Department of Electromechanical Engineering

Industrial Automation and Process Control

Chapter-3: Multiloop System

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Chapter Outlines:
✓ Ratio Control
✓ Selective and over-ride control
✓ Cascade Control
✓ Feedforward Plus Feedback Control (Hybrid)
✓ Process deadtime compensation

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1. Ratio Control Method
▪ Ratio control systems are installed to maintain the
relationship b/w two variables to control a third
variable.
▪ Ratio control systems are the elementary form of
feedforward control(will be discussed in future).
▪ Ratio control is applied almost exclusively to
flows, known as wild flow.
▪ Wild flow can be uncontrolled, controlled
independently, or controlled by another controller
that responds to variables of pressure, level, etc..
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Ratio Control Conceptual Diagram
▪ Conceptual diagram shows that the flow rate of one
of the streams feeding the mixed flow, designated as
the wild feed, can change freely based on
maintenance options, product demand, energy
availability, the actions of another controller in the
plant.
▪ The other stream shown feeding the mixed flow is
designated as the controlled feed.

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Ratio control conceptual diagram

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Ratio Control Conceptual Diagram
▪ A final control element (FCE) in the controlled feed
stream receives and reacts to the controller output
signal, COc, from the ratio control architecture.

Note: Other flow manipulation devices such as

variable speed pumps or compressors may also be
used in ratio control implementations.

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Relays in the Ratio Architecture
▪ As the conceptual diagram illustrates, we measure
the flow rate of the wild feed and pass the signal to a
relay, designated as RY in the diagram.
▪ The relay is typically one of two types:
▪ Ratio relay: where the mix ratio is entered once
during configuration and is not accessible for
change during normal operation.

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Relays in the Ratio Architecture
▪ Multiplying relay: where the mix ratio is presented as an
adjustable parameter on the operations display and is
thus readily accessible for change.
▪ In either case, the relay multiplies the measured flow rate
of the wild feed stream (PVw), by the entered mix ratio to
arrive at a desired or set point value (SPc),for the
controlled feed stream.
▪ A flow controller then regulates the controlled feed flow
rate to this set point value (SPc), resulting in a mixed flow
stream of specified proportions between the controlled
and wild streams.

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Ratio controller Method I & II design

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Example: Ratio control scheme for ammonia synthesis reactor

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Flow Fraction (Ratio) Controller
▪ Instead of using a relay, an alternative ratio control
architecture based on a flow fraction controller (FFC)
can also be used.
▪ The FFC is essentially a "pure" ratio controller in that
it receives the wild feed and controlled feed signals
directly as inputs.
▪ Ratio set point value is entered into the FCC, along
with tuning parameters and other values required for
any controller implementation.

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Flow Fraction (Ratio) Controller

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▪ Ratio control for wastewater neutralization

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2. Selective & Over-ride Control
Selective control system
▪ These are control systems that involve one
manipulated variable and several controlled outputs.
▪ Since with one manipulated variable we can control
only one output, the selective control systems
transfer control action from one controlled output to
another according to need.

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Override control
▪ During the normal operation of a plant or during its
startup or shutdown it is possible that dangerous
situations may arise which may lead to destruction of
equipment and operating personnel.
▪ In such cases it is necessary to change from the
normal control action and attempt to prevent a
process variable from exceeding an allowable upper
or lower limit.
▪ This can be achieved through the use of special
types of switches:

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▪ HSS (high selector switch):- whenever a variable
should not exceed an upper limit.
▪ LSS (low selector switch):- to prevent a process
variable from exceeding a lower limit.

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Example 1: Override control to protect a boiler system
Discharge
Line Steam

Loop 1
Loop 2
PT
Boiler
LT LC LSS PC

Water
NB: A boiler is a closed vessel in which fluid (generally water)
is heated. The fluid does not necessarily boil. The heated or
vaporized fluid exits the boiler for use in various processes or
heating applications, including water heating, central heating,
boiler-based power generation, cooking, and sanitation.
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▪ Steam pressure in the boiler is controlled through the use
of a pressure control loop on the discharge line (Loop 1).
▪ Water level in the boiler should not fall below a lower
limit necessary to keep the heating coil immersed in
water thus preventing its burning out.
▪ Therefore an override control system using an LSS is
used.
▪ If liquid level falls below the allowable limit, the LSS
switches the control action from pressure control to level
control (Loop 2) whenever discharge pressure reaches
the upper limit.

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Example 2: Override control to protect a compressor
▪ An override control with HSS is used to prevent
discharge pressure from exceeding an upper limit. It
transfers control action from the flow control to the
pressure control loop (Loop 2).

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 HSS FC

Loop 2 Loop 1
SC PC

FT
PT

Gas in

Gas out

Motor
NB: A compressor is a mechanical
device that increases the pressure
Compressor of a gas by reducing its volume.

Figure: Override control to protect a compressor

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3. Multi-Position Controllers
▪ Two popular control strategies for improved
disturbance rejection & performance are cascade
control and feedforward-feedback trim.
▪ Improved performance comes at a price.
▪ Both strategies require that additional instrumentation
(i.e. sensors, …) be purchased, installed and
maintained.

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3. Multi-Position Controllers
▪ Both also require additional engineering time for
strategy design, tuning and implementation.
▪ The cascade architecture offers attractive additional
benefits such as the ability to address multiple
disturbances to our process and to improve set point
response performance.
▪ In contrast, feed forward with feedback trim
architecture is designed to address a single
measured disturbance and does not impact set point
response performance in any fashion.

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3.1 Cascade Control
▪ Cascade control is widely used within the process
industries.
▪ Cascade control is used to improve the response of a
single feedback strategy.
▪ The idea is similar to that of feedforward control: to
take corrective action in response to disturbance
variable (DV) before the CV deviates from setpoint.

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Cascade Control
▪ There are two nested feedback control loops.
▪ There is a secondary control loop located inside a
primary control loop.
▪ The primary loop controller is used to calculate the
setpoint for the inner (secondary) control loop.
▪ The secondary control loop is located so that it
recognises the upset condition sooner than the
primary loop.

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Design of Cascade control system

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Design of Cascade control system
▪ The Inner Secondary Loop
▪ The dashed line in the block diagram, circles a
feedback control loop.
▪ Here "inner secondary" have been added to the
block descriptions.
▪ Variable labels also have a "2" (secondary) after
them.

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Nested Cascade Architecture
▪ To construct a cascade architecture, we nest the
secondary control loop inside a primary loop as
shown in the block diagram.
▪ Note that outer primary PV1 is our process variable
of interest in this implementation.
▪ PV1 is the variable we would be measuring and
controlling if we had chosen a traditional single loop
architecture instead of a cascade.

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Nested Cascade Architecture

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Cascade control: Early Warning System
Measurement and Control of an "early warning"
process variable is essential element for success in a
cascade design.

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Cascade control: Early Warning System
▪ In the cascade architecture, inner secondary PV2
serves as an ‘‘early warning process variable’’.
▪ Essential design characteristics for selecting PV2
include that:
✓It be measurable with a sensor,
✓Same FCE (valve) used to manipulate PV1 also
manipulates PV2,
✓The same disturbances that are of concern for
PV1 also disrupt PV2.

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Cascade control: Early Warning System
▪ PV2 responds before PV1 to disturbances of concern
and to FCE manipulations.
▪ Since PV2 sees the disruption first, it provides our
"early warning" that a disturbance has occurred and
is heading toward PV1.
▪ The inner secondary controller can begin corrective
action immediately.

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Cascade control: Early Warning System
▪ Since PV2 responds first to final control element
(e.g., valve) manipulations, disturbance rejection can
be well underway even before primary variable PV1
has been substantially impacted by the disturbance.
▪ With such a cascade architecture, the control of the
outer primary process variable PV1 benefits from
the corrective actions applied to the upstream early
warning measurement PV2.

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Outer Disturbance must impact Early Warning
Variable PV2
▪ With a cascade structure, there will likely be
disturbances that impact PV1 but do not impact early
warning variable PV2.
▪ The inner secondary controller offers no "early
action" benefit for these outer disturbances.

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Outer Disturbance must impact Early Warning
Variable PV2
▪ They are ultimately addressed by the outer primary
controller as the disturbance moves PV1 from set
point.
▪ So, a proper cascade can improve rejection
performance for any of a host of disturbances
that directly impact PV2 before disrupting
PV1.

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Outer Disturbance must impact Early Warning
Variable PV2

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Example 1: Tank level controller

Single loop control Cascade loop control

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Example 2: Tank temperature controller

Single loop control Cascade loop control

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Level-to-Flow Cascade Block Diagram
▪ A level-to-flow cascade structure includes:
▪ Two controllers: the outer primary level controller
(LC) and inner secondary feed flow controller (FC)
▪ Two measured process variable sensors: the outer
primary liquid level (PV1) and inner secondary feed
flow rate (PV2)
▪ One final control element (FCE): the valve in the
liquid feed stream.

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Level-to-Flow Cascade Block Diagram
▪ As required for a successful design, the inner
secondary flow control loop is nested inside the
primary outer level control loop. That is:
▪ The feed flow rate (PV2) responds before the tank
level (PV1) when header pressure disturbs the
process or when the feed valve moves.

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Level-to-Flow Cascade Block Diagram
▪ The output of the primary controller, CO1, is wired
such that it becomes the set point of the secondary
controller, SP2.
▪ Ultimately, level measurement, PV1, is our process
variable of primary concern.
▪ Protecting PV1 from header pressure disturbances is
the goal of the cascade.

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3.2 Feed Forward & Feedback Control

Simplified block diagrams for

feedforward & feedback control

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3.2 Feed Forward & Feedback Control
Feedforward-feedback architecture:
▪ The feedforward with feedback architecture is
constructed by coupling a feed-forward-only
controller to a traditional feedback controller.
▪ The feedforward controller seeks to reject the
impact of one specific disturbance (D), that is
measured before it reaches our primary process
variable, PV, and starts its disruption to stable
operation.

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Feed Forward & Feedback Control
▪ Typically, this disturbance is one that has been
identified as causing repeated and costly upsets, thus
justifying the expense of both installing a sensor to
measure it, and developing and implementing the
feedforward computation element to counteract it.

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Combined Feedforward & Feedback Controllers
▪ Combinations of feedback and feedforward control
give us.
▪ Benefits of feedback control: controlling unknown
disturbances and not having to know exactly how a
system will respond.
▪ Benefits of feedforward control: responding to
disturbances before they can affect the system.

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Feedforward with Feedback Trim Architecture

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Feed Forward with Feedback Trim Architecture
where:
CO = controller output signal
D = measured disturbance variable
e(t) = controller error, SP – PV
FCE = final control element (e.g.,
valve, variable speed pump or
compressor)
PV = measured process variable
SP = set point

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▪ FeedForward Element Uses a Process and Disturbance
Model

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▪ The process model (CO −› PV) in the feedforward element
describes or predicts how each change in CO will impact PV.
The disturbance model (D −› PV) describes or predicts how
each change in D will impact PV.
▪ In practice, these models (D −› PV) can range from simple
scaling multipliers (static feedforward) through sophisticated
differential equations (dynamic feedforward).
▪ Sophisticated dynamic models can better describe actual
process and disturbance behaviours, often resulting in
improved disturbance rejection performance.
▪ Such models can also be challenging to derive and implement,
increasing the time and expense of a project.

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Dynamic Feed Forward Based on the FOPDT Model

▪ We first develop a general feedforward element

using dynamic models (differential equations).
▪ Later, we will explore how we can simplify this
general construction into a static feed forward
element.
▪ Static feed forward is widely employed in industrial
practice, in part because it can be implemented with
an ordinary multiplying relay that scales the
disturbance signal.

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▪ A dynamic feed forward element accounts for the
“how far” gain, the “how fast” time constant and the
“how much delay” dead time behaviour of both the
process (CO −› PV) and disturbance (D −› PV)
relationships.

▪ The simplest differential equation that describes

such “how far, how fast, and with how much delay”
behaviour for either the process or disturbance
dynamics is the familiar first order plus dead time
(FOPDT) model.
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Example:
The CO −› PV Process Model
▪ Describing the CO −› PV process behaviour with a FOPDT
model is not a new challenge. For example, we presented all
details as we developed the FOPDT dynamic CO −› PV model
for the gravity drained tanks process from step test data as:

▪ Which matches the general FOPDT (first order plus dead time)
dynamic model form:

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▪ Where for a change in CO, the FOPDT model
parameters are:
✓ Kp = process gain (the direction and how far PV will travel)
✓ Tp = process time constant (how fast PV moves after it
begins its response)
✓ Өp = process dead time (how much delay before PV first
begins to respond)

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▪ The D −› PV Disturbance Model

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▪ We presume that an analogous graphical modelling procedure
can be followed to determine the “how far, how fast, and with
how much delay” dynamic D −› PV disturbance model:

▪ Where for a step change in D:

✓ KD = disturbance gain (the direction and how far PV will travel)
✓ TD = disturbance time constant (how fast PV moves after it begins its
response)
✓ ӨD = disturbance dead time (how much delay before PV first begins
to respond)

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▪ To account for model inaccuracies, the feed forward
signal is combined with traditional feedback control
action, COfeedback, to create a total controller output,
COtotal.
▪ Whether it be a P-Only, PI, PID or PID w/ CO Filter
algorithm, the feedback controller plays the important
role of:
✓ Minimizing the impact of disturbance variables other than D that
can disrupt the PV,
✓ Providing set point tracking capability to the overall strategy, and
✓ Correcting for the simplifying approximations used in
constructing the feed forward computation element that ultimately
makes it imperfect in its actions.

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Dynamic Feed Forward in Math
Leaving the exact form of the models undefined for now, we develop
our feed forward element with the following steps:
1) Our generic CO −› PV process model, Gp, allows us to compute a
PV response to changes in CO as:
PV = Gp·CO
With the generic model approach, we can rearrange the above to
compute controller output actions that would reproduce a known or
specified PV as:
CO = (1/Gp)·PV
2) Our generic D −› PV disturbance model, GD, lets us compute a PV
response to changes in D as:
PV = GD·D

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3) Following the logic in the above thought experiment, we use
the D −› PV model of step 2 to predict an impact profile on PV for
any measured disturbance D:
PVimpact = GD·D
4) We then use our rearranged equation of step 1 to back-
calculate a series of corrective feed forward control signals that
will move PV in a pattern that is opposite (and thus negative in
sign) to the predicted PV impact profile from Step 3:
COfeedforward = ─ (1/Gp)·PVimpact
5) We finish by substituting the “PVimpact = GD·D” equation of
step 3 into the COfeedforward equation of step 4:
COfeedforward = ─ (1/Gp)·(GD·D)

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▪ And rearrange to arrive at our final feed forward computational
element composed of a disturbance model divided by a
process model:

𝑮𝑫(𝒔)
COfeedforward = ─ .D(s)
𝑮𝒑(𝒔)
Therefore:;

𝐺𝐷(𝑠)
Feedforward element = ─
𝐺𝑝(𝑠)

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Example:
Feedforward only controller

Process with FF Control

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Analysis (drop the “s” for convenience)
Y = Z1 + Z 2 (1)
Y = Gd D + GPU (2)
Y = Gd D + GP GV G f Gt D (3)

For “perfect control” we want Y = 0 even though D 

0. Then rearranging Eq. (3), with Y = 0 , gives a
design equation.
Gd
Gf = − (15 − 21)
Gt GV GP

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For simplicity, consider the design expression in the Eqn.
then: G
Gf = − d

Gt GV GP
Kd KP
1) Suppose: Gd = − , GP = − , Gt GV = 1
 d s +1  Ps +1
Then,
 Kd    P s + 1 
Gf = −    (lead/lag)
 K P   d s + 1 
2) Let Kd K P e− s
Gd = , GP =
 d s +1  Ps +1
Then, K d ( P s + 1)
Gf = − e + s e + -s Implies prediction
KT KV K P ( d s + 1) of future disturbances

The ideal controller is physically unrealizable.

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 KP
3) Suppose G P =
(1s + 1)(2s + 1) , same Gd

To implement this controller, we would have to take the

second derivative of the load measurements (not possible).

Then, K d (1s + 1)( 2 s + 1) (15-27)

Gf = −
KT KV K P ( d s + 1)
This ideal controller is also unrealizable.

However, approximate FF controllers can result in

significantly improved control.

(e.g., set s=0 in unrealizable part)

See references books for lead-lag process responses.

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Stability Analysis of FF controller

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 Stability Analysis of FF controller

Characteristic equation
1 + G CG V G PG M = 0
The roots of the characteristic equation determine
system stability. But the equation does not contain
Gf.
** Therefore, FF control does NOT affect stability of
FB system.

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Comparison of Feedback & Feedforward Control
Feedback (FB) Control
Advantages
▪ Corrective action occurs regardless of the source and
type of disturbances.
▪ Requires little knowledge about the process (process
model is not necessary).
▪ Versatile and robust (Conditions change? May have to re-
tune controller).

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Comparison of Feedback & Feedforward Control
Feedback (FB) Control
Disadvantages
▪ FB control takes no corrective action until a
deviation in the controlled variable occurs. It is
incapable of correcting a deviation from set point at
the time of its detection.
▪ Theoretically not capable of achieving “perfect
control”.
▪ For frequent and severe disturbances, process may
not settle out.

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Comparison of Feedback & Feedforward Control
Feedforward (FF) Control
Advantages:
▪ Takes corrective action before the process is upset.
▪ Theoretically capable of “perfect control”.
▪ Does not affect system stability.

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Comparison of Feedback & Feedforward Control
Feedforward (FF) Control
Disadvantages:
▪ Disturbance must be measured (capital, operating costs)
▪ Requires more knowledge of the process to be controlled
(process model)
▪ Ideal controllers that result in "perfect control”: may be
physically unrealizable. Use practical controllers such as
lead-lag units.

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Feedforward control of exit composition using a flow control loop

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Feedforward-feedback control of exit composition in the blending system
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Block diagram for feedforward-feedback control of the blending system

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4. Process dead-time compensation
Causes of Dead-Time
▪ Transportation lag (long pipelines).
▪ Sampling downstream of the process.
▪ Slow measuring device.
▪ Large number of first-order time constants in series (e.g.
distillation column).
▪ Sampling delays introduced by computer control.

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Effects of Dead-Time (Time Delay)
▪ Process with large dead time (relative to the time
constant of the process) are difficult to control by pure
feedback alone:
▪ Effect of disturbances is not seen by controller for a while
▪ Effect of control action is not seen at the output for a
while. This causes controller to take additional
compensation unnecessary.
▪ This results in a loop that has inherently built in
limitations to control.

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Thank you!

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