The Control Loop
Control loops in the
industry work in the
same way, requiring
three tasks to occur:
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
The position of the correcting element is fixed.
It is unable to compensate for any disturbances in the process.
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
value is not equal to the set point. Subsequently, the controller
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
The position of the correcting element is variable
It is able to compensate for any disturbances in the process.
COMPONENTS OF CONTROL LOOPS
This section describes the instruments, technologies, and equipment
used to develop and maintain process control loops.
Control Loop Equipment and Technology
The basic elements of control as measurement, comparison, and
practice, there are instruments and strategies to
adjustment. In p
accomplish each of these essential tasks.
Signals: There are three kinds of signals that exist for the process
industry to transmit the process variable measurement f
instrument to a centralized control system.
1. Pneumatic signal: e ign l p od ed b h nging
1 Pne matic 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. Digital i
3 Di i l signal: are discrete levels or values that are combined in
bi d i
specific ways to represent process variables and also carry other
information, such as diagnostic information. The methodology used to
combine the digital signals is referred to as protocol.
actions of controllers can be divided into
groups based upon the functions of their
type of controller has advantages and
t ll h
disadvantages and will meet the needs of
Controllers are grouped as:
controllers (On/ Off)
Discrete controllers (ON/ OFF): These controllers
have only two modes or positions: on and off (twostep). 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
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.
Summary of "On" "Off" Control
Two-position control can only be in one of two positions, either
0% or 100% A switch i an example of On/Off control.
it h is
f O /Off
» On/Off control makes "troubleshooting" very easy and requires
only basic types of instruments.
» The process oscillates.
» Th fi l control element (usually a control valve) is always
t l l
l )i l
opening and closing and this cause excessive wear.
» There is no fixed operating point
There are three basic control actions that
are often applied to continuous control:
Derivative ( )
It is also necessary to consider these in
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
required response, it is important to
remember that both the integral and
derivative actions are usually corrective
functions of a basic proportional control
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
the parameters that have been set in the controller.
The tuning parameters essentially d t
Th t i
ti ll 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.
How long the correction should be applied? The duration
of 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
mode of the controller.
Proportional Control (Mode)
With proportional control,
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
t e de at o bet ee
the deviation between measured value and set point is
easu ed a ue a d
po t s
Usually, the set point and measured value are equal when the
output is midway of the controller output signal range.
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 signal
i.e. the larger the input error the larger the output response from
Th actual size of the output depends on another factor, the
The t l i
th f t th
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%
change in controller output?“ PB = ∆ Input (% Span) For 100%
» 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 is
expressed as: Gain, (Kc) = ∆ Output% / ∆ Input %
Proportional Controller Equation:
m = Controller output
e = Error (difference between PV and SP)
Kp = Proportional gain
b = Bias
Proportional band and gain
Gain is just the inverse of PB multiplied by 100 or gain = 100/PB
PB = 100/Gain
Also recall that: Gain = 100% / PB
Gain (Kc) = ∆ Output% / ∆ Input %
PB= ∆ Input (%Span) For 100% ∆ Output
PB 200% = Gain 0.5
PB 100% = Gain 1
PB 50% = Gain 2
PB 150% = Gain 0.67
If the gain is set too high, there
will be oscillations as the PV
converges on a new setpoint
t i t
If the gain is set too low, the process
response will be stable under steadystate conditions, but “sluggish” to
changes in setpoint because the
controller does not take aggressive
enough action to cause quick changes
in the process:
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:
Summary of Proportional control
With Proportional Control:
Fast to respond,
Long settling time,
∆ Controller Output = (Change in Error)(Gain)
Proportional Mode Responds only to a change in error
Proportional mode alone will not return the PV to SP.
Suffers from offset due to load changes.
Slow to respond,
Quick to settle’
Proportional control used in process where load changes are
small and the offset can be tolerated.
Integral Control (Mode)
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 a
function of the duration of the error.
Integral action is used i conjunction with
l ti i
proportional action to eliminate offset problem
lti from P control.
This is accomplished by repeating the action of the
proportional mode as long as an error exists.
If we add an integral term to the controller equation, we get
something that looks like this:
m = Controller Output
e = Error (d ff
(difference between PV and SP)
Kp = Proportional gain
τi = Integral time constant (minutes)
t = Time
b = Bias
Summary of integral action (Reset)
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
Disadvantages: Makes the process less stable and take longer
to settle down.
Can suffer from integral saturation or wind-up on batch
Fast Reset (Large Repeats/Min., Small Min./Repeat)
ast eset ( a ge epeats/
» High Gain
» Fast Return to Setpoint
» Possible Cycling
Slow Reset (Small Repeats/Min., Large Min./Repeats)
» Low Gain
Slow Return to S t i t
» Stable Loop
P + I controller is used when offset must be eliminated
automatically and integral saturation due to a sustained offset is
not a problem.
P+ I Controller Reaction at Optimum Settings
Why Derivative Mode?
Wh D i ti
M d ?
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 p
process ( heat exchanger) may
react very slowly to a small change in controller output. To
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.
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
derivative setting, in minutes). The derivative mode immediately
increases the output by that amount.
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
some number of minutes in the future.
Advantages - Rapid output reduces the time that is required to return
PV to SP i slow process.
Disadvantage - Has no effect on offset. Dramatically amplifies noisy
signals; can cause cycling in fast processes.
Large O t t Change
Small Output Change
Proportional, PI, and PID Control
By using all three control algorithms together process operators
Hold the process near setpoint without major fluctuations with
Achieve rapid response to major disturbances with derivative control
Eliminate offset with integral control
Not every process requires a full PID control strategy. If a small
offset has no impact on the process, then proportional control
alone may be sufficient.
P I, and D Responses Graphed
A very helpful method for understanding the
operation of proportional, integral, and derivative
control terms is to analyze their respective responses
to the same input conditions over time.
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
direct-acting (i e
increase in process variable results in an increase in
Responses to a single step-change
Proportional action directly
mimics the shape of the input
change (a step) Integral
action ramps at a rate
proportional to the magnitude
of the input step. Since the
f h i
input step holds a constant
value, the integral action
ramps at a constant rate (a
constant slope). Derivative
action interprets the step as
an infinite rate of change, and
so generates a “spike” driving
the output to saturation
When combined into one PID
output, the three actions
produce this response:
Responses to a momentary step-and-return
Proportional action directly mimics
the shape of the input change (an
up and down step).
Integral action ramps at a rate
proportional to the magnitude of the
input step, for as long as the PV is
unequal to the SP. Once PV = SP
again, integral action stops ramping
and simply holds the last value.
d i l h ld th l t l
Derivative action interprets both
steps as infinite rates of change,
and so generates a “spike” at the
leading and at the trailing edges of
Note how the leading (rising) edge
causes derivative action to saturate
high while the trailing (falling) edge
causes it to saturate low.
Responses to a ramp-and-hold
Proportional action directly
mimics the ramp and hold
shape of the input.
Integral action ramps
slowly at first (when the
error is small) but increases
ramping rate as error
increases. When error
stabilizes, integral rate
Derivative action offsets
the output according to the
input’s ramping rate.
Why Controllers Need Tuning?
Controllers are tuned to achieve two goals:
» The system responds quickly to errors.
» The system remains stable (PV does not oscillate around the
Controller tuning is performed to adjust the manner in which a
co t o a e (o ot e
control valve (or other final control element) responds to a
a co t o e e e t) espo ds
change 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
eliminate error, but not so great a change as to cause
instability or cycling.
Before you tune . . .
The recommended considerations prior to making adjustments to
the t i
th 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 whether it is a tuning problem, a field instrument
problem, and/or a design problem
PID tuning procedure is a step-by-step approach leading
directly to a set of numerical values to be used in a PID
A “closed loop” tuning procedure is implemented with the
d ih h
controller in automatic mode: adjusting tuning parameters
to 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.
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
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
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.
Look for curve B that represents the continuous oscillation
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.
Optimum setting calculation
For proportional action only
Proportional + Integral
PB% = 2 Bu %
PB% = 2.2 Bu %
Integral action time = Pu / 1 2 minutes/repeat
l ti ti
P 1.2 i t /
Proportional + Integral + Derivative
Integral action time = Pu / 2 minutes/repeat
Derivative action = Pu / 8 minutes
CONTROL LOOPS CATEGORIES
Control loops can be divided into two
Single variable loops and
SINGLE LOOP CONTROL
This is the simplest control loop involving just one controlled
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 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:
Feedback Control loop measures a process variable
and sends the measurement to a controller f
comparison to setpoint. If the process variable is not at
setpoint, control action is taken to return the process
variable to setpoint.
Feedback loops are commonly used in the process control
The advantage of feedback control is that it is a very simple
technique 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
The disadvantage of feedback control is that it can
compensate for a disturbance only after the controlled
variable has deviated from set point. That is, the disturbance
must propagate through the entire p
p p g
process before the
feedback control scheme can initiate action to compensate for
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
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:
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
Multi-Loop Control/ Multi-variable Loops
Multivariable loops are control loops in which
a primary controller controls one process
variable by sending signals to a controller of a
different loop that impacts the process variable
of the primary loop.
The f ll i
Th following are termed as multiple control
loops: » Feedback plus feedforward
» Cascade Control
» Ratio Control
» Limit, Selector, and Override controls
Feedforward Plus Feedback
Because of the difficulty of accounting for every
possible load disturbance in a feedforward system,
feedforward systems are often combined with
Controllers with summing functions are used in
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.
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.
Cascade control is a technique Where two
independent variables need to be controlled with
Its purpose is to provide increased stability to
par-ticularly complex process control problems.
In cascade control the output from one controller
"called the MASTER" is the set point for another
controller "commonly referred to as the SLAVE".
The master will have an independent plant
measurement Only the slave controller has an
output to the final control element.
» Variations of the process variable measurement by
the master controller are corrected by the slave
» Speed of response of the master control loop is
» 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)
» However, cascade control is more costly. Thus, it is
normally used when highly accurate control is
required and where random process disturbances are
Practical Consideration in Implementing Cascade Control
A 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.
The slave controller does not depend on good tuning in the master
controller in order to control the slave loop.
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 welltuned 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
Clearly then, the slave controller’s response is essential to the
process variable, therefore
master controller being able to control its p
the slave controller must be the first one to tune.
Where the ratio of one flow rate to another is controlled for
some desired outcome Many industrial processes also
require the precise mixing of two or more ingredients to
produce a desired product.
Not l do these i
N t only d th
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 will.
A simple example of ratio control is in the production of
paint, where a base liquid must be mixed with one or more
i t h
i d ith
pigments to achieve a desired consistency and color.
All the human operator needs to do now is move the
one link to increase or decrease mixed paint
Mechanical link ratiocontrol systems are
commonly used to
the flow rates of fuel
and air for clean,
A photograph of such
a system appears
here, showing how the
fuel gas valve and air
damper motions are
coordinated by a
single rotary actuator.
A more automated approach to the general problem of ratio
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 for the flow control loop: The ratio of pigment to base
flo cont ol loop
will be 1:1 (equal).
We may incorporate convenient ratio adjustment into this system by
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)
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 =
One way to achieve the proper ratio of hydrocarbon gas to steam flow is
to i t ll
t install a normal flow control loop on one of these two reactant feed
t tf d
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
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
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
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
feedstock composition (i.e. percentage concentration of methane in the
hydrocarbon gas input) changes:
A more common method of ratio control is using separate units
t provide the ratio system. In this figure, the measurement of
I thi fi
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
Limit, Selector, and Override controls
Another 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
need 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:
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
this cascaded setpoint can attain, thereby protecting the refractory brick
of the furnace from being exposed to excessive air temperatures:
This same control strategy could have been implemented using a low
select function block rather than a high limit:
Selector 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
hottest measured temperature at setpoint, since the reaction happens to
be exothermic (heat-releasing):
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
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 failure
The median select function may be implemented one of two ways using
high- and low-select function blocks:
An “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
functioning of the control system continues; when the set
i d ti
Consider this water pumping system, where a water pump is
driven b a variable-speed electric motor t draw water from a
d l t i
t to d
well and provide constant water pressure to a customer:
A potential problem with this system i the pump running
t ti l
“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.
One solution to this problem would be to install a level switch in
th well, sensing water level and shutting off the electric motor
d h tti
l t i
driving the pump if the water level ever gets too low:
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
level 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
limit for continuous pump operation:
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
integrate 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