The document provides an extensive overview of process control, including definitions of key terms, types of control modes (open-loop, closed-loop, feedback, and feedforward), and various control algorithms like PID. It emphasizes the importance of choosing the right control strategy to maintain product quality, optimize energy use, and ensure safety. Additionally, it discusses the characteristics and performance aspects of control elements such as valves and transmitters in controlling mass and energy processes.

2. Definitions

3. Process
It Is defined as:
• Physical or chemical change of matter.
• Energy conversion
e.g., change in pressure, temperature, speed, electrical
potential, etc.
A process in a collection of
vessels, pipes, fittings, gauges etc., is built for the
purpose of producing a product or group of products.

4. Process Control
The regulation or manipulation of variables influencing
the conduct of a process in such a way as to obtain a
product of desired quality and quantity in an efficient
manner.

5. Input to Process: Mass or energy applied to the process.
Output of Process: The product delivered by the
process. This is a dynamic variable.
Supply: Source of mass or energy input to process.
Control Valve: Consists of the final actuator and final
controlling elements. This is the forward controlling
element which directly changes the value of the
manipulated variable.
Load: Anything that affects the value of the controlled
variable under a constant supply input.

6. Open Loop: Control without feedback. Open loop can not
cope with load upsets. Example of open loop: automatic
dishwasher, automatic water sprinkling system, a control
loop with the controller in manual.
Primary Element: The measuring element that
quantitatively converts the measured variable energy
into a form suitable for measurement.
Transmitter: A transducer which responds to a measured
variable by means of a sensing element, and converts it
to a standardized transmission signal which is a function
only of the measured variable.

7. Controlled Variable: A variable the value of which is
sensed to originate a feedback signal. (Also known as the
process variable.)
Controller: A device which operates automatically to
regulate a controlled variable.
Controller Algorithm (PID): A mathematical
representation of the control action to be performed.
Set Point: An input variable which sets the desired value
of the controlled variable.

8. Error: In process instrumentation, the algebraic
difference between the real value and ideal value of the
measured signal. It is the quantity which when
algebraically subtracted from the indicated signal gives
the ideal value.
Manipulated Variable: A quantity or condition which is
varied as a function of the algebraic error signal so as to
cause a change to the value of the directly controlled
variable.

9. Feedback Control: Control action in which a measured
variable is compared to its desired value to produce an
actuating error signal which is acted upon in such a way
as to reduce the magnitude of the error.
Cascade Control: Control in which the output of one
controller is introduced as the set point for another
controller.
Feedforward Control: Control action in which
information concerning one or more conditions that can
disturb the controlled variable is converted, outside of
any feedback loop, into corrective action to minimize
deviations of the controlled variable.

13. Open Loop Control
The operator walked up and down a plant, looking at gauges
and opening and closing valves is effective only at the time
when the operator moves the valve.
At that instant the loop is closed.
Open loop control works only when the load(s) on the
process are constant.
Any load change or supply upset can affect the product
quality.

14. Advantages of Closed Loop Control
Increased productivity: Automatic closed loop control allows the
amount of products made in a particular process to be maximized.
On Spec Products: Industrial products are produced to meet
certain purity levels.
Energy and Material Conservation: A closed loop control
application minimizes the amount of material and energy used in
production.
Safety: Closed loop control is the first line of defense before
Emergency Shutdown Devices (ESD) override regulatory control
devices.

15. Types of Control
• Continuous Control is used on continuous processes. A
continuous process is one in which process material is
continually flowing through the process equipment.
• Sequential is often referred to as on/off control. It is a
series of discrete control actions performed in a specific
order or sequence.
• Batch control is a combination of sequential and continuous
control. A batch process is a process where the operation is
time-dependent and repeatable.

16. Positive Feedback
•It can be defined as the control action in which the error is
reinforced until a limit is eventually reached.
•This obviously is not a desirable outcome of control action
and should be avoided.
•Imagine a tank in which level is being controlled. When the
level exceeds the set point, the control action will increase
the level further until the tank overflows.

17. Negative Feedback
•It can be defined as the control action in which the error is
minimized, made as small as possible, depending on the
algorithm of the controller.
•This obviously is a desirable outcome of the control action
and should be achieved in all feedback loops.

18. Direct Acting Element is one in which the value of the output
signal increases as the value of the input signal increases.

19. Reverse Acting Element is one in which the value of the
output signal decreases as the value of the input increases.

20. Control Valves
A control valve consists of a valve connected to
an actuator mechanism. The actuator, in
response to a signal from the controlling
system, can change the position of a flow-
controlling element in the control valve.
The action of the final actuator is the first choice
and is based on “Fail-Safe Control Valve Action”.
(open, closed, and in place).

23. Transmitters
It can be set up (calibrated) as either direct acting
or reverse acting.

24. Processes
It can be either direct or reverse acting.
Most processes are direct acting.
Energy Flow Process
1.Heat Exchanger
2.Refrigeration
Mass Flow Process
1. Level Tank
2. Pipe Flow

29. Rule for Achieving Negative Feedback
To achieve negative feedback in a control loop you must
have an odd number of reverse acting elements in the
loop.

30. The odd number of reverse-acting elements for
negative feedback can be determined through
an open loop test, conducted in the following
manner.
Place the controller in manual (open loop), and
step up the output of the controller (5-10%) and
observe (record) the output of the transmitter.

32. Control Loop Elements And
Their Contribution To Loop Performance

33. Transmitters

34. Accuracy (Error) = Precision Error + Bias Error

35. Range: The region between the limits within which a quantity is measured
is the range of that measurement.
Span: The measurement span is the algebraic difference between the
upper and lower range values.
Minimum Span : The minimum span of measurement that the primary
element can be used to measure within its accuracy rating.
Maximum Span: The maximum span of measurement that the primary
element can be used to measure within its accuracy rating.
Rangeability (Turndown): In flow applications, rangeability is the ratio of
the maximum flow rate to the minimum flow rate within the stated
accuracy rating.
Zero Elevation and Suppression: The range at which the zero value of the
measured variable is not at the lower range value.

36. Response Time: An output expressed as a function of time, resulting
from the application of a specified input (step) under specific
operating conditions.
Time Constant: This is a specific measure of a response time. It is the
time required for a first order system to reach 63.2% of the total
change when forced by a step.

37. Characteristic Curve (Input-Output Relationship): A
curve that shows the ideal value of an input-output
relationship at steady state.
Reproducibility: There should be a closeness of
agreement among repeated measurements of the
output for the same value of the input made under the
same operating conditions over a period of
time, approaching from both directions.
Noise: In process instrumentation noise is an unwanted
component of a signal or a process variable.

38. Control Valve

39. Flow Coefficient, CV - Is a capacity coefficient which is defined
as the number of U.S gpm of 60°F water which will flow
through a wide-open valve with a constant pressure drop of 1
psi across the valve.

41. Current to Pressure Signal Converters, I/P

42. Analog to Digital, A/D, or Digital to Analog, D/A

43. Volume Booster

44. Valve Positioner
A valve positioner is a proportional-only controller whose main
function is to eliminate or minimize valve hysteresis

45. Valve Sequencing
The practical rangeability of a control valve is limited to
approximately 100/1 with most valves falling below 50/1. These
rangeability values are sufficient for most control applications.
In some applications however, such as pH, the rangeability
required may exceed 1000/1 and the control scheme must be
designed to satisfy this requirement in order to achieve good
control.
In split ranged or sequenced strategies, the controller's output
actuates more than one valve, typically two valves.

46. Process Modeled Through
Dead Time And Capacity

47. DEAD-TIME-ONLY PROCESSES

49. Steady State Gain (K) of Dead Time Process
The steady state gain of the dead-time element is the ratio of the
output amplitude to the input amplitude when both are time
invariant.

50. Capacity Processes Level Tank - Stores Mass

51. Capacity Processes Heater - Stores Energy

52. Non-self-regulating or integrating capacity (NSR)
A capacity is termed non-self-regulating when a change in the
controlled variable has no affect on the process load.

54. Self-Regulating-Capacity or First-Order Lag
In the self-regulating-capacity process, load is not independent of
level. When level changes in this process the load also changes.
Self regulation always tries to restore equilibrium and achieve
steady state.

56. This process operates as though it has a built-in automatic
controller that achieves steady state by making fi = fo. In fact we
would not need to control this process if the tank was very large
( ). Obviously, it is more practical to have a smaller tank and put
a control loop on it.

57. Interacting Capacities
Interacting capacities are identified as types of capacities in
which the downstream capacities affect upstream capacities. C3
affects C2 and C2 affects C1.

58. Non-Interacting Capacities
The non-interacting capacity can be identified as a capacity that
has no effect upstream i.e. C3 does not affect C2 and C2 does not
affect C1.

59. Input/Output Relationship
of Non-Interacting Capacity Processes

60. Input/Output Relationship
of Non-Interacting Capacity Processes

61. Input/Output Relationship
of Interacting Capacity Processes

62. Basic Control Modes And
Choice Of Controller Algorithm

63. INTRODUCTION
The effective control of a process in a feedback loop
depends on the correct choice of the controller mode
or algorithm required for the given application.
The controller algorithm is a mathematical expression
described as the PID consisting of proportional, integral
and derivative components.
Each of these PID components affects the response of
the loop and has certain advantages and limitations.

64. On-Off Algorithm
The simplest and most common type of control
mode, considering home applications.
Although there are multi-position discontinuous
controllers available in industry, generally On-Off control
refers to the two-position version.
A consequence of this is that under On-Off control the
loop never stabilizes.

68. Application of On-Off Control
1) Processes where precise set point control, is not
required e.g. some level tanks; and processes such as
home heating, cooling or refrigeration.
2) Part of an emergency shutdown process (ESD). The
objective here is not regulatory control but safe
operation.
3) Large capacity processes having a low dynamic gain
and a potentially small (acceptable) amplitude of
oscillation.

69. Advantages and Limitations of On-Off Control
Advantages Limitations
Extremely simple Demand not balanced by
supply
Inexpensive controller Loop always cycles
No tuning required for More energy used by the
start up valve
Less expensive valves

70. Proportional Algorithm
Proportional control is the minimum controller
algorithm capable of balancing supply with the demand
of the process and achieving steady state.
A properly adjusted proportional controller can
eliminate the oscillations that are inherently part of
On-Off control.

72. Assume initially that everything is balanced.
The inflow to the tank equals the outflow of the tank
at 50% and the process is in a steady state condition.
Fin = Fout = 50%

73. Also assume that at the 50% load (Fout) for this
particular tank:
Measurement = Set Point = 50%
c = r = 50%
If this condition persists, that is Fin = Fout @ 50%
load, and c=r, the operator does not need to take any
control action since the supply is already balanced by
the load.

74. Assume in this example that suddenly the load (Fout)
changes from 50% to 60%.
The first indication of the load increase will be a change
in the level of the tank.
Acting as a proportional controller, its task is to open
the supply valve in order to stop the level from
changing.
When a balance is achieved between the supply and the
demand such that Fin = Fout = 60%, the level stops
changing.

75. Unfortunately, at this new steady state condition, the
measurement is at a new value below the set point.
The error (r-c) is called offset. It is a steady state error
and is characteristic of all proportional controllers.
The magnitude of the offset depends on the size of the
load change and the capacity (size) of the tank.

78. The output of the proportional controller is proportional to the
input.
m = Ge
When the controller is switched to automatic its output goes to
zero since the error is zero.
m = G (r-c) = 0
As the output goes to zero the valve shuts, decreasing the Fin to
0% and causing the level to decrease. The level will stop
decreasing only when the supply balances the load. This balance
will occur only if Fin becomes 50% again.
If the process dictates that the gain of the controller should be 20
when controlling at 50% load. The controller will operate with a
2.5% error.
50 = 20 (2.5)

79. 1. Proportional controllers always operate with an
error.
2. The higher the controller gain, as dictated by the
process gain, the smaller the error.
(It should be pointed that the controller gain can not be set
arbitrarily. It is dictated by the process gain and for a given loop
gain has a reciprocal relationship to the controller gain).

80. To accommodate zero error situations
m = Ge + Bias
The Bias term has a fixed value and does not have the ability to
change. The Bias is the output of the controller whenever the
error is zero.
m = Bias , if e = 0
Apply this algorithm to the previous example.
Assume that we put the controller in manual and adjust all the
signals to 50%: r = c = Fin = Fout = 50%. When we place the
controller in automatic:
m = Ge + Bias
m = 0 + Bias = Bias
A typical Bias setting being 50%, m = 50%

81. If the load changes an error will occur once again.
m = Ge + Bias
60 = 20(e) + 50
20(e) = 10
e = 0.5%
Some manufacturers write the expression
m = (100/PB) e + Bias
Proportional band is defined as the change in input required to
produce a full range change in output due to proportional control
action.
It may also be seen as the change in measurement required to
change the output 100% or to fully stroke the valve.

82. Different Proportional Bands and Gains

83. Proportional Offset
m = (100/PB)e + Bias
Offset = e = (m - Bias)(PB/100)
There are two conditions which can make the offset equal to
zero or a very small value.
1) Small values of PB or high gains on the controller. Remember
that the process dictates the controller gain or PB. It is not
an arbitrarily assigned value.
2) If (m = bias): in this situation, when the load is equal to the
Bias, there will be no offset. Since the Bias is fixed this implies
that the load is also fixed.

84. Open Loop Response

85. Closed Loop Response

86. Application of Proportional-Only Control
Proportional-only control is not a common control application.
1) Processes where precise control at the set point is not
required. Processes where offset can be tolerated.
2) Processes where the load changes are infrequent (seasonal).
This allows matching load with Bias to eliminate or minimize the
offset.
3) Low gain processes. Typically these are large capacity
processes with low process gains. The low gain of the process
allows a high gain on the controller minimizing the offset.

87. Advantages and Limitations of
Proportional-Only Control
Advantages Limitations
Immediate response Offset
Easy to tune
Good period of response
Simple

88. Integral Algorithm
The error in proportional algorithm could be eliminated if
the two terms in the parenthesis were made to equal each
other.
Offset = e = (m - Bias) PB/100
Since the output of the controller m is directly related to the
load our only choice is to vary the Bias term by making the
Bias = m and thus eliminating the error.
The integral mode fulfills this requirement by providing the
variable Bias capability that automatically achieves this load
balancing task while eliminating errors at steady state.

89. mI=(1/I) edt + mo
mI = Ti edt + mo
where
I = min./rep
Ti = rep./min.
mI : is the output of the integral-only controller.
I : is the gain adjustment for the integral-only controller known
as the integral or reset time.
mo : is the controller output at the time integration starts

90. Open Loop Response

91. Closed Loop Response

92. Application of Integral-Only Control
Whenever the integral mode is required in an application it is
customary to have a small amount of proportional along with it.
The integral mode eliminates the offset at a cost of slower loop
response.
Integral can be justified and should be the major contributor for
the following applications.
1. Slow loops designed to produce slow corrective action.
2. The integral mode is the major contributor in fast flow control
applications usually with a minor contribution from the
proportional controller.

93. Windup
Saturation of the integral mode of a controller
developing during times when control cannot be
achieved, which causes the controlled variable to
overshoot its setpoint when the obstacle to control is
removed.

94. Advantages and Limitations
of Integral-Only Control
Advantages Limitations
Eliminates offset Slows the response
Easy to tune Potential windup or
saturation
Reduces integrated error Unstable with NSR
capacity. (Always oscillates
with NSR)

95. Proportional Plus Integral Algorithm
The need for precise control with zero error at steady
state brought the integral mode in the picture.
The integral mode eliminated the error at steady state
but at an unacceptable cost of a slow loop response.
Combining the two modes in a PI controller is a very
effective compromise suitable for most process
applications.

96. The following observations should be made:
1) Integral mode is a must for precise control.
2) The cost of integration is a slower response.
3) If unable to eliminate the error at steady state the
potential exists for loss of control through what is
known as windup or saturation.

97. The PI is by far the most common algorithm used in
process control applications.
In most plants the PI controller is used in excess of 80%
of the time.
The reason for its popularity is due to the fact that the
algorithm benefits by getting an instantaneous response
due to error from the proportional mode and the
elimination of steady state error from the integral mode.

98. m = (100/PB) [e + (1/I) edt]

99. Open Loop Response of PI Controllers

100. Closed Loop Response of PI Controllers

101. Advantages and Limitations
of PI Control
Advantages Limitations
No offset More difficult to tune
Can minimize integrated Windup or saturation
error potential
Reasonably good period of
response

102. Derivative Algorithm
• In some applications the increased period of response
due to the integral mode is not acceptable
• Especially if we recognize that after an upset it takes
about 3 cycles for a loop to settle down and reach
steady state.
• Furthermore in approximately 10% of the processes
the natural period of the loop is rather long and the
penalty of even longer periods due to the need of
having integral is not desirable.

103. •The natural period of a distillation column is typically
several hours.
•If a given column has a natural period of 4 hours
and, assuming a penalty of a 50% longer period due to
the integral mode.
•It would take approximately 18 hours (4 x 3 x 1.5 = 18)
for this loop to reach steady state.
•The problem gets further aggravated if other upset(s)
occurs before steady state is reached.

105. Open Loop Response (D Setting Fixed)

106. Proportional plus Derivative Algorithm
•Remember that derivative-only controllers do not
exist.
•The derivative mode must be combined with a
proportional or a proportional plus integral controller
and the phase will be limited to some value less than
+90%.

107. The older version with the Derivative on error
m = 100/PB ( e + Dde/dt ) + Bias

108. The newer version with the Derivative on measurement
m = 100/PB ( e - Ddc/dt ) + Bias

109. Application of Proportional
plus Derivative Controllers
The proportional plus derivative controller is not a frequent
choice in process control applications.
Its major limitation is its inability to eliminate offset or
steady state error.
To apply the derivative mode we have to make sure that the
controlled variable is free of noise.

110. Regarding offset it has the same problem as the
proportional-only controller.
The addition of derivative however produces an
improvement in the speed of response.
PD controllers are recommended for large capacity
processes where precise (set point) control is not
required.
The major application of this controller is in batch
processes where because of the nature of the process
(integrating process) it may not be desirable to use the
integral mode.

111. Advantages and Limitations of PD
Controllers
Advantages Limitations
Good response period Offset
Fastest to reach steady Can not handle noise
state
Easier to tune than PID Insufficient benefit on fast
processes

112. PID Algorithm
This three-mode controller has the attributes of all the
modes along with their limitations.
In summary the PID uses the immediate response of the
proportional mode followed by the integral mode's ability to
eliminate the offset.
The slowing down of the response due to integration is
compensated for by the derivative mode.

113. To justify the application of the PID controller the
process should satisfy the following conditions:
1. The controlled variable should be free of noise.
2. The process should have a large capacity for optimum
benefit.
3. The slower response due to the integral mode is not
acceptable for good control.

114. Summary of Closed Loop Responses

115. Advantages and Limitations of PID
Controllers
Advantages Limitations
Good period of response Noisy measurement
Compensates for the slow Difficult to tune
integral
Minimizes integrated Windup concerns
errors
Optimizes control loops

116. Procedure for Determining
Process Characteristics
1. Let the system stabilize.
2. Open the loop by placing the controller in manual.
3. Make sure the system is at steady state, the output
and the controlled variable maintaining their values.
4. Introduce a small disturbance by stepping up the
output of the controller.
5. Record the reaction of the controlled variable.
6. Bring the output back to the normal operating point
and switch to auto.

119. Steady State Gains

120. Steady State Gains of Elements
Steady state gain is simply the slope of the input-
output relationship of the element's response curve
when both the input and output are time invariant (do
not vary with time).

122. Linearization For Constant Loop Gain
Instead of tuning at the highest gain condition to be on
the safe side, a better solution to the non-linearity
problem is to use a complementary linearizing element
in the loop through either the valve or other element.
The objective of good control is to make the loop gain
independent of the operating point as much as
possible.

124. THE STEADY STATE GAIN OF
MEASURING ELEMENTS/TRANSMITTERS

125. Flow Transmitters
The most common industrial flow applications involve one of the
following measuring Devices.
LINEAR DEVICES NON LINEAR DEVICES
Magnetic Flow Meters Orifice
Positive Displacement Meters Venturi
Vortex Meters Flow Nozzle
Turbine Meters Elbow Meters
Ultrasonic Target Meters
Rotameter Weirs
Coriolis Flumes

126. Linearizing Differential Producers

127. Linearizing With A Compensating Response
It is possible to linearize the differential producer (orifice
plate) with a complementary response curve.
To find a curve (b) type function from one of the other
elements in the loop, i.e. the valve.
The advantage of this approach is the elimination of the
need for a square root extractor.
The disadvantage is that the loop will be operating with
(Flow)2 information.

128. Linearizing the Valve Characteristic

130. Non-Linear Controllers
As electronic controllers were introduced, it was possible to
build non-linear PID controllers.
In some applications it is not desirable to have a constant
gain controller.
Non-linear controllers were designed to handle processes
with variable gain.
They were set up to have low gain in the high-gain region of
the process and high gain in the low-gain region of the
process.

131. Linearizing Process Characteristic with a
Non-Linear Controller

132. Level Process

133. Linearizing a Non-Linear Process - Non-
Uniform Tank

134. Heat Exchanger Process

135. Linearizing Processes Whose Gain Varies
Inversely With Load

136. Tuning Feedback Control Loops

137. Acceptable Tuning Criteria Used in the
Process Industry

138. • If safety is the primary concern, speed and efficiency
can be sacrificed and a critically damped response might
be the best choice.
• If the objective is to eliminate the error and achieve
steady state as quickly as possible after an upset, then
some form of underdamped response will be the choice.
Generally most of the better tuning techniques lead to
an underdamped response, with some decay ratio and a
specific speed of response (period.)

139. Tuning Criteria Using
Error Minimization Approaches
The objective of a well-tuned loop is to eliminate the
error as quickly as possible by bringing the
measurement equal to the set point.

140. Quarter Amplitude Decay Criteria
(QAD) is one of the most common under-damped response
criteria.
The controller gain is adjusted so that the amplitude of each
successive cycle is one quarter of the previous amplitude.
Unfortunately, this criteria does not completely define the
response.
Beyond an amplitude decay ratio, it gives no other
information as to what the optimum period of the response
should be.

141. There is no mathematical justification for the QAD response. Its
popularity and acceptance are due to its open loop gain, which
between 0.5 and 0.6 seems to be a reasonable compromise in
damping and period.

142. The main criticism of QAD as a criterion is that it gives no
information about speed of response, or period of a
loop, and as such, it does not indicate an optimum
response.
In two or three mode controllers such as PI or PID there
are an infinite number of settings that will give you a
QAD response, only one of which will have the correct
period for optimum response.

143. Tuning Criteria Using Integral Error
Minimization
These techniques are especially useful if energy is used to make
the product.
Minimization of the area (error) under the curve leads to less
energy consumption and higher efficiency.
There are various error minimization criteria, each having certain
advantages and limitations, and different PID settings.

144. Integrated Error (IE)
IE = e dt
Integral Absolute Error (IAE)
IAE = e dt
Integrated Squared Error (ISE)
ISE = e2 dt
Integrated Time Absolute Error (ITAE)
ITAE = e t dt

145. Robustness
•A loop tuned to particular criteria raises the question of
loop stability when process conditions change.
• A robust control loop, has a safety factor built in to the
controller tuning settings, allowing the loop to maintain
stability even if the process undergoes moderate
changes in gain or dead time.

146. • A robustness plot allows an analysis of how safely a loop is
tuned.
The gain ratio is the ratio of the current process gain to the
original process steady-state gain.
The delay ratio is the ratio of the process dead time to the
dead time existing when the process was tuned.

147. Making PID Adjustments and Observing their
Effect on Loop Response

148. Proportional Band or Gain Adjustment

149. To change the response of the loop, adjust only with:
PB or Gain. Decrease the loop gain to less than one in
order to dampen the response.
The obvious choices of response for this controller
would range from an overdamped response to a
Quarter Amplitude Decay response (QAD).
To get a QAD response the Proportional Band would
have to be doubled (2 x PBu) to drive the loop gain to
0.5.

151. The proportional band or gain adjustment can be
summarized as follows:
• Changing gain or PB affects only the damping of
the response.
• Increasing the PB setting decreases gain while the
period stays roughly the same.

152. Any change of period length over n is of minor
consequence. The amount depending on the process
characteristics.
•For dead-time only processes there would be no period
change at all.
•For dead-time plus capacity processes the period might
increase by 10 - 15% over the natural period n.
It is best to consider the proportional adjustment as a
gain adjustment with no significant effect on the period
of response.

153. PI Adjustment

154. PD Adjustment

155. PID Adjustment
Suppose we find our damping to be acceptable, but
the period of response, o is too long.
We need to maintain our loop gain constant, but to
either increase derivative action or decrease integral
action.
Changing either one alone will not only change o, but
will also change the gain vector which will in turn
affect loop gain.

156. The correct procedure in this case would be to increase
derivative gain GD, by increasing derivative time D,
while at the same time to decrease integral gain GI by
increasing integral time I.
This will tend to increase derivative action while
maintaining the length of the PID vector constant.
As a result, damping will remain unchanged while
response period o is decreased.

157. Interacting And Noninteracting PID
There are at least two ways in which three-mode PID
controllers can be built.
The PID algorithm discussed so far is an ideal noninteracting
controller algorithm.
The noninteracting controller is designed such that its
derivative and integral modes are in a parallel path and act
independently of each other.
The interacting PID controller is designed such that the
integral and derivative modes interact.

160. Effective PID values in terms
of the actual settings

161. Reasons for Tuning Methods
Over the years many tuning methods or approaches
have been developed and used with varying degrees of
success.
There is no general agreement as to what method is the
best to use, the preferred choice usually being the
one, that the individual has the most experience with.

162. • Some of the methods are trial and error solutions to
finding the desired response; others rely on
mathematical relationships.
• The preferred tuning method might be, it is desirable
to have the capability to apply more than one approach.
• In some cases, process or operational constraints
dictate the method to use.
• With experience, you develop a feel of what approach
works best for a given application, and tune accordingly.

163. Keep in mind that any tuning method, will give you only
preliminary settings, which require fine tuning later for
optimum response.
The various tuning methods can be grouped into closed-
loop and open-loop categories.

164. The main distinction between the two is as follows:
•In the closed-loop methods, adjustments are made
and tested with the controller in automatic.
•In the open-loop methods, preliminary settings are
calculated by an open loop test, with the controller in
manual. These preliminary adjustments are
introduced in the controller and tuning is continued
with the controller in automatic.

165. Summary of making PID adjustments and
observing their effect on loop response
The table is designed to assist the user in deciding which direction the adjustments should be made.

166. Procedure for Trial and Error
Constant Cycling Method
P-Only Controller
1. Place controller in manual.
2. Increase proportional band to a safe wide value
3. Place controller in automatic.
4. Make a 5 - 10% set point change around the operating
point.
5. Reduce PB until constant amplitude cycling occurs.
6. Double PB for QAD. Controller is tuned.
7. Make a small upset and observe the response.
Measurement will not be at set-point at steady state.

167. P + I Controller
1. Increase I-time to maximum min/rep or minimum rep/min.
(This eliminates the integral action.)
2. Tune as a P-Only Controller.
3. Increase Integral gain until constant amplitude cycling
occurs.
4. Double the I-time in min/rep for QAD. (Halve the I-time if
in rep/min.)
5. Make upset and observe the response. Measurement
should reach set-point at steady state.

168. PID Controller (Interacting Types)
1. Adjust the integral time min/rep and proportional band to high
values.
2. Adjust derivative time to a very low value.
3. Reduce PB until constant amplitude cycling just occurs.
4. Double PB for QAD.
5. Controller is now tuned as P-Only.
6. Increase derivative time until constant amplitude cycling occurs.
7. Cut derivative time by 1/2 for QAD.
8. Set integral time to a value of 2 to 4 times that of the derivative
time.
9. Make upset and observe the response. Measurement should be
at the set-point at steady state.
10. Readjust PB, I, and D small amounts to get desired response.

169. Procedure for Ziegler-Nichols and Cohen-Coon
Constant Amplitude Cycling Method
1. With the controller in manual, remove the Derivative and
Integral modes. (Remove or turn off Derivative action. Set
Integral to its lowest gain value, by setting to maximum
min/rep or minimum rep/min.) Set the Proportional Band or
gain to a safe value depending on the process.
Examples of safe values of PB or Gain:
· Flow PB 300-500 % or Gain 0.2 to 0.3
· Temperature PB 100 % or Gain 1.0
At this point, you have a low-gain, Proportional-only controller.

170. 2. Switch the controller to automatic, put a small upset by
introducing a 5-10% set-point change around the operating point
and observing the response. You should get a safe sluggish
response.
3. Increase the gain or decrease the Proportional Band and repeat
step (2) until uniform or sustained oscillations occur as shown in
curve (C). If the gain is too low such as curve (A) increase the gain
or lower the PB. Avoid unstable responses such as curve (B). Record
the following information at uniform oscillation. Make sure the
oscillation is due to the loop gain and not due to a limit cycle. (e. g.,
Valve hitting the stops produces what looks like uniform oscillation
but the gain > 1).

173. Procedure for Obtaining a Process Reaction Curve
and Optimum PID Settings from Ziegler-Nichols or
Cohen-Coon Process Reaction Method

174. 1. Let the system stabilize at the normal operating point (set point
and load at normal.)
2. Open the loop by placing the controller in manual. The output
should hold at the same value as in step (1).
3. Make sure the system is at steady state with the output and the
controlled variable maintaining their values.
4. Introduce a small disturbance by stepping up the output of the
controller. The resulting output change should have enough
resolution for analysis.
5. Record the reaction of the controlled variable. This is where a
fast speed recorder at the output of the transmitter (in the order 1
in./min) comes in handy.
6. Bring the output back to the normal operating point and switch
controller back to auto.

175. After obtaining the Process Reaction Curve, proceed to determine
P, PI, or PID settings using either Ziegler-Nichols or Cohen and Coon
equations as shown.

177. Procedure and Summary of Integral Criteria-
Driven Open-Loop Method
Obtain a process reaction curve

179. Cascade Control

180. •If the load (Fw) suddenly increases, the temperature (T2)
decreases.
•The controller senses this and acts on this error through its
algorithm.
•In two to three cycles, the loop stabilizes.

182. Cascade Control may be defined as, "control in which the output
of one controller is the set point for another controller."
The set point to the flow controller defines the amount of flow
required. On an upset in flow, the controller repositions the valve
to bring the flow to the set point, r.

183. These cascade loops are known as the primary and
secondary loops.
The loop closest to the controlled variable is the primary
loop and the loop manipulating the valve is the secondary
loop.
The primary loop is known also as the master loop, outer
loop, or the slower loop.
The secondary loop may be called the slave loop, the inner
loop, or the faster loop.

184. The purpose of cascading is to have the secondary loop
compensate for any supply upsets that may occur
before they can influence the primary controlled
variable.
A supply upset to the primary loop is in effect a load
upset to the secondary loop, and a fast-acting
secondary can immediately correct for it.

188. Results and Considerations
In order for the cascaded control scheme to function
without adversely affecting the gain of the primary loop,
The 1/ 2 ratio must exceed 4.
The higher the ratio, the easier it is to cascade.

189. Advantages of Cascade
1. Cascade control eliminates the effects of supply upsets.
2. Quicker return to set point in the primary loop and less
integrated absolute error (IAE).
3. The secondary loop is more responsive to the demands of
the primary.
4. The primary loop sets the amount of supply input rather
than valve position. Thus, the effects of valve characteristics
(including non-linearities) are minimized, and effectively
removed.

190. Limitations of Cascade
1. More expensive because of additional hardware needs.
2. The primary loop must be substantially slower than the
secondary loop.
3. In some applications it is difficult to break the process into
a primary and secondary loop and identify the supply
variable.
4. Compared to a feedback loop, it is more difficult to start up
and tune a cascade loop.

191. Specific Cascade Applications
Valve Positioner
The primary reason for having a positioner is to remove hysteresis
from the valve.

192. Limit Cycling
Limit cycling can be another consequence of hysteresis, or dead
band. The limit cycle is a clipped sine wave of the manipulated
variable. Controller adjustments (tuning) cannot eliminate these
oscillations. Widening PB will increase the amplitude and the
period of oscillation, while decreasing integral action reduces
amplitude and increases the period.
Recognizing a limit cycle wave (clipped sine wave) can eliminate
some frustrating and unsuccessful tuning effort. The only solutions
to a limit cycle are as follows:
• Use a valve positioner or other cascade application.
• Remove integral action from the controller.

193. Temperature On Flow Cascade Control
Temperature on flow is a good candidate for cascade control. The
supply is well defined and the flow and temperature processes
have significantly different natural periods allowing a good cascade
within the natural period ratio criteria.

194. Temperature-On-Temperature Cascade Control Of An Exothermic
Reactor
The idea here is to keep the temperature inside the reactor (T1) at
the desired value by controlling the temperature of the jacket (T2)
by manipulating cooling water flow to the jacket.

195. Flow as the Inner Loop
The secondary loop is frequently a flow loop as seen in
the various temperature cascades.
The benefits are that the flow loop protects the primary
loop from supply upsets;
overcomes non-linear valve characteristics;
and, reduces the effect of valve friction on the primary
controlled variable.

196. Level on Flow (Valve Positioner) Cascade
A level application requiring precise control and unable
to attain it due to valve hysteresis or frequent supply
upsets.
It is a good candidate for level valve position cascade.
A cascade through either a valve positioner or a flow
loop can be used since the level loop (primary) is most
likely four times slower than the valve position loop, so
that the criteria 1/ 2 > 4 is not violated.

197. Integral Windup Preventing Measures in Cascaded
Loops
If in attempting to eliminate a sustained error, the
controller output goes beyond 0 to 100%, the controller
is wound up.
Windup occurs if the error persists, with the valve fully
open and the controller output at 100%.
The controller becomes saturated, with loss of control.

199. Windup Prevention Measures
Place controller in manual.
The operator can intervene to get any controller
(analog on digital) out of the windup state by putting
it in manual.
This is a simple solution, but not practical in most
applications.
Sooner or later this approach fails.

200. Tuning Cascade Loops
Pre-Startup Check

201. 1. Place the primary controller in manual and the secondary
controller to the local set point.
2. Tune the secondary controller as if it were the only control
loop present.
3. Return the secondary controller to remote set point and
place the primary controller in auto.
4. Now tune the primary loop as if it were the only control
loop present.
Remember, when tuning the primary controller that there
should be no interaction between the primary and secondary
loops.

202. Feedforward Control

203. Feedback Loop Advantages
• Does not require extensive knowledge of the process.
• Easy to implement (start up and tune).
• Requires minimal amount of hardware (least
expensive control strategy.)
• Can be successfully implemented most of the time.
(Feedback is sufficient 80 -90 % of the time.)
• Reasonably good control.

204. Feedback Loop Disadvantages
• Process characteristics dictate the response.
• Response is oscillatory.
• Cannot handle frequent load upsets.
• Trial and error solution to valve position consumes
more energy.

205. If in addition to the load upsets the process was also
subject to frequent supply upsets, cascade control was
the solution.

206. Feedforward or calculation control is the alternative
control strategy when we are unwilling or unable to
accept an oscillatory type of response in a given
application, or if the load upsets are very frequent (<
3 n) the controlled variable does not have a chance to
settle out.

208. Feedforward Advantages
• Can handle processes with frequent load upsets (< 3tn).
• Potentially perfect control without oscillations.
• Response virtually independent of process
characteristics.
• Minimum integrated errors (IE, IAE) can approach zero.
• Avoiding a trial error search of valve position conserves
energy.

209. Feedforward Disadvantages
• Requires more knowledge of the process.
• Requires additional engineering effort and time.
• Requires additional hardware for implementation.
• More expensive than feedback control.
• Economic justification to implement feedforward is made
conditionally.

210. Feedback Trim Loops
The feedforward model attempts to predict the effect of
steady state and dynamic loads on the product being
made.
It is not feasible to include all the loads that affect the
product, in order to have a perfect feedforward model.
It is impossible to come up with a perfect feedforward
requiring the need to have a corrective feedback loop
known as the feedback trim loop.

212. Mass Flow Processes
@ S.S. LEVEL = CONSTANT
as dh/dt = 0
Thus the steady state calculation in this example will simply make the
flow input equal to the flow output.
@ S.S. Fin = Fout
Therefore
Fin = Fout

213. Level Tank Application

214. Applying Feedback Trim Loop
to Tank Level Application

215. Single Element Drum Level
Application

216. •For negative feedback, an odd number of reverse-acting
elements is needed.
•The final actuator, process and transmitter are all direct-acting
elements.
•The controller is put in a reverse-acting mode for negative
feedback.

217. •In open-loop test to check, it is found that as the steam flow
or load increases, the level in the drum initially increases
(instead of decreasing as expected.)
•Typically, the level will go up initially and then come down as
shown, temporarily creating a positive feedback situation and
loss of control.
•This happens because as the load increases due to more
steam flow, the pressure in the drum decreases, causing the
liquid in the drum to temporarily increase or swell.

219. Two-Element Feedforward
Drum Level Application
•During steady state operation the steam flow (load)
information is used to control the feed water flow on a
pound-to-pound basis responding immediately to any
load changes.
•The drum-level feedback trim loop provides the
necessary slow corrections to bring measurement back
to the set point.
•This configuration assumes a linear and repeatable
relationship between the load and the feed water valve.
•If this is true then two-element control is sufficient.

221. Three-Element Feedforward
Drum Level Application

222. Energy Flow
Feedforward Applications
• Energy flow processes vary in their complexity.
• These processes must be sufficiently well defined
before attempting feedforward control.
• For a given process there may be several loads that
affect the product from the steady state point of view.

223. • Some of these load contributions are nonlinear and in
some cases difficult to evaluate and implement in the
model.
• These are the type of processes that consist of multiple
lags and long dead-times which make them difficult to
control with a feedback loop and thus good candidates
for a feedforward strategy.

224. Simple Energy Flow Example
•To implement this in a feedforward loop, measure Qout and put
an equal amount of Qin.
•If succeed, the temperature in the vessel will stay constant.

225. Heat Exchanger Energy Flow Example

226. Recognize that this equation is:
1. Steady state without any dynamic considerations.
2. Only the major loads are represented in the model.
3. Minor loads are not accounted for. These include:
• losses to ambient,
• measuring element and transmitter accuracy,
• change in efficiency due to fouling (scaling) or change in operating point,
• heat lost in condensate.
4. Supply variations relating to the energy of the steam (enthalpy) are not
accounted for. This might dictate cascade for supply upsets, not uncommon in
this type of application.

229. Applying A Feedback Trim Loop To
The Feedforward

230. Trim Loop Characteristics:
• Use a P + I controller tuned for a slow response, no
QAD.
• Typical settings require wide proportional bands (low
gain) and relatively long integral times in min/rep (i.e. 2-
5 min/rep), no derivative action.
• The idea is to take slow corrective action without
affecting the major feedforward scheme.
• Do not introduce non-linear elements that affect the
gain versus operating point relationship of the loop.

231. • Remember, if unable to linearize for constant loop
gain, tune at the highest gain, sluggish response is
acceptable in this case.
• If the feedforward model is reasonably accurate, the
trim controllers output should be 50% during normal
operation.
• If this is not the case, i.e., output of trim either high or
low, there is a good chance that the model does not
accurately represent all major loads.

232. Ratio Control

233. Ratio Control Scheme
• Ratio is a rudimentary form of feedforward where one
variable is controlled in ratio to another.
• It is used in processes where two components are
mixed together in a certain proportion or ratio.
• The controlled variable in effect is the ratio.

235. Simple Ratio Example

236. Ratio Controller Application

237. Adding Feedback Trim

238. Selective Control

240. Median Selectors

241. The typical applications of selector systems can
be categorized as follows:
• Protection against instrument failure
• Control through most critical measurement
• Protection of equipment (safety)

242. Protection Against Instrument Failures
Furnace Pressure Measurement Protection

243. Exothermic Reactors

244. Control Through Most Critical
Measurement

245. Protection of Equipment (Safety)
Parallel Metering Combustion Scheme
In boiler applications the furnace control system must
satisfy various needs:
•Maintenance of safe furnace conditions
•Maintenance of safe furnace pressure in balanced
draft units
•Satisfaction of the energy demand
•Maintenance of correct air/fuel ratios

247. Pumping Station On a Pipeline
The system should provide protection against the following:
• Cavitation. If the suction pressure drops below a
predetermined low value, the valve starts closing to bring
suction pressure up and avoid cavitation.
• Motor Load. As the motor draws a current exceeding the
motor specifications, the valve starts closing to protect the
motor.
• Downstream Pressure. If the discharge pressure attempts to
exceed the maximum recommended downstream pressure, the
valve closes to prevent overpressurizing process piping.

249. Tuning Selective Loops
• Tune each loop and testing the system for
functionality.
• When all loops are tuned, check scheme
performance.
• Control should alternate smoothly, without a
"bump," automatically transferring from one
controller to another through the selective system.

250. Adaptive Control

251. •The word adapt means to change or fit by modification to new
conditions.
•An adaptive control system may be defined as a system whose
parameters automatically change in response to changing process
characteristics.
•The automatic change of the control parameters allows
compensation for the changes in the process characteristics and
the maintenance of a constant loop gain.
•A simple linearization to achieve constant steady state is not
considered adaptation since all the controller functions remain the
same.

252. •A nonlinear controller typically used in a pH application
operates at different gains based on the loop operating point.
•This controller is not considered adaptive since its controller
functions are fixed.

253. •If the titration curve drifts (changes shape) the linearization loses its
effectiveness and there is nothing the controller can do to take care of the
problem.
•Therefore, this is strictly nonlinear control. Remember, to be adaptive, the
controller must change its parameters in order to accommodate the
changing process parameters.
•To accomplish this requires a more capable controller as well as additional
communication between the process and the controller.

254. Approaches to Adaptation
A few approaches have been used to implement
adaptive control strategies:
• Gain scheduling or programmed adaptation - based
on a change in a process variable i.e. the set point.
• Feedforward adaptation - based on a change in load.
• Feedback adaptation - based on a change in the
controlled variable (measurement.)

256. Example of Programmed Adaptation Using
Process Variable Information

259. Multivariable Control

262. Process Equations:
C1 = K11g11m1 + K12g12m2
C2 = K21g21m1 + K22g22m2
Changing m1 affects both C1 and C2.
Changing m2 affects both C2 and C1.

264. Simultaneous Control of Pressure and Flow
•This involves the simultaneous control of pressure and flow with the
fact that both valves affect both the flow and the pressure.
•The first consideration is to decide which valve should be assigned to
control a particular variable.
•The second consideration is whether a control system can be designed
to cancel the interaction between two loops.

265. Control Blocks

266. AI - Analog Input
The Analog Input block takes the input data from the Transducer block, selected by
channel number, and makes it available to other function blocks at its output.
266

267. DI - Discrete Input
The DI block takes the manufacturer’s discrete input data, selected by channel
number, and makes it available to other function blocks at its output.
267

268. PUL – Pulse Input
The Pulse Input Block provides analog values based on a pulse (counter) transducer input.
There are two primary outputs available. An accumulation output is intended to be
connected to an integrator block for differencing, conversion, and integration. This is most
useful when the count rate is low relative to the block execution rate. For high count
rates, the accumulated count of pulses per block execution can be interpreted as an
analog rate (vs. accumulation) value and can be alarmed.
268

269. PID - PID Control
The PID block offers a lot of control algorithms that use the Proportional, integral and
derivative terms.
269

270. EPID – Enhanced PID Control
The EPID block has all parameters of the PID block. Additionally it provides 4 types for
bumpless transference from Manual mode to Auto mode, and also a special treatment
for tracking outputs.
APID – Advanced PID Control
The advanced PID function block provides the following additional features comparing
to the standard PID algorithm and the enhanced PID:
• Selection of the terms (proportional, integral, derivative) calculated on error or
process variable
• PI Sampling algorithm
• Adaptive gain
• Configurable Limits of anti reset wind-up
• Special treatment for the error
• Discrete output to indicate the actual mode
270

271. ARTH - Arithmetic
The ARTH block can be used in calculating measurements from combinations of signals
from sensors. It is not intended to be used in a control path, so it does not support
cascades or back calculation. It does no conversions to percent, so scaling is not
supported. It has no process alarms.
271

272. SPLT-Splitter
The Splitter block provides the capability to drive multiple outputs from a single
input, usually a PID. This block would normally be used in split ranging or sequencing of
multiple valve applications. Included in the block features are the capability to open
valves as part of a predetermined schedule and leave open or closed a given valve after
the controller has transitioned off the valve. The splitter supports two outputs. Since this
block will participate in the control path after a PID block, back calculation support is
included.
272

273. CHAR - Signal Characterizer
•The block calculates OUT_1 from IN_1 and OUT_2 from IN_2, according to a curve
given by the points:
[x1 ;y1 ], [x2 ; y2 ]..............[x21 ; y21]
Where x corresponds to the Input and y to the Output.
•OUT_1 is related to IN_1 and OUT_2 is related to IN_2 using the same curve, but there
is no correlation between IN_1 and IN_2 or between OUT_1 and OUT_2.
273

274. INTG – Integrator
•The Integrator Function Block integrates a variable in function of the time or
accumulates the counting of a Pulse Input block. The integrated value may go
up, starting from zero, or down, starting from the trip value (parameter SP). The block
has two inputs to calculate flow.
•This block is normally used to totalize flow, giving total mass or volume over a certain
time, or totalize power, giving the total energy.
274

275. OSDL - Output Signal Selector and Dynamic Limiter
The output signal selector and dynamic limiter block (OSDL) provides two different
algorithms types.
•As Output Selector the cascade input may be routed for one of two outputs based on
the value of the OP_SELECT input parameter.
•As Dynamic Limiter the cascade input is transferred to both output, but it is limited by
the secondary inputs multiplied by a gain, plus a bias. The Dynamic LIMITER is extremely
useful in one of its most important applications: combustion control with double cross
limits.
275

276. FMTH – Flexible Mathematical Block
This block provides mathematical expression execution with inputs, outputs and
auxiliary variables generated by the user, and also including conditional expressions.
The FMTH block has the following characteristics:
• It allows execute several mathematical expressions “customized” by user with input
and output values, and also using auxiliary variables in these expressions.
• Friendly edition of the mathematical expressions, similar to the Microsoft Excel.
276

277. • It allows the usage of the following operations described in the table below:
277

278. AO - Analog Output
The Analog Output Block is a function block used by devices that work as output
elements in a control loop, like valves, actuators, positioners, etc. The AO block receives
a signal from another function block and passes its results to an output transducer block
through an internal channel reference.
278

279. DO - Discrete Output
The DO block converts the value in SP_D to something useful for the hardware found at
the CHANNEL selection.
279

280. 280

281. 281

282. 282

283. 283

284. 284

285. 285

286. WorkShops