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Chapter 6 Chapter 6 BASIC CONTROL THEORY

Ch. 6 basic control theory

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Page 1: Ch. 6 basic control theory

Chapter 6Chapter 6BASIC CONTROL THEORY

Page 2: Ch. 6 basic control theory

The Control Loop

Control loops in the

process control process control

industry work in the

same way, requiring

three tasks to occur:

Measurement

Comparison

Adjustment

Page 3: Ch. 6 basic control theory

Open and Closed Control Loops An open control loop exists where the process variable is not

compared, and action is taken not in response to feedback on the condition of the process variable, but is instead taken without regard to process variable conditions.

Open loop control has no information or feedback about the measured value.

The position of the correcting element is fixed.

It is unable to compensate for any disturbances in the process.

Page 4: Ch. 6 basic control theory

A closed control loop exists where a process variable is measured, compared to a setpoint, and action is taken to correct any deviation from setpoint.

In a closed loop control system the output of the measuring element is fed into the loop controller where it is compared with the set point An error signal is generated when the measured the set point. An error signal is generated when the measured value is not equal to the set point. Subsequently, the controller adjusts the position of the control valve until the measured adjusts the position of the control valve until the measured value fed into the controller is equal to the set point.

Closed loop control has information and feedback about the Closed loop control has information and feedback about the measured value.

The position of the correcting element is variable The position of the correcting element is variable.

It is able to compensate for any disturbances in the process.

Page 5: Ch. 6 basic control theory
Page 6: Ch. 6 basic control theory

COMPONENTS OF CONTROL LOOPS This section describes the instruments, technologies, and equipment

used to develop and maintain process control loops. CControl Loop Equipment and Technology The basic elements of control as measurement, comparison, and

adjustment. In practice, there are instruments and strategies to j p , gaccomplish each of these essential tasks.

Page 7: Ch. 6 basic control theory

Signals: There are three kinds of signals that exist for the process findustry to transmit the process variable measurement from the

instrument to a centralized control system.

1 Pne matic signal e ign l p od ed b h nging the i 1. Pneumatic signal: are signals produced by changing the air pressure in a signal pipe in proportion to the measured change in a process variable. The common industry standard pneumatic signal range is 3–15 psig.

2. Analog signal: The most common standard electrical signal is the 4–20 mA current signal. With this signal, a transmitter sends a small current through a set of wires.

3 Di i l i l di l l l h bi d i 3. Digital signal: are discrete levels or values that are combined in specific ways to represent process variables and also carry other information, such as diagnostic information. The methodology used to , g gycombine the digital signals is referred to as protocol.

Page 8: Ch. 6 basic control theory

Controller Algorithmsg The actions of controllers can be divided into

groups based upon the functions of their groups based upon the functions of their control mechanism. E h t f t ll h d t d Each type of controller has advantages and disadvantages and will meet the needs of diff t li ti different applications.

The Controllers are grouped as:g pDiscrete controllers (On/ Off)

Continuous controllersContinuous controllers

Page 9: Ch. 6 basic control theory

Discrete controllers (ON/ OFF): These controllers Discrete controllers (ON/ OFF): These controllers

have only two modes or positions: on and off (two-

step). This type of control doesn’t actually hold the

variable at setpoint, but keeps the variable within

proximity of setpoint in what is known as a dead

zone.

Two-step is the simplest of all the control modes. The Two step is the simplest of all the control modes. The

output from the controller is either on or off with the

controller's output changing from one extreme to the

other regardless of the size of the error. g

Page 10: Ch. 6 basic control theory
Page 11: Ch. 6 basic control theory

Summary of "On" "Off" ControlSummary of On Off Control

Two-position control can only be in one of two positions, either 0% 100% A it h i l f O /Off t l0% or 100%. A switch is an example of On/Off control.

Advantages:

» On/Off control makes "troubleshooting" very easy and requires only basic types of instruments.

Disadvantages: Disadvantages:

» The process oscillates.

Th fi l t l l t ( ll t l l ) i l » The final control element (usually a control valve) is always opening and closing and this cause excessive wear.

» There is no fixed operating point» There is no fixed operating point.

Page 12: Ch. 6 basic control theory

Discrete (On/ Off) Control Reaction CurveDiscrete (On/ Off) Control Reaction Curve

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Continuous Control There are three basic control actions that

are often applied to continuous control:1. Proportional (P)2. Integral (I)

( )3. Derivative (D) It is also necessary to consider these in

combination such as P + I P + D P + I + D combination such as P + I, P + D, P + I + D. Although it is possible to combine the different actions, and all help to produce the different actions, and all help to produce the required response, it is important to remember that both the integral and derivative actions are usually corrective derivative actions are usually corrective functions of a basic proportional control action.act o

Page 14: Ch. 6 basic control theory
Page 15: Ch. 6 basic control theory

Continuous Controllers Controllers automatically compare the value of the PV to the SP to determine if

an error exists. If there is an error, the controller adjusts its output according to j p g

the parameters that have been set in the controller.

Page 16: Ch. 6 basic control theory

Th t i t ti ll d t iThe tuning parameters essentially determine:

How much correction should be made? The magnitude of

the correction (change in controller output) is determined by

the proportional mode of the controller.p p

How long the correction should be applied? The duration

fof the adjustment to the controller output is determined by

the integral mode of the controller

How fast should the correction be applied? The speed at

which a correction is made is determined by the derivative which a correction is made is determined by the derivative

mode of the controller.

Page 17: Ch. 6 basic control theory

Proportional Control (Mode)

With proportional control,

h l d d h h the correcting element is adjusted In proportion to the change

in the measured value from the set point.

The largest movement is made to the correcting element when

the deviation between measured value and set point is t e de at o bet ee easu ed a ue a d set po t s

greatest.

Usually, the set point and measured value are equal when the

output is midway of the controller output signal range.

Page 18: Ch. 6 basic control theory
Page 19: Ch. 6 basic control theory
Page 20: Ch. 6 basic control theory

Proportional Band (PB):The simplest and most common form of control action to be found on

a controller is proportional. With this form of control the output from the controller is directly proportional to the input error signalfrom the controller is directly proportional to the input error signal, i.e. the larger the input error the larger the output response from the controller.Th t l i f th t t d d th f t th The actual size of the output depends on another factor, the controller's proportional band or gain (the controller's sensitivity). The setting for the proportional mode may be expressed as either:» Proportional Band (PB) is another way of representing the

same information and answers this question: "What percentage of change of the controller input span will cause a 100%of change of the controller input span will cause a 100% change in controller output?“ PB = ∆ Input (% Span) For 100% ∆ Output.

» Proportional Gain (Kc) answers the question: "What is the percentage change of the controller output relative to the percentage change in controller input?“ Proportional Gain ispercentage change in controller input? Proportional Gain is expressed as: Gain, (Kc) = ∆ Output% / ∆ Input %

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Proportional Controller Equation:Proportional Controller Equation:

Where,

m = Controller output

e = Error (difference between PV and SP)( )

Kp = Proportional gain

b = Bias

Page 22: Ch. 6 basic control theory

Proportional band and gainGain is just the inverse of PB multiplied by 100 or gain = 100/PB PB = 100/Gain Also recall that: Gain = 100% / PB Also recall that: Gain = 100% / PB Gain (Kc) = ∆ Output% / ∆ Input % PB= ∆ Input (%Span) For 100% ∆ Output

Page 23: Ch. 6 basic control theory

PB 100% = Gain 1 PB 200% = Gain 0.5

PB 50% = Gain 2 PB 150% = Gain 0.67

Page 24: Ch. 6 basic control theory

If the gain is set too high there If the gain is set too high, there

will be oscillations as the PV

t i t converges on a new setpoint

value:

If the gain is set too low, the process

response will be stable under steady-

state conditions, but “sluggish” to

changes in setpoint because the

controller does not take aggressive

enough action to cause quick changes

in the process:

Page 25: Ch. 6 basic control theory

With proportional-only control, the only way to obtain fast-acting

response to setpoint changes or “upsets” in the process is to set

the gain constant high enough that some “overshoot” results:g g g

Page 26: Ch. 6 basic control theory

Summary of Proportional controlWith Proportional Control:

∆ Controller Output = (Change in Error)(Gain) Proportional Mode Responds only to a change in errorp p y g Proportional mode alone will not return the PV to SP. Stable control Suffers from offset due to load changes.g

Narrow PB% Fast to respond, Large overshoot Large overshoot, Long settling time, Small offset

Wide PB% Wide PB% Slow to respond, Quick to settle’ Large offset Large offset

Proportional control used in process where load changes are small and the offset can be tolerated.

Page 27: Ch. 6 basic control theory

Integral Control (Mode)Integral Control (Mode)Integral Action Another component of error is the duration of the Another component of error is the duration of the

error, i.e., how long has the error existed?. The controller output from the integral or reset mode is acontroller output from the integral or reset mode is a function of the duration of the error.I t l ti i d i j ti ith Integral action is used in conjunction with proportional action to eliminate offset problem

lti f P t lresulting from P control. This is accomplished by repeating the action of the

proportional mode as long as an error exists.

Page 28: Ch. 6 basic control theory

If we add an integral term to the controller equation, we get

something that looks like this:

Where:

m = Controller Output

(d ff b d )e = Error (difference between PV and SP)

Kp = Proportional gainp

τi = Integral time constant (minutes)

t = Time

b = Biasb = Bias

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Page 30: Ch. 6 basic control theory

Integral Action Effect

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Integral Saturation or Reset Wind-up

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Summary of integral action (Reset) Integral (Reset) Summary - Output is a repeat of the Integral (Reset) Summary - Output is a repeat of the

proportional action as long as error exists. The units are in terms of repeats per minute or minutes per repeat.

Advantages - Eliminates error Advantages - Eliminates error Disadvantages: Makes the process less stable and take longer

to settle down. Can suffer from integral saturation or wind-up on batch

processes. Fast Reset (Large Repeats/Min., Small Min./Repeat)ast eset ( a ge epeats/ , S a / epeat)

» High Gain» Fast Return to Setpoint» Possible Cycling» Possible Cycling

Slow Reset (Small Repeats/Min., Large Min./Repeats)» Low Gain

Sl R t t S t i t» Slow Return to Setpoint» Stable Loop

P + I controller is used when offset must be eliminated automatically and integral saturation due to a sustained offset is automatically and integral saturation due to a sustained offset is not a problem.

Page 33: Ch. 6 basic control theory

P+ I Controller Reaction at Optimum Settingsp g

Page 34: Ch. 6 basic control theory

Derivative ModeWh D i ti M d ?Why Derivative Mode?

Some large and/or slow process do not respond well to small

changes in controller output. For example, a large liquid level

process or a large thermal process (a heat exchanger) may p g p ( g ) y

react very slowly to a small change in controller output. To

improve response, a large initial change in controller output may improve response, a large initial change in controller output may

be applied. This action is the role of the derivative mode.

The derivative action is initiated whenever there is a change in

the rate of change of the error (the slope of the PV). The

magnitude of the derivative action is determined by the setting

of the derivative.

Page 35: Ch. 6 basic control theory

In operation, the controller first compares the current PV with the last value of the PV. If there is a change in the slope of the PV, the controller determines what its output would be at a future point in time (the future point in time is determined by the value of the time (the future point in time is determined by the value of the derivative setting, in minutes). The derivative mode immediately increases the output by that amount. p y

Page 36: Ch. 6 basic control theory
Page 37: Ch. 6 basic control theory

Summary of Derivative action (Rate)

Rate action is a function of the speed of change of the error. The units are minutes. The action is to apply an immediate response that is equal to the proportional plus reset action that would have occurred equal to the proportional plus reset action that would have occurred some number of minutes in the future.

Advantages - Rapid output reduces the time that is required to return PV t SP i l PV to SP in slow process.

Disadvantage - Has no effect on offset. Dramatically amplifies noisy signals; can cause cycling in fast processes.g ; y g p

Large (Minutes): High Gain L O t t Ch Large Output Change Possible Cycling

Small (Minutes): Low Gain Small Output Change Stable Loop

Page 38: Ch. 6 basic control theory
Page 39: Ch. 6 basic control theory

Proportional, PI, and PID ControlBy using all three control algorithms together process operators By using all three control algorithms together, process operators can:

Achieve rapid response to major disturbances with derivative control Achieve rapid response to major disturbances with derivative control

Hold the process near setpoint without major fluctuations with proportional control

Eliminate offset with integral control

Not every process requires a full PID control strategy. If a small ff h i h h i l l offset has no impact on the process, then proportional control

alone may be sufficient.

Page 40: Ch. 6 basic control theory

P I and D Responses GraphedP, I, and D Responses GraphedA very helpful method for understanding the operation of proportional, integral, and derivative control terms is to analyze their respective responses y p pto the same input conditions over time.

The following graphs showing P I and D responses The following graphs showing P, I, and D responses for several different input conditions. In each graph, the controller is assumed to be direct acting (i e an the controller is assumed to be direct-acting (i.e. an increase in process variable results in an increase in output)output).

Page 41: Ch. 6 basic control theory

Responses to a single step-change

Proportional action directly mimics the shape of the input change (a step) Integralchange (a step). Integral action ramps at a rate proportional to the magnitude f h i Si hof the input step. Since the

input step holds a constant value, the integral action ramps at a constant rate (a constant slope). Derivative action interprets the step as p pan infinite rate of change, and so generates a “spike” driving the output to saturationthe output to saturation. When combined into one PID output, the three actions produce this response:produce this response:

Page 42: Ch. 6 basic control theory

Responses to a momentary step-and-returnProportional action directly mimics the shape of the input change (an up-and-down step)up and down step).Integral action ramps at a rate proportional to the magnitude of the input step for as long as the PV isinput step, for as long as the PV is unequal to the SP. Once PV = SP again, integral action stops ramping

d i l h ld th l t land simply holds the last value. Derivative action interprets both steps as infinite rates of change, and so generates a “spike” at the leading and at the trailing edges of the step. pNote how the leading (rising) edge causes derivative action to saturate high while the trailing (falling) edgehigh, while the trailing (falling) edge causes it to saturate low.

Page 43: Ch. 6 basic control theory

Responses to a ramp-and-hold

Proportional action directly mimics the ramp-and-holdmimics the ramp and hold shape of the input.

Integral action rampsIntegral action ramps slowly at first (when the error is small) but increases )ramping rate as error increases. When error t bili i t l tstabilizes, integral rate

likewise stabilizes. Derivative action offsetsDerivative action offsets the output according to the input’s ramping rate.p p g

Page 44: Ch. 6 basic control theory

Summary of Control modes and responses

Page 45: Ch. 6 basic control theory

Controller TuningWhy Controllers Need Tuning?Why Controllers Need Tuning?

Controllers are tuned to achieve two goals:

h d kl» The system responds quickly to errors.

» The system remains stable (PV does not oscillate around the SP)SP)

Controller tuning is performed to adjust the manner in which a control valve (or other final control element) responds to a co t o a e (o ot e a co t o e e e t) espo ds to achange in error.

In particular, we are interested in adjusting the controller’s modes (gain, Integral and derivative), such that a change in controller input will result in a change in controller output that will, in turn, cause sufficient change in valve position to , , g peliminate error, but not so great a change as to cause instability or cycling.

Page 46: Ch. 6 basic control theory

Before you tune . . .The recommended considerations prior to making adjustments to

th t i f l t llthe tuning of a loop controller:

• Identifying operational needs (i.e. “How do the operators want

the system to respond?”)

• Identifying process and system hazards before manipulating the Identifying process and system hazards before manipulating the

loop

• Identifying whether it is a tuning problem, a field instrument

problem, and/or a design problem

Page 47: Ch. 6 basic control theory

PID tuningPID tuning procedure is a step-by-step approach leading directly to a set of numerical values to be used in a PID directly to a set of numerical values to be used in a PID controller.

A “ l d l ” i d i i l d i h h A “closed loop” tuning procedure is implemented with the controller in automatic mode: adjusting tuning parameters

fto achieve an easily-defined result, then using those PID parameter values and information from a graph of the process variable over time to calculate new PID parameters.

Page 48: Ch. 6 basic control theory

Ziegler-Nichols Closed-Loop (“Ultimate Gain”)Ziegler Nichols Closed Loop ( Ultimate Gain )

The closed loop or ultimate method involves finding

the point where the system becomes unstable and

using this as a basis to calculate the optimum g p

settings.

Page 49: Ch. 6 basic control theory

The following steps may be used to determine ultimate The following steps may be used to determine ultimate

PB and ultimate periodic time:

1. Switch the controller to Manual and set the proportional band to

high value.g

2. Turn off all integral and derivative action.

3. Switch the controller to automatic and reduce the proportional

band value to the point where the system becomes unstable and

oscillates with constant amplitude. Sometimes a small step

change is required to force the system into its unstable mode.g q y

Page 50: Ch. 6 basic control theory

Look for curve B that represents the continuous oscillation

Page 51: Ch. 6 basic control theory

4 The proportional band that required causing 4. The proportional band that required causing

continuous oscillation is the ultimate value Bu.

5. The ultimate periodic time is Pu.

6. From these two values the optimum setting can be

calculated as per the following procedures. calculated as per the following procedures.

Page 52: Ch. 6 basic control theory

Optimum setting calculationOptimum setting calculation For proportional action only

» PB% = 2 Bu % Proportional + Integral Proportional Integral

» PB% = 2.2 Bu %I t l ti ti P / 1 2 i t / t» Integral action time = Pu / 1.2 minutes/repeat

Proportional + Integral + Derivativep g» PB%=1.67Bu» Integral action time = Pu / 2 minutes/repeat» Integral action time = Pu / 2 minutes/repeat» Derivative action = Pu / 8 minutes

Page 53: Ch. 6 basic control theory
Page 54: Ch. 6 basic control theory

CONTROL LOOPS CATEGORIES

Control loops can be divided into two

categories:

Single variable loops and Single variable loops, and

Multi-variable loopsp

Page 55: Ch. 6 basic control theory

SINGLE LOOP CONTROL

This is the simplest control loop involving just one controlled variable.

The controller compares the signal from the sensor to the set point on the controller. If there is a difference, the controller sends a signal to the actuator of the valve, which in turn moves the valve to a new position.

Single control loops provide the vast majority of control for heating systems and industrial processes.

The common terms used for single control loops include:

Feedback control. Feedback control.

Feedforward

Page 56: Ch. 6 basic control theory

Feedback controlFeedback control may be viewed as a sort of information “loop,”

from the transmitter, to the controller, to the final control element,

and through the process itself, back to the transmitter. Block

diagram of feedback control looks like a loop:g p

Page 57: Ch. 6 basic control theory

Feedback Control loop measures a process variable d d h ll fand sends the measurement to a controller for

comparison to setpoint. If the process variable is not at setpoint, control action is taken to return the process setpoint, control action is taken to return the process variable to setpoint.

Page 58: Ch. 6 basic control theory

Feedback loops are commonly used in the process control industry.

The advantage of feedback control is that it is a very simple g y ptechnique that directly controls the desired process variable and compensates for all disturbances. Any disturbance affects the controlled variable, and once this variable deviates from set point, the controller changes its output in such a way as to return the variable to set point return the variable to set point.

The disadvantage of feedback control is that it can compensate for a disturbance only after the controlled compensate for a disturbance only after the controlled variable has deviated from set point. That is, the disturbance must propagate through the entire process before the p p g g pfeedback control scheme can initiate action to compensate for it.

Page 59: Ch. 6 basic control theory

Examples of feedback Control Loops

Page 60: Ch. 6 basic control theory

Feedforward ControlFeedforward control addresses this weakness by taking a fundamentally Feedforward control addresses this weakness by taking a fundamentally different approach, basing final control decisions on the states of load variables rather than the process variable. In other words, a feedforward control system monitors all the factors influencing a process and decides how control system monitors all the factors influencing a process and decides how to compensate for these factors ahead of time before they have the opportunity to affect the process variable. If all loads are accurately measured, and the control algorithm realistic enough to predict process response for these known load values, the process variable does not even need to be measured at all:

Page 61: Ch. 6 basic control theory

Feedforward control is a control system that anticipates load disturbances and controls them before they can impact the process variable. In the figure the flow transmitter opens or closes a hot steam valve based on how much cold fluid passes through the flow sensor.

An advantage of feedforward control is that error is prevented, rather than corrected. However, it is difficult to account for all possible load disturbances in a system through feedforward control.

Factors such as outside temperature, buildup in pipes, consistency of raw materials, humidity, and moisture content can all become load disturbances and cannot always be effectively accounted for in a feedforward system.

Page 62: Ch. 6 basic control theory
Page 63: Ch. 6 basic control theory

Multi-Loop Control/ Multi-variable Loops

Multivariable loops are control loops in which a primary controller controls one process a primary controller controls one process variable by sending signals to a controller of a different loop that impacts the process variable different loop that impacts the process variable of the primary loop. Th f ll i t d lti l t l The following are termed as multiple control loops: -»Feedback plus feedforward»Cascade Control»Cascade Control»Ratio Control»Limit, Selector, and Override controls

Page 64: Ch. 6 basic control theory

Feedforward Plus Feedback Because of the difficulty of accounting for every

possible load disturbance in a feedforward system,

feedforward systems are often combined with y

feedback systems.

Controllers with summing functions are used in

these combined systems to total the input from both these combined systems to total the input from both

the feedforward loop and the feedback loop, and

send a unified signal to the final control element.

Page 65: Ch. 6 basic control theory

In the figure a feedforward-plus-feedback loop in which both a flow transmitter and a temperature transmitter provide information for controlling a hot steam valve.

Page 66: Ch. 6 basic control theory
Page 67: Ch. 6 basic control theory

Cascade Control Cascade control is a technique Where two

independent variables need to be controlled with pone valve.

Its purpose is to provide increased stability to Its purpose is to provide increased stability to par-ticularly complex process control problems.

In cascade control the output from one controller In cascade control the output from one controller "called the MASTER" is the set point for another controller "commonly referred to as the SLAVE"controller commonly referred to as the SLAVE .

The master will have an independent plant measurement Only the slave controller has an measurement. Only the slave controller has an output to the final control element.

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The advantages:The advantages:» Variations of the process variable measurement by

the master controller are corrected by the slave ycontrol systems.

» Speed of response of the master control loop is p p pincreased.

» Slave controller permits an exact manipulation of the flow of mass or energy by the master (to maintain the process variable, measured by the master controller within the normal operating limits)controller within the normal operating limits)

Disadvantage:» However, cascade control is more costly. Thus, it is

normally used when highly accurate control is required and where random process disturbances are required and where random process disturbances are expected.

Page 73: Ch. 6 basic control theory

Practical Consideration in Implementing Cascade ControlA necessary step in implementing cascade control is to ensure the

secondary (“slave”) controller is well-tuned before any attempt is made to tune the primary (“master”) controller. made to tune the primary ( master ) controller.

The slave controller does not depend on good tuning in the master controller in order to control the slave loop. p

If the master controller were placed in manual, the slave controller would simply control to a constant setpoint. However, the master controller most definitely depends on the slave controller being well-tuned in order to fulfill the master’s “expectations.”

If the slave controller were placed in manual mode, the master controller would not be able to exert any control over its process variable whatsoever. variable whatsoever.

Clearly then, the slave controller’s response is essential to the master controller being able to control its process variable, therefore g pthe slave controller must be the first one to tune.

Page 74: Ch. 6 basic control theory

Ratio ControlWhere the ratio of one flow rate to another is controlled for

some desired outcome Many industrial processes alsosome desired outcome. Many industrial processes also

require the precise mixing of two or more ingredients to

produce a desired product.

N t l d th i di t d t b i d iNot only do these ingredients need to be mixed in proper

proportion, but it is usually desirable to have the total flow

rate subject to arbitrary increases and decreases so

production rate as a whole may be altered at willproduction rate as a whole may be altered at will.

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A simple example of ratio control is in the production of i t h b li id t b i d ithpaint, where a base liquid must be mixed with one or more

pigments to achieve a desired consistency and color.

Page 76: Ch. 6 basic control theory

All the human operator needs to do now is move the pone link to increase or decrease mixed paint production:

Page 77: Ch. 6 basic control theory

Mechanical link ratio-lcontrol systems are

commonly used to manage simplemanage simple burners, proportioning the flow rates of fuel and air for clean, efficient combustion.

A photograph of such a system appearsa system appears here, showing how the fuel gas valve and air gdamper motions are coordinated by a i l t t tsingle rotary actuator.

Page 78: Ch. 6 basic control theory

A more automated approach to the general problem of ratio control involves the installation of a flow control loop on one of control involves the installation of a flow control loop on one of the lines, while keeping just a flow transmitter on the other line. The signal coming from the uncontrolled flow transmitter becomes the setpoint fo the flo cont ol loop The atio of pigment to base the setpoint for the flow control loop: The ratio of pigment to base will be 1:1 (equal).

Page 79: Ch. 6 basic control theory

We may incorporate convenient ratio adjustment into this system by adding another component (or function block) to the control scheme: a adding another component (or function block) to the control scheme: a device called a signal multiplying relay (or alternatively, a ratio station). This device (or computer function) takes the flow signal from the base (wild) flow transmitter and multiplies it by some constant value (k) (wild) flow transmitter and multiplies it by some constant value (k) before sending the signal to the pigment (captive) flow controller as a set point, the ratio will be 1:1 when k = 1; the ratio will be 2:1 when k = 2 etc 2, etc.

Page 80: Ch. 6 basic control theory

One way to achieve the proper ratio of hydrocarbon gas to steam flow is t i t ll l fl t l l f th t t t f d to install a normal flow control loop on one of these two reactant feed lines, then use that process variable (flow) signal as a setpoint to a flow controller installed on the other reactant feed line. This way, the second controller will maintain a proper balance of flow to proportionately match controller will maintain a proper balance of flow to proportionately match the flow rate of the other reactant. An example P&ID is shown here, where the methane gas flow rate establishes the setpoint for steam flow control:control:

Page 81: Ch. 6 basic control theory

We could add another layer of sophistication to this ratio control system by installing a gas analyzer at the outlet of the reaction furnace designed by installing a gas analyzer at the outlet of the reaction furnace designed to measure the composition of the product stream. This analyzer’s signal could be used to adjust the value of k so the ratio of steam to methane would automatically vary to ensure optimum production quality even if the would automatically vary to ensure optimum production quality even if the feedstock composition (i.e. percentage concentration of methane in the hydrocarbon gas input) changes:

Page 82: Ch. 6 basic control theory

A more common method of ratio control is using separate units t id th ti t I thi fi th t f to provide the ratio system. In this figure, the measurement of an uncontrolled flow transmitted to a ratio unit where it is multiplied by a ratio factor, and the output of the ratio unit becomes the set point of the secondary controller.

The ratio unit normally has a manually adjusted scale to adjust the ratio between the two variables the ratio between the two variables.

Page 83: Ch. 6 basic control theory

Limit, Selector, and Override controlsh f l l h f l lAnother category of control strategies involves the use of signal relays or

function blocks with the ability to switch between different signal values, or re-direct signals to new pathways. Such functions are useful when we g p yneed a control system to choose between multiple signals of differing value in order to make the best control decisions.

The “building blocks” of such control strategies are special relays (or function blocks in a digital control system) shown here:

Page 84: Ch. 6 basic control theory
Page 85: Ch. 6 basic control theory

Limit ControlsIn the following example a cascade control system regulates the In the following example, a cascade control system regulates the temperature of molten metal in a furnace, the output of the master (metal temperature) controller becoming the setpoint of the slave (air temperature) controller A high limit function limits the maximum value temperature) controller. A high limit function limits the maximum value this cascaded setpoint can attain, thereby protecting the refractory brick of the furnace from being exposed to excessive air temperatures:

Page 86: Ch. 6 basic control theory

This same control strategy could have been implemented using a low select function block rather than a high limit:

Page 87: Ch. 6 basic control theory

Selector ControlsSelector control strategy is where we must select a process variable signal from multiple transmitters. For example, consider this chemical reactor, where the control system must throttle the flow of coolant to keep the where the control system must throttle the flow of coolant to keep the hottest measured temperature at setpoint, since the reaction happens to be exothermic (heat-releasing):

Page 88: Ch. 6 basic control theory

Another use of selector relays (or function blocks) is for the determination of a median process measurement This sort of strategy is often used on of a median process measurement. This sort of strategy is often used on triple-redundant measurement systems, where three transmitters are installed to measure the exact same process variable, providing a valid measurement even in the event of transmitter failuremeasurement even in the event of transmitter failure.

The median select function may be implemented one of two ways using high- and low-select function blocks:high and low select function blocks:

Page 89: Ch. 6 basic control theory

Override ControlsAn “override” control strategy involves a selection between two or more controller output signals, where only one controller at a time gets the opportunity to exert control over a process. All other “de-selected” controllers are thus overridden by the selected controller.

In process control systems it often becomes desirable to limit a process variable to some low or high value to avoid damage to process equipment or to the product. This is accomplished by override devices. As long as the variable is within the limits set by the override devices, normal f f h l h hfunctioning of the control system continues; when the set limits are exceeded, the override devices take

d t i d tipredetermined actions.

Page 90: Ch. 6 basic control theory

Consider this water pumping system, where a water pump is d i b i bl d l t i t t d t f driven by a variable-speed electric motor to draw water from a well and provide constant water pressure to a customer:

A t ti l bl ith thi t i th i A potential problem with this system is the pump running “dry” if the water level in the well gets too low, as might happen during summer months when rainfall is low and customer demand is high.

Page 91: Ch. 6 basic control theory

One solution to this problem would be to install a level switch in th ll i t l l d h tti ff th l t i t the well, sensing water level and shutting off the electric motor driving the pump if the water level ever gets too low:

Page 92: Ch. 6 basic control theory

We may create just such a control strategy by replacing the well water level switch with a level transmitter, connecting the level transmitter to a , glevel controller, and using a low-select relay or function block to select the lowest-valued output between the pressure and level controllers. The level controller’s setpoint will be set at some low level above the acceptable p plimit for continuous pump operation:

Page 93: Ch. 6 basic control theory

Bear in mind that the concept of a low-level switch completely shutting off the pump is not an entirely bad idea. In fact, it might be prudent to p p y , g pintegrate such a “hard” shutdown control in the override control system, just in case something goes wrong with the level controller (e.g. an improperly adjusted setpoint or poor tuning) or the low-select function. With two layers of safety control for the pump, this system provides both a “soft constraint” providing moderated action and a “hard constraint” providing aggressive action to protect the pump from dry operation:

Page 94: Ch. 6 basic control theory