APC Training- General

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BASIC AND ADVANCED CONTROLS

• Process Identification
• PID Control and Tuning
• Cascade Control
• Feed Forward Control
• Non-linear Level Control
• Ratio Control
• Override Control
• Dead Time Compensation
• Pass Balancing

• Constraint Control
• Relative Gains
• Background of MPC
• Implementation of MPC
• Fractionator Control
• Fractionator Conceptual Model
• Inferred Properties Model
• Inferred Properties Control
• Benefit Calculations

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Process Identification,
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BASIC DEFINITIONS
F,T
To
AIR
FO
The variables (Flow, Temperature, Pressure,
Composition) associated with chemical process are
divided into 2 groups INPUT VARIABLE Which
denote the effect of surroundings on the
process. OUTPUT VARIABLES Which denote the
effect of process on surroundings The input
variables can be further classified
into MANIPULATED (or adjustable) Variables
which can be adjusted freely. DISTURBANCE
VARIABLES All input variables other than
manipulated variable. Disturbance Variables can
be Measured
Unmeasured
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Process Identification Why is it required? TO
INVESTIGATE, How the behavior of a process
(outputs) changes with time under influence of
changes in external disturbance and Manipulated
Variable. To design an appropriate controller

• Better insight into process behavior leads to
  better control.
• For a given change in input to a process, we
  need to know how much the output will ultimately
  change.
• In which direction will the change take place?.
  How long it will take for output to change?
• What trajectory the output will follow.

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SELF REGULATORY PROCESS
For a step change in input, output attains a new
steady state. Even when no control
(feedback)action exists.
e. g increase feed to column temperature will
attain a new equilibrium level without any
contrast
NON-SELF REGULATORY PROCESS
For a step change in input, the output does not
attain a new Steady State, if no control
(feedback) action exists. e . g increase water
to tank and level will continue to increase
unless control is exercised
Level will keep building
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LINEARITY THE RESPONSE IS PROPORTIONAL TO THE
MAGNITUDE OF INPUT.
OUTPUT
INPUT
TIME
NON LINEARITY
OUTPUT
INPUT
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INVERSE RESPONSE
INVERSE RESPONSE
OUTPUT
INPUT
TIME
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PROCESS DYNAMICS
Process control is concerned with the operation
of process under steady state and unsteady state
(dynamic)conditions.
STEADY STATE
Defined by steady state material and energy
balance equations(as got from steady state
simulator for e.g.) Process variables do not
change with time.
UNSTEADY STATE (DYNAMIC)
Defined by unsteady state equations. Process
variables change with time before attaining a new
steady state. The way a process behaves between
2 steady states is known as its transient
response. Process design affects transient
response
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PROCESS GAIN (Kp) or STEADY STATE GAIN
Change in output Change in input Where,
change is the change from one steady state to
another. PROCESS GAIN is a measure of the
sensitivity of the Process. A Process having a
very small gain would be rather insensitive to
input. This can be compensated by controlling the
Process with a controller having a high gain.
Kp
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TIME CONSTANT (?) TIME CONSTANT is a measure of
the capacitance of the Process. Capacitance slows
down Process dynamics. TIME CONSTANT can be
defined as Hold-up of the
Process Flow through the Process
TIME CONSTANT (?)
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CAPACITANCE SLOWS PROCESS DYNAMICS
CASE 1
T1
VERY LOW CAPACITANCE ( ALSO CALLED INSTANTANEOUS
PROCESS ) HENCE MINIMAL DYNAMICS
CASE 2
T1
IN THIS CASE DYNAMICS ARE SLOWER BECAUSE OF
LARGE CAPACITANCE IN TANK
----------
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DELAY OR DEAD TIME (?) A process transportation
delay can also adversely affect dynamics. A
typical example is plug flow through a pipeline.
Any disturbance at the inlet of the pipeline is
sensed at the outlet only after a delay, which
can be expressed as Length of the
pipeline Velocity of the fluid
DELAY (?)
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OUTPUT
PIPELINE
CONVEYOR
OUTPUT
THE OUTPUT DOES NOT SENSE THE DISTURBANCE WHICH
HAS ENTERED THE SYSTEM FOR SOME
FINITE TIME ( DEAD TIME ) AFTER WHICH IT REACTS
ABRUPTLY.
DELAY DEAD TIME
DELAY

LENGTH
OUTPUT
VELOCITY
DEAD TIME WHENEVER AN INPUT VARIABLE CHANGES,
THERE IS A TIME INTERVAL (SHORT OR LONG) DURING
WHICH NO EFFECT IS OBSERVED ON THE OUPUTS OF THE
SYSTEM. THIS TIME INTERVAL IS CALLED DEAD TIME,
OR TRANSPORTATION LAG, OR PURE LAG, OR DISTANCE
VELOCITY LAG.

• Capacitance enable the process to remain at or
  near Steady State even when distributed.
• Capacitance helps control
• while process delay (dead time) makes control
  difficult.

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Process Identification
A TYPICAL SELF REGULATORY PROCESS CAN BE
APPROXIMATED BY A TRANSFER FUNCITON MODEL OF 3
PARAMETERS TIME CONSTANT ? , DEAD TIME
?, PROCESS GAIN Kp WE CAN USE THESE
PARAMETERS TO MODEL A PROCESS AS FIRST-ORDER,
FIRST ORDER WITH DEAD TIME OR A HIGHER ORDER
PROCESS ( RARE ) TYPICALLY A PROCESS IS
MODELLED AS A FIRST ORDER PROCESS WITH DEAD TIME
OUTPUT CHANGE INPUT CHANGE
Y(s) X(s) Kp . e (- ?S ) 1 t s
TRANSFER FUNCTION


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• In this time domain this equation becomes
• OUTPUT
• INPUT
• Where,
• t elapsed time
• time constant of the process
• Kp steady state gain of the process
• It is evident that when the elapsed time equals 1
  time constant then
• OUTPUT
• INPUT

Kp ( 1 - e-t/? )
Kp ( 1 - e -1 ) 0.632 Kp
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Method BROIDA Model Y(s) Kpe-?s
X(s) ?s 1 ? 5.5 (t2-t1) ?
2.8 t1 1.8 t2
Where Kp Process Gain ? Dead Time ? Time
Constant
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tA
tB
tA tB
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Non-self regulatory Process
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PID Control Tuning
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Introduction to Basic Controls
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Basics Concepts and Terminology for Process
Control
SIGNAL TO CTL ROOM
STEAM
T
HOT WATER
COLD WATER
COND
Controlled Variable e.g Water outlet
Temperature Manipulated Variable e.g Steam
Pressure Load Variable e.g Water Flow
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• The Control Problem Relationship among
  controlled, manipulated and load variable
  qualifies the need for process control.
• The Control system is required to keep the
  controlled variables at its desired value.
• The Control problem can be solved in only two
  ways, each of which corresponds to basic control
  system.
• FEEDBACK SYSTEM
• FEED FORWARD SYSTEM
• Feed Back System
• Solves the control problem through trial and
  error procedure.
• Starts working when there is imbalance between
  the controlled variable and set point.

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WHAT A FEED BACK CAN AND CAN NOT DO

• Very rugged works irrespective of source and type
  of disturbances.
• Is very simple to implement and tune without much
  knowledge about the process. Tuning can be done
  online.
• B u t
• Starts working only after some damage is already
  done.
• An error must exist for the controller to start.
  Thus incapable of perfect control.
• May perform poorly if lags delays are large.

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NEGATIVE FEEDBACK

• For a feedback loop to be successful, it must
  have negative feedback.The controller must change
  its output in the direction that opposes the
  change in measurement variable
• While negative feedback is necessary, combination
  of negative feedback and lags in the process
  means that oscillation is the natural response of
  a feedback control loop to an upset.
• The characteristics of this oscillation are the
  primary means for evaluating the performance of
  the control loop. Engineers are interested in
  period and the dampening ratio of the cycle.
• For good control,the cycle in pv and mv should
  steadily decay and end with the pv returned to sp
  and mv at the new value.
• Oscillation represents the trial and error
  search for the new solution to the control
  problem as the controller is not aware of load
  variables.

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Feedback Control Modes (PID)

• PROPORTIONAL CONTROLS
• The controller response should be proportional to
  the size of the error.
• OP ? ERROR
• Where, ERROR (SP - PV)
• OP Kc (SP - PV) BIAS
  BIAS 50
• ? OP Kc ? E
• DYNAMIC PROPERTIES OF PROPORTIONAL ACTION
• The output change occurs simultaneously with
  error change. No delay occurs in the proportional
  response. Each value of the error for given
  proportional gain generates a unique value of the
  output. This is limitation of proportional only
  controller.
• The proportional only controller always has
  offset which varies with the load.

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MANIPULATED VARIABLE
LT
LC
SP
PV
CONTROLLED VARIABLE
LOAD
75 50 25 0
OUTFLOW
75 50 25 0
LEVEL
75 50 25 0
CONTROLLER OP
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Integral Controls
O Kc . ? E . dt Bias
Ti
SET POINT
Measurement
A B C D
E F
TIME
OUTPUT
TIME
INTEGRAL ACTION RESPONDS TO SIGN SIZE AND
DURATION OF ERROR
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For constant error, up to time Ti O Kc. ? E
. dt Kc . Ti / Ti Kc
Ti
Ti
1 repeat
Ti
Integral Time min / repeat
Where as proportional action has unique output at
one error, the integral action can achieve any
output value and stopping when error is zero.
This property of integral action eliminates the
offset.
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Proportional plus integral Control. O Kc E
Kc ?edt Constant, Where E SP - PV here
bais Kc / Ti Edt
Ti