adjust the flow into or out of the tank to keep it constant.
Alternative control systems
Figure 9.4 shows the two alternative control systems available for feedback control of the level. Both are equally valid and the decision as to which to use is based on
What is upstream or downstream of the tank?
Which streams are already being controlled?
The relative sizes of the flow rates, if there are several input or output flows.
Alternative control system
As can be seen the control system consists of:
- A Level Transducer denoted by LT in the diagram
- A Control Valve
- A Level Controller denoted by LC: The level can be regulated by altering the flow via the adjustment of the valve position
- Control Algorithms: It is possible to control the level in a tank using
- On/Off control
- Proportional control
- Extensions to proportional control
The theory behind the algorithms will be found in a later section. There is also a level control experiment based on an actual experiment carried out by the undergraduates in the laboratory. Note that a link to this can be found in the Case Study Section
Pressure control systems
In gas or vapour systems we regulate inventory as pressure. A typical system is shown in figure 9.5. Both the inlet and outlet are gas or vapour. Therefore if the control valve is shut then the pressure in the tank will rise and vice versa.
Gas/vapour system
In principle we might, like the level control system, have the valve either upstream or downstream of the tank. In practice in gas systems it is more likely to be downstream for the following reason.
Raising the pressure of a gas requires energy, and normally some mechanical device, such as a compressor, imparts this energy. Both the compressor itself, and the energy to drive it, is expensive. To minimise the first cost we try to minimise the number of compressors in a process. Where possible we would use only one, locate it at the front of the process, and perform any subsequent manipulations to obtain the required pressure by downstream valves.
The energy used in compression is expensive, and throttling through a control valve throws this energy away. Therefore in processes where compressor costs are very significant we may sometimes avoid such valves and manipulate the compressor speed in order to maintain the system at the required pressure. This control system is shown in the figure 9.6
Pressure control system
When we have vapour we usually also have liquids. Regulating pressure in two-phase systems can be somewhat different. This is dealt with later.
9.3.3 Temperature control systems
In this section the control of temperature is to be discussed. Again only simple feedback loops are considered.
To change the temperature of something it is necessary to add or take away energy. This can be achieved in one of two ways.
- Transfer energy indirectly, using a second stream, through coils, tubes, jackets etc. The second stream could be, for example, steam, cooling water, another process stream or even a source of power as in an electric element
- Mix in a second stream directly. This stream will have a different energy content from the original
There are advantages and disadvantages for both methods. With the first there is the problem of transferring heat through the walls of the ‘coil’. In the second the energy is absorbed directly but with the additional problem of increased flow rate/volume.
Diagrams of these alternative schemes can be found below.
Temperature control system
9.3.4 Composition control systems
The control of composition is probably the most important objective in the chemical industry due to the requirement for specification on products. It is thus a strategic rather than an operational control problem and can only be considered sensibly in the context of whole process control.
Simple composition control problem
To illustrate composition control considers the simplest process in which composition can be changed, namely blending. Here two streams of different compositions are mixed together e.g. a concentrate and a diluent as shown in the figure 9.8.
Simple composition control problem
Either of the above schemes could be used although the first is preferred. The reasons are discussed in a later section. It is worth mentioning that the composition of a stream is rarely measured directly.
Typical composition analyzers include:
- Gas chromatographs
- Spectroscopic analysers
Features of this type of hardware, which make them ineffective for control purposes, are:
- Large time delay in their response
- Low operational reliability
- Relatively high cost
Thus an alternative method has to be sought to control the composition. This could be via the:
- Temperature of the mixture
- Pressure of the mixture
9.3.5 Pressure control in two-phase systems
An example of a process, which contains both a vapour and a liquid, is distillation. We generally wish to regulate the pressure in the column, which contains mainly vapour. This could be done by placing a valve in the vapour line leaving the column, exactly as we did with the simple tank.
Pressure control in two-phase systems
There are several disadvantages to this system. One is that the control valve is on a vapour line. These are generally much bigger than liquid lines and hence require a much bigger valve i.e. of a much-increased cost.
However, we remember that in a two-phase system temperature and pressure are not independent. We can thus change the pressure of a vapour, which is in equilibrium with a liquid, by changing the temperature of the system. Raising the temperature raises the vapour pressure of the liquid, which must equal the equilibrium pressure of the system.
Hence we can manipulate the temperature in the condenser by means of a small valve on the cooling water line, thus changing the pressure in both condenser and column.
Cooling water line
9.4 Control actions
This tutorial will show you the characteristics of the each of proportional (P), the integral (I), and the derivative (D) controls, and how to use them to obtain a desired response. In this tutorial, we will consider the following unity feedback system:
- Plant: A system to be controlled
- Controller: Provides the excitation for the plant; Designed to control the overall system behavior
Unity feedback system
9.4.1 Characteristics of P, I, and D controllers
A proportional controller (Kp) will have the effect of reducing the rise time and will reduce, but never eliminate, the steady-state error. An integral control (Ki) will have the effect of eliminating the steady-state error, but it may make the transient response worse. A derivative control (Kd) will have the effect of increasing the stability of the system, reducing the overshoot, and improving the transient response
9.5 Examples of control
9.5.1 Cruise control
This is a simple example of the modeling and control of a first order system. This model takes inertia and damping into account, and simple controllers are designed.
Pressure
9.5.2 Motor speed control
A DC motor has second order speed dynamics when mechanical properties such as inertia and damping as well as electrical properties such as inductance and resistance are taken into account. The controller’s objective is to maintain the speed of rotation of the motor shaft with a particular step response. This electromechanical system example demonstrates slightly more complicated dynamics than does the cruise control example, requiring more sophisticated controllers.
DC motor
9.5.3 Open-loop control system
An open-loop control system is one in which the control action is totally independent of the output.
A suggested example (Figure 9.14) of an open-loop control system is a chemical addition pump with a variable speed control. An operator, who is not part of the control system, determines the feed rate of chemicals that maintain proper chemistry of a system. If the process variables of the system change, the pump cannot respond by adjusting its feed rate (speed) without operator action.
Open-loop control system
9.5.4 Closed-loop control system
A closed-loop control system is one in which control action is always dependent on the output. Feedback is information in a closed-loop control system about the condition of a process variable. This variable is compared with a desired condition to produce the proper control action on the process. Information is continually “fed back” to the control circuit in response to control action.
In the previous example, the actual storage tank water level, sensed by the level transmitter, is feedback to the level controller. This feedback is compared with a desired level to produce the required control action that will position the level control as needed to maintain the desired level. Figure 9.15 shows this relationship.
Feedback in a closed-loop control system
9.5.5 Cascade control
Cascade control is the second alternative to simple feedback control. In this setup there is:
- One manipulated variable
- More than one measured variable
- An inner and outer control loop is formed each with an individual feedback controller. The outer loop controller is also known as the master or primary controller
- The input to this controller is the measured value of the variable to be controlled
- The operator supplies the set point. It passes its output signal to the inner control loop
- The inner loop controller is known as the slave or secondary controller. It measures a second variable whose value affects the controlled variable
- The set point is supplied by the output from the outer loop. Its output signal is used as the signal to the manipulated variable
The above points can be shown clearly in a diagram.
Cascade control
The major benefit from using cascade control is that the secondary controller corrects disturbances arising within the secondary loop before they can affect the value of the primary controlled output. Cascade control is especially effective if the inner loop is much faster than the outer loop and if the main disturbances affect the inner loop first.
Below are described examples of cascade control in practice. It should be noted that in two of the three examples, the secondary loop is used to compensate for flow rate changes. In process systems this is generally the case
Example 1 - Reactor temperature control
In this example the aim is to keep T2 at its set point. The primary control loop detects and eliminates changes in T1, the temperature of the reactants. The secondary control loop detects changes in the temperature of the cooling water. Hence it can adjust the flow accordingly before the effects are detected by the primary control loop. If there was no second controller the effect of the cooling water would take a long time to materalise and hence eliminated
Reactor temperature control
Example 2 - Distillation bottoms temperature control
In this example the primary loop detects changes in the temperature brought about by changes in composition, pressure, etc. The secondary loop detects changes in the steam flow rate and hence eliminates anticipated effects on the temperature.
Distillation bottoms temperature control
Example 3 - Heat exchanger temperature control
This is similar to example 2. The aim is to keep T2 constant. Again the secondary loop is used to compensate for flow rate changes.
Heat exchanger temperature control
9.5.6 Split range control
The final alternative to simple feedback control to be discussed in this section is Split-Range Control. This is distinguished by the fact that it has:
- One measurement only (the controlled variable)
- More than one manipulated variable
The control signal is split into several parts each associated with one of the manipulated variables. A single process is controlled by coordinating the actions of several manipulated variables, all of which have the same effect on the controlled output.
Below are two situations where split-range control is used in chemical processes.
Example 1 – Control of pressure in a reactor
The aim of this loop is to control the pressure in the reactor. It may be possible to operate this system with only one of the valves but the second valve is added to provide additional safety and operational optimality.
Control of pressure in a reactor
In this case the action of the two valves should be coordinated. Thus for example if the operating pressure is between 0.5 and 1.5 bar then the control algorithm could be
- If the pressure is below 0.5 bars then valve 1 is completely open and 2 is completely closed
- If the pressure is between 0.5 and 1 bar then valve 1 is completely open while 2 is opened continuously as the pressure rises. Note that both these actions lead to a reduction in pressure
- If there is a large increase in pressure and it rises to above 1 bar then valve 2 is completely open while 1 is closed continuously
- If the pressure reaches 1.5 bar then valve 1 is shut and 2 is open
A graph of these valve positions with respect to pressure is shown below.
Valve positions with respect to pressure
Example 2 – Control of pressure in a steam header
The aim of this control loop is to maintain a constant pressure in the steam header subject to differing demands for steam further downstream. In this case the signal is split and the steam flow from every boiler is manipulated. An alternative manipulated variable could be the steam production rate at each boiler via the firing rate. A similar control scheme to the above could be developed for the pressure control of a common discharge or suction header for N parallel compressors.
Control of pressure in a steam header
9.5.7 Feed forward control
In this configuration, a sensor or measuring device is used to directly measure the disturbance as it enters the process and the sensor transmits this information to the feed forward controller. The feed forward controller determines the needed change in the manipulated variable, so that, when the effect of the disturbance is combined with the effect of the change in the manipulated variable, there will be no change in the controlled variable at all. The controlled variable is always kept at its set point and hence disturbances have no effect on the process. This perfect compensation is a difficult goal to obtain. It is, however, the objective for which feed forward control is structural. A typical feed forward control loop is shown in the figure below.
Open loop control
Another name for feed forward control is open loop control. The reason is that the measured signal goes to the controller parallel to the process. This can be seen in the next figure. This is in contrast to feedback or closed loop control.
Closed loop control
As mentioned previously the main advantage of feed forward control is that it works to prevent errors from occurring and disturbances have no effect on the process at all. However, there are some significant difficulties.
9.6 Control loop diagrams
A loop diagram is basically a “roadmap” that traces process fluids through the system and designates variables that can disrupt the balance of the system.
A block diagram is also a pictorial representation of the cause and effect relationship between the input and output of a physical system. A block diagram provides a means to easily identify the functional relationships among the various components of a control system.
The simplest form of a block diagram is the block and arrows diagram. It consists of a single block with one input and one output. The block usually contains the name of the element or the symbol of a mathematical operation to be performed on the input to obtain the desired output. Arrows identify the direction of information or signal flow.
Block and arrows
Although blocks are used to identify many types of mathematical operations, operations involving addition and subtraction are represented by a circle, called a summing point. As shown in figure 9.26, summing point may have one or several inputs.
Each input has its own appropriate plus or minus sign. A summing point has only one output and is equal to the algebraic sum of the inputs.
Summing up points
9.7 Modes of automatic control
The mode of control is the manner in which a control system makes corrections relative to an error that exists between the desired value (set point) of a controlled variable and its actual value. The mode of control used for a specific application depends on the characteristics of the process being controlled. For example, some processes can be operated over a wide band, while others must be maintained very close to the set point. Also, some processes change relatively slowly, while others change almost immediately.
Deviation is the difference between the set point of a process variable and its actual value. This is a key term used when discussing various modes of control.
Four modes of control commonly used for most applications are:
- Proportional
- Proportional plus reset (PI)
- Proportional plus rate (PD)
- Proportional plus reset plus rate (PID)
Each mode of control has characteristic advantages and limitations.
9.7.1 Proportional control system
Control mode
In the proportional control mode, the final control element is throttled to various positions that are dependent on the process system conditions. For example, a proportional controller provides a linear stepless output that can position a valve at intermediate positions, as well as “full open” or “full shut.” The controller operates within a band that is between the 0% output point and the 100% output point and where the output of the controller is proportional to the input signal.
Proportional band
With proportional control, the final control element has a definite position for each value of the measured variable. In other words, the output has a linear relationship with the input. Proportional band is the change in input required to produce a full range of change in the output due to the proportional control action. Or simply, it is the percent change of the input signal required to change the output signal from 0% to 100%.
The proportional band determines the range of output values from the controller that operate the final control element. The final control element acts on the manipulated variable to determine the value of the controlled variable. The controlled variable is maintained within a specified band of control points around a set point.
Consider the example (Figure 9.27.) of a proportional level control system; the flow of supply water into the tank is controlled to maintain the tank water level within prescribed limits. The demand that disturbances placed on the process system are such that the actual flow rates cannot be predicted. Therefore, the system is designed to control tank level within a narrow band in order to minimize the chance of a large demand disturbance causing overflow or run out. A fulcrum and lever assembly is used as the proportional controller. A float chamber is the level-measuring element, and a 4-in stroke valve is the final control element. The fulcrum point is set such that a level change of 4-in causes a full 4-in stroke of the valve. Therefore, a 100% change in the controller output equals 4-in.
Proportional system controller
The proportional band is the input band over which the controller provides a proportional output and is defined as follows:
For this example, the fulcrum point is such that a full 4-in change in float height causes a full 4-in stroke of the valve.
Therefore:
The controller has a proportional band of 100%, which means the input must change 100% to cause a 100% change in the output of the controller.
If the fulcrum setting were changed so that a level change of 2 in, or 50% of the input, causes the full 3-in stroke, or 100% of the output, the proportional band would become 50%. The proportional band of a proportional controller is important because it determines the range of outputs for given inputs.
9.7.2 Proportional plus reset
This type control is actually a combination of two previously discussed control modes, proportional and integral.
Combining the two modes results in gaining the advantages and compensating for the disadvantages of the two individual modes.
The main advantage of the proportional control mode is that an immediate proportional output is produced as soon as an error signal exists at the controller as shown in figure 9.28. The proportional controller is considered a fast-acting device. This immediate output change enables the proportional controller to reposition the final control element within a relatively short period of time in response to the error.
Response of proportional plus reset control
The main disadvantage of the proportional control mode is that a residual offset error exists between the measured variable and the set point for all but one set of system conditions.
The main advantage of the integral control mode is that the controller output continues to reposition the final control element until the error is reduced to zero. This results in the elimination of the residual offset error allowed by the proportional mode.
The main disadvantage of the integral mode is that the controller output does not immediately direct the final control element to a new position in response to an error signal. The controller output changes at a defined rate of change, and time is needed for the final control element to be repositioned.
The combination of the two control modes is called the proportional plus reset (PI) control mode. It combines the immediate output characteristics of a proportional control mode with the zero residual offset characteristics of the integral mode.
9.7.3 Proportional plus rate control
Proportional-derivative
Proportional plus rate describes a control mode in which a derivative section is added to a proportional controller. This derivative section responds to the rate of change of the error signal, not the amplitude; this derivative action responds to the rate of change the instant it starts. This causes the controller output to be initially larger in direct relation with the error signal rate of change. The higher the error signal rate of change, the sooner the final control element is positioned to the desired value. The added derivative action reduces initial overshoot of the measured variable, and therefore aids in stabilizing the process sooner.
This control mode is called proportional plus rate (PD) control because the derivative section responds to the rate of change of the error signal.
Definition of derivative control
A device that produces a derivative signal is called a differentiator. Figure 9.29 shows the input versus output relationship of a differentiator.
Derivative output for a constant rate of change input
The differentiator provides an output that is directly related to the rate of change of the input and a constant that specifies the function of differentiation. The derivative constant is expressed in units of seconds and defines the differential controller output.
The differentiator acts to transform a changing signal to a constant magnitude signal as shown in figure 9.30. As long as the input rate of change is constant, the magnitude of the output is constant. A new input rate of change would give a new output magnitude.
Rate control output
Derivative cannot be used alone as a control mode. This is because a steady-state input produces a zero output in a differentiator. If the differentiator were used as a controller, the input signal it would receive is the error signal. As just described, a steady-state error signal corresponds to any number of necessary output signals for the positioning of the final control element. Therefore, derivative action is combined with proportional action in a manner such that the proportional section output serves as the derivative section input.
Proportional plus rate controllers take advantage of both proportional and rate control modes.
As seen in figure 9.31, proportional action provides an output proportional to the error. If the error is not a step change, but is slowly changing, the proportional action is slow. Rate action, when added, provides quick response to the error.
Response of proportional plus rate control
9.7.4 Reset integral control system
Reset control (Integral)
Integral control describes a controller in which the output rate of change is dependent on the magnitude of the input. Specifically, a smaller amplitude input causes a slower rate of change of the output. This controller is called an integral controller because it approximates the mathematical function of integration. The integral control method is also known as reset control.
Definition of integral control
A device that performs the mathematical function of integration is called an integrator. The mathematical result of integration is called the integral. The integrator provides a linear output with a rate of change that is directly related to the amplitude of the step change input and a constant that specifies the function of integration.
For the example shown in figure 9.31, the step change has amplitude of 10%, and the constant of the integrator causes the output to change 0.2% per second for each 1 % of the input.
The integrator acts to transform the step change into a gradually changing signal. As you can see, the input amplitude is repeated in the output every 5 seconds. As long as the input remains constant at 10%, the output will continue to ramp up every 5 seconds until the integrator saturates.
Integral output for a fixed input
With integral control, the final control element’s position changes at a rate determined by the amplitude of the input error signal. Recall that:
Error = Set point - Measured Variable
If a large difference exists between the set point and the measured variable, a large error results. This causes the final control element to change position rapidly. If, however, only a small difference exists, the small error signal causes the final control element to change position slowly.
Integral flow rate controller
Figure 9.33, illustrates a process using an integral controller to maintain a constant flow rate. Also included is the equivalent block diagram of the controller.
Initially, the system is set up on an anticipated flow demand of 50 gpm, which corresponds to a control valve opening of 50%. With the set point equal to 50 gpm and the actual flow measured at 50 gpm, a zero error signal is sent to the input of the integral controller. The controller output is initially set for a 50%, or 9 psi, output to position the 6-in control valve to a position of 3 in open. The output rate of change of this integral controller is given by:
Output rate of change = Integral constant × % Error
If the measured variable decreases from its initial value of 50 gpm to a new value of 45 gpm, as seen in figure 9.34, a positive error of 5% is produced and applied to the input of the integral controller. The controller has a constant of 0.1 seconds-’, so the controller output rate of change is 0.5% per second.
The positive 0.5% per second indicates that the controller output increases from its initial point of 50% at 0.5% per second. This causes the control valve to open further at a rate of 0.5% per second, increasing flow.
The controller acts to return the process to the set points. This is accomplished by the repositioning of the control valve. As the controller causes the control valve to reposition, the measured variable moves closer to the set point, and a new error signal is produced. The cycle repeats itself until no error exists.
The integral controller responds to both the amplitude and the time duration of the error signal. Some error signals that are large or exist for a long period of time can cause the final control element to reach its “fully open” or “fully shut” position before the error is reduced to zero. If this occurs, the final control element remains at the extreme position, and the error must be reduced by other means in the actual operation of the process system.
Reset controller response
Properties of integral control
The major advantage of integral controllers is that they have the unique ability to return the controlled variable back to the exact set point following a disturbance.
Disadvantages of the integral control mode are that it responds relatively slowly to an error signal and that it can initially allow a large deviation at the instant the error is produced. This can lead to system instability and cyclic operation. For this reason, the integral control mode is not normally used alone, but is combined with another control mode.
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