Process Dynamics and Control

Process Control
Enhanced process safety
Satisfying environmental constraints
Meeting ever-stricter product quality specifications
More efficient use of raw materials and energy
Increased profitability
 COMPONENTS OF A CONTROL SYSTEM

Process (stirred-tank heater).

Measuring element (thermometer).
Controller.
Final control element (variable transformer or control
valve).
BLOCK DIAGRAM OF A SIMPLE CONTROL SYSTEM
Closed loop: The measured value of the controlled variable is fed back to
the controller.

Controller: A device that outputs a signal to the process or final control

element based on the magnitude of the error signal. A proportional
controller outputs a signal proportional to the error.

Deviation variable: The difference between the actual value of a variable

and its steady-state value. Block diagrams are always constructed using
deviation variables.

Error: The difference between the value of the set point and that of the
measured variable.

Final control element: A device that provides a modulated input to the

process in response to a signal from the controller. For example, this may
be a heater, a control valve, or a variety of other devices.
Load: The change in any process variable that can cause the controlled
variable to change.

Measuring element: A sensor used to determine the value of the

controlled variable and to send it to the comparator /controller.
Examples include a thermocouple temperature), a strain gage
(pressure), a gas chromatograph (composition), and a pH electrode
These sensors typically have some dynamic behavior associated with
them and can affect the design of the control system.

Negative feedback: The error is the difference between the set point and
the measured variable (this is usually the desired configuration).

Positive feedback: The measured variable is added to the set point. (This
is usually an undesirable situation, and frequently it leads to instability.)
Regulator problem: The goal of a control system for this
type of problem is to enable the system to compensate for
load changes and maintain the controlled variable at the
set point.
Servo problem: The goal of a control system for this type of
problem is to force the system to “track” the requested
set point changes.
Set point: The desired value of the controlled variable.
CONTROL SYSTEM FOR A STIRRED-TANK HEATER
 A liquid stream at a temperature Ti enters an insulated, well-stirred
tank at a constant flow rate w (mass/time).

 It is desired to maintain (or control) the temperature in the tank at TR

by means of the controller. If the measured tank temperature Tm differs
from the desired temperature TR, the controller senses the difference or
error ε

 For that changes the heat input in such a way as to reduce

the magnitude of e.

 If the controller changes the heat input to the tank by an amount that
is proportional to e, we have proportional control.
 It is indicated that the source of heat input q may be electricity or
steam.

 If an electrical source were used, the final control element might be a

variable transformer that is used to adjust current to a resistance
heating element

 If steam were used, the final control element would be a control valve
that adjusts the flow of steam.

 In either case, the output signal from the controller should adjust q in
such a way as to
maintain control of the temperature in the tank.
 Negative Feedback
 The feedback principle, which involves the use of the controlled variable T
to maintain itself at a desired value TR.

 Negative feedback ensures that the difference between TR and Tm is used

to adjust the control element so that the tendency is to reduce the error.

 For example, assume that the system is at steady state and that T= Tm = TR.
If the load Ti should increase, T and Tm would start to increase, which
would cause the error e to become negative.

 With proportional control, the decrease in error would cause the controller
and final control element to decrease the flow of heat to the system, with
the result that the flow of heat would eventually be reduced to a value such
that T approaches TR .
Liquid Level control
 Process: In general, a process consists of an assembly of equipment and
material that is related to some manufacturing operation or sequence.

 Measurement: Measurement refers to the conversion of the process variable

into an analog or digital signal that can be used by the control system. The
device that performs the initial measurement is called a sensor or instrument.
Typical measurements are pressure, level, temperature, flow, position, and
speed.

 Evaluation: In the evaluation step of the process control sequence, the

measurement value is examined, compared with the desired value or set
point, and the amount of corrective action needed to maintain proper control
is determined. A device called a controller performs this evaluation.
 The controller can be a pneumatic, electronic, or mechanical device mounted
in a control panel or on the process equipment. It can also be part of a
computer control system, in which case the control function is performed by
software.
 Control: he control element in a control loop is the device that exerts a
direct influence on the process or manufacturing sequence. This final
control element accepts an input from the controller and transforms it into
some proportional operation that is performed on the process. In most
cases, this final control element will be a control valve that adjusts the flow
of fluid in a process.
 Devices such as electrical motors, pumps, and dampers are also
used as control elements.
 Laplace Transform
 The Laplace transform method provides an efficient way to solve linear,
ordinary, differential equations with constant coefficients.
 Laplace transform of a function f (t) is defined to be F (s) according to
the equation

Find the Laplace transform of the function

Tutorial 1
Also f(t)

Find the f (t) value

 FIRST ORDER TRANSFER FUNCTION
Overall Transfer Function

MERCURY THERMOMETER:
Consider the thermometer to be located in a flowing stream of fluid for which the temperature x
varies with time. The response of thermometer is y for a particular change in surrounding
environment x.

Content of notes is being used for academic purposes only, and is intended
only for students (Btech 3rd year) NIT JALANDHAR.
RESPONSES OF FIRST-ORDER : SYSTEMS TO COMMON INPUTS

As t »∞, Sinusoid Response is

RESPONSES OF FIRST ORDER SYSTEMS IN CASE OF DIFFERENT
INPUTS
The unit-step responses for the two cases are plotted to
show the effect of interaction

From this figure, it can be seen that interaction slows up the response. At any time
t1 following the introduction of the step input, q1 for the interacting case will be
less than for the noninteracting case with the result that h2 (or q2 ) will increase at
a slower rate.
NONINTERACTING SYSTEMS IN SERIES

Transfer lag is
increased as the
number of stages
increases
RESPONSES OF SECOND-ORDER :
Examples of second order system:
 Working of manometer
 Damping Vibrator
 Controlled Systems
 Chemical Process System

 Multiple Capacity Systems in Series

Characteristic Equation
 Y ( t) is plotted against the dimensionless variable t /τ for several
values of τ.

 for τ < 1 all the response curves are oscillatory in nature and become
less oscillatory as τ is increased. The response of a second-order
system for τ < 1 is said to be underdamped.

 What is the physical significance of an underdamped response?

Using the manometer as an example, if we step-change the pressure
difference across an underdamped manometer, the liquid levels in
the two legs will oscillate before stabilizing.

 The oscillations are characteristic of an underdamped response.


Natural period of oscillation:
If the damping is eliminated, the system oscillates continuously
without attenuation in amplitude. Under these “natural” or
undamped conditions, the radian frequency is 1/τ. This frequency
is referred to as the natural frequency.


Settling Time :
Overshoot is a measure of how much the response exceeds the
ultimate value.

Why are we concerned about overshoot? The temperature in our

chemical reactor cannot be allowed to exceed a specified temperature
to protect the catalyst from deactivation.

or

If it’s a level control system, we don’t want the tank to overflow. If we
know these physical limitations, we can determine allowable values
of τ and choose our control system parameters to be sure to stay with
in those limits.
TRANSPORTATION LAG:

The temperature x of the entering fluid varies with time, and

it is desired to find the response of the outlet temperature
y(t) in terms of a transfer function.
If a step change were made in x ( t) at t = 0, the change would
not be detected at the end of the tube until τ second later,
where τ is the time required for the entering fluid to pass
through the tube.
 COMPONENTS OF A CONTROL SYSTEM

Process (stirred-tank heater).

Measuring element (thermometer).
Controller.
Final control element (variable transformer or control
valve).
BLOCK DIAGRAM OF A SIMPLE CONTROL SYSTEM
Closed loop: The measured value of the controlled variable is fed back to
the controller.

Controller: A device that outputs a signal to the process or final control

element based on the magnitude of the error signal. A proportional
controller outputs a signal proportional to the error.

Deviation variable: The difference between the actual value of a variable

and its steady-state value. Block diagrams are always constructed using
deviation variables.

Error: The difference between the value of the set point and that of the
measured variable.

Final control element: A device that provides a modulated input to the

process in response to a signal from the controller. For example, this may
be a heater, a control valve, or a variety of other devices.
Load: The change in any process variable that can cause the controlled
variable to change.

Measuring element: A sensor used to determine the value of the

controlled variable and to send it to the comparator /controller.
Examples include a thermocouple temperature), a strain gage
(pressure), a gas chromatograph (composition), and a pH electrode
(acidity).
These sensors typically have some dynamic behavior associated with
them and can affect the design of the control system.

Negative feedback: The error is the difference between the set point and
the measured variable (this is usually the desired configuration).

Positive feedback: The measured variable is added to the set point. (This
is usually an undesirable situation, and frequently it leads to instability.)
Regulator problem: The goal of a control system for this
type of problem is to enable the system to compensate for
load changes and maintain the controlled variable at the
set point.
Servo problem: The goal of a control system for this type of
problem is to force the system to “track” the requested
set point changes.
Set point: The desired value of the controlled variable.
CONTROL SYSTEM FOR A STIRRED-TANK HEATER
 A liquid stream at a temperature Ti enters an insulated, well-stirred
tank at a constant flow rate w (mass/time).

 It is desired to maintain (or control) the temperature in the tank at TR

by means of the controller. If the measured tank temperature Tm differs
from the desired temperature TR, the controller senses the difference or
error ε

 For that changes the heat input in such a way as to reduce

the magnitude of e.

 If the controller changes the heat input to the tank by an amount that
is proportional to e, we have proportional control.
 It is indicated that the source of heat input q may be electricity or
steam.

 If an electrical source were used, the final control element might be a

variable transformer that is used to adjust current to a resistance
heating element

 If steam were used, the final control element would be a control valve
that adjusts the flow of steam.

 In either case, the output signal from the controller should adjust q in
such a way as to
maintain control of the temperature in the tank.
 Negative Feedback
 The feedback principle, which involves the use of the controlled variable T
to maintain itself at a desired value TR.

 Negative feedback ensures that the difference between TR and Tm is used

to adjust the control element so that the tendency is to reduce the error.

 For example, assume that the system is at steady state and that T= Tm = TR.
If the load Ti should increase, T and Tm would start to increase, which
would cause the error e to become negative.

 With proportional control, the decrease in error would cause the controller
and final control element to decrease the flow of heat to the system, with
the result that the flow of heat would eventually be reduced to a value such
that T approaches TR .
Positive Feedback
 If the signal to the comparator were obtained by adding TR and Tm, we
would have a positive feedback system, which is inherently unstable. If
again assume that the system is at steady state and that T= Tm = TR .

 If Ti were to increase, T and Tm would increase, which would cause the

signal from the comparator to increase, with the result that the heat to
the system would increase.

 However, this action, which is just the opposite of that needed, would
cause T to increase further.

 It should be clear that this situation would cause T to “run away” and
control would not be achieved.
 Control Valve
The control action in any control loop system, is executed by the final control
element. The most common type of final control element used in chemical and
other process control is the control valve.

A control valve is normally driven by a diaphragm type pneumatic actuator that

throttles the flow of the manipulating variable for obtaining the desired control
action.

 A control valve essentially consists of a plug and a stem. The stem can be raised or
lowered by air pressure and the plug changes the effective area of an orifice in the
flow path.

 A typical control valve action can be explained using following Fig. When the air
pressure increases, the downward force of the diaphragm moves the stem
downward against the spring
Control valves are available in different types and shapes. They can be Classified in
different ways; based on: (a) action, (b) number of plugs, and (c) flow characteristics.
1. Action: Control valves operated through pneumatic actuators can
be either (i) air to open, or (ii) air to close.
 In the air-to-close valve, as the air pressure increases, the plug moves
downward and restricts the flow of fluid through the valve.

 In the air-to-open valve, the valve opens and allows greater flow as the valve-
top air pressure increases.

 The choice between air-to-open and air-to-close is usually made based on

safety considerations. If the instrument air pressure fails. we would like the
valve to fail in a safe position for the process.

 For example, if the control valve were on the cooling water inlet to a cooling
jacket for an exothermic chemical reactor, we would want the valve to fail open
so that we do not lose cooling water flow to the reactor. In such a situation, we
would choose an air-to-close valve.
 AIR-TO-OPEN (Fail closed) AND AIR-TO-CLOSE (Fail open)
Valve motors are often constructed so that the valve stem position is
proportional to the valve-top pressure. Most commercial valves move from
fully open to fully closed as the valve-top pressure changes from 3 to 15 psig.
2. NUMBER OF PLUGS: Control valves can also be characterized in terms of the
number of plugs present, as single-seated valve and double-seated valve
3.Flow Characteristics: It describes how the flow rate changes with the
movement or lift of the stem. The shape of the plug primarily decides the
flow characteristics.
 The function of a control valve is to vary the flow of fluid through the valve by
means of a change of pressure to the valve top.
 The relation between the flow through the valve and the valve stem position
(or lift) is called the valve characteristic, which can be conveniently described
by means of a graph as shown in Fig. where three types of characteristics are