P1D CONTROL OF A LIQUID DESICCANT AIR DEHUMIDIFICATION UNIT:
PERFORMANCE VS. CONTROL ALGORITHM IMPLEMENTATION
by
Edgar S. Trotter, III
B.S., University of California at Davis, 1992
B.A., Westmont College, 1992
A thesis submitted to the
University of Colorado at Denver
in partial fulfillment
of the requirements for the degree of
Master of Science
Electrical Engineering
This thesis for the Master of Science
degree by
Edgar S. Trotter, III
has been approved
Jan E. Bialasiewicz
Miloje S. Radenkovic
Date
Trotter, Edgar S., Ill (M.S., Electrical Engineering)
PID Control Of A Liquid Desiccant Air Dehumidification Unit: Performance vs. Control Algorithm
Implementation
Thesis directed by Assistant Professor Jan E. Bialasievvicz
This thesis compares the performance of six commonly applied control algorithms as
implemented in the temperature control system of a liquiddesiccant dehumidification unit. The
algorithms studied are OnOff with Deadband, OnOff, Proportional, Proportional + Derivative,
Proportional + Integral, and Proportional + Integral + Derivative. The algorithms are compared for
the temperature control loop using step response tests performed on an actual dehumidifier. The
dehumidifier is a Kathabar Kathapac Dehumidifier. The bandwidth of the various control algorithms
is also compared using frequency response analysis performed on a nonlinear model of the
compensated system using computer software.
This abstract accurately represents the content of the candidates thesis.
ABSTRACT
Signed
Jan E. Bialasiewicz
m
ACKNOWLEDGEMENTS
I would like to thank my wife, Tracy, for her encouragement and love while I researched and
wrote this thesis. I would also like to thank the following people: Dr. Charles Max Fry who
recommended I pursue a Masters degree in the first place and helped me develop the skills needed to
model physical systems; Bob Tucker who shared with me many insights into how things work and
kindled my interest in PID control; Kathabar Systems, Inc. the manufacturer of the dehumidification
equipment analyzed in this thesis; my many professors who taught me many of the pieces that were
necessary to understand the physical world; Bill Karlin at Coors Brewing Company who was project
engineer for the dehumidifier installation; Doug Armstrong and Don Krueger at Behrent Engineering
Company who are a perpetual joy to work with and whose confidence in me as a young engineer led
to the opportunity to install and study this dehumidification system; Dr. Jan Bialasiewicz, my thesis
adviser, who provided me with helpful guidance; and Integrated Systems, Inc. developer of the
MatrixX software used in modeling and simulation of the dehumidifier for providing me with a
complimentary copy of the software for use during this thesis.
Finally, I am amazed at the incredible detail and care that the God who created us has put
into the world. His love and power are evident to me even in the way moisture moves through the
atmosphere. The insights presented in this thesis do not even begin to scratch the surface of how
moisture is controlled.
CONTENTS
Figures.....................................................................................viii
Tables...................................................................................... x
Chapter
1. Introduction............................................................................. 1
1.1 Thesis Overview.......................................................................... 1
1.2 Reason for Choosing this Topic.......................................................... 2
2. Principles of Humidity Control........................................................... 3
3. Description of Liquid Desiccant Dehumidification Equipment............................... 7
3.1 Conditioner............................................................................. 9
3.2 Regenerator............................................................................ 11
3.3 Conditioner Solution Cooler............................................................ 13
3.4 Temperature Control Valve.............................................................. 14
3.5 Temperature Controller................................................................. 15
3.6 Conditioner Pump Tank.................................................................. 17
3.7 Solution Level Controller.............................................................. 17
3.8 Regenerator Solution Heater............................................................ 17
3.9 Supply Air Temperature Sensor.......................................................... 18
4. Installation of Actual System in Plant.................................................. 20
4.1 Installation Layout.................................................................... 21
4.2 Installation Performance Criteria...................................................... 21
5. Temperature Control Loop Model.......................................................... 23
5.1 Loop Components........................................................................ 23
v
5.2 Dehumidifier Temperature Control Equipment............................................ 24
5.2.1 Temperature Control Valve........................................................... 24
5.2.2 Solution Cooler.................................................................... 28
5.2.3 Conditioner........................................................................ 28
5.2.4 System Time Delay.................................................................. 29
5.3 Temperature Sensor................................................................... 29
5.4 System OpenLoop Frequency Response.................................................. 30
6. Temperature Control Algorithms.........................................................32
6.1 OnOff Control with Deadband......................................................... 33
6.2 OnOff Control....................................................................... 34
6.3 Proportional Control................................................................. 34
6.4 Proportional + Derivative Control.................................................... 36
6.5 Proportional + Integral Control.......................................................37
6.6 Proportional + Integral + Derivative Control..........................................40
7. Performance Testing of Control Systems on Dehumidifier.................................42
7.1 ClosedLoop Tuning and Determination of Controller Parameters.........................42
7.2 ClosedLoop Tuning Results............................................................44
7.3 Step Response Tests on Actual System................................................. 45
7.4 Step and Frequency Response Tests on Simulation Model................................ 46
8. Comparison of Control System Performance.............................................. 48
8.1 OnOff Control with Deadband......................................................... 48
8.2 OnOff Control with No Deadband.......................................................50
8.3 Proportional Control................................................................. 52
8.4 Proportional + Derivative Control.................................................... 55
8.5 Proportional + Integral Control...................................................... 58
vi
8.6 Proportional + Integral + Derivative Control............................................ 61
9. Analysis of Control System Performance and Conclusions..................................64
9.1 Algorithm Step Response Rise Time......................................................64
9.2 Algorithm Oscillation Period.......................................................... 65
9.3 Algorithm Maximum Overshoot for Step Response......................................... 66
9.4 Algorithm Average SteadyState Error.................................................. 67
9.5 Algorithm Bandwidth................................................................... 68
9.6 Conclusions.............................................................................69
References...................................................................................71
vii
FIGURES
Figure
2 1 Moisture Transfer Process in the Atmosphere..........................................5
3 1 Dehumidifier System Schematic........................................................8
32 Photograph of Kathabar Conditioner and Pump Tank....................................10
33 Photograph of Kathabar Regenerator..................................................12
34 Plate and Frame Heat Exchanger Flow Schematic.......................................13
35 Photograph of Plate and Frame Heat Exchanger........................................13
36 Photograph of Globe Valve Assembly with Actuator....................................14
37 Temperature Controller Display......................................................16
3 8 Cutaway Photograph of Shell and Tube Heat Exchanger.................................18
4 1 Cold Storage Facility Dehumidification System Arrangement...........................20
4 2 Dehumidifier Design Criteria........................................................22
5 1 Temperature Control Loop Flow Diagram...............................................24
52 Dehumidifier Temperature Control Equipment Component Characteristics................27
53 Component Block Diagram Model in Frequency Domain...................................27
54 Temperature Sensor Block Diagram Model in Frequency Domain..........................30
5 5 OpenLoop Frequency Response of the Uncompensated System............................31
6 1 Proportional Controller Block Diagram Model in Frequency Domain.....................35
62 Proportional + Derivative Controller Block Diagram Model in Frequency Domain........37
63 Proportional + Integral Controller Block Diagram Model in Frequency Domain..........39
viii
6 4 Proportional + Integral + Derivative Controller
Block Diagram Model in Frequency Domain..........................................41
7 1 Temperature Oscillation at Critical Gain during Tuning.............................44
8 1 OnOff Control (with 0.5% Deadband) Step ResponseActual System....................49
82 OnOff (with no Deadband) Step ResponseActual System..............................51
83 Proportional Control Step ResponseActual System...................................53
84 Proportional Control Step ResponseSimulation Model................................53
85 Proportional Control Step OpenLoop Frequency ResponseSimulation Model............54
86 Proportional + Derivative Control Step ResponseActual System......................56
87 Proportional + Derivative Control Step ResponseSimulation Model...................56
88 Proportional + Derivative Control OpenLoop Frequency ResponseSimulation Model....57
89 Proportional + Integral Control Step ResponseActual System........................59
810 Proportional + Integral Control Step ResponseSimulation Model.....................59
811 Proportional + Derivative Control OpenLoop Frequency ResponseSimulation Model....60
812 Proportional + Integral + Derivative Control Step ResponseActual System...........62
813 Proportional + Integral + Derivative Control Step Response Simulation Model.......62
813 Proportional + Integral + Derivative Control OpenLoop
Frequency ResponseSimulation Model..............................................63
IX
TABLES
Table
71 Tuning Guidelines and Resulting Numerical Controller Settings Model...............45
72 Control Algorithms Tested with Step Response......................................46
91 Comparison of Rise Time by Control Algorithm....................................65
92 Comparison of Oscillation Period by Control Algorithm...........................66
93 Comparison of Maximum Overshoot by Control Algorithm............................67
94 Comparison of Average SteadyState Error by Control Algorithm...................68
95 Comparison of Bandwidth by Control Algorithm......................................69
x
1. Introduction
1.1 Thesis Overview
Liquid desiccants offer the ability to regulate humidity in industrial environments by adding
or removing moisture from a process or building space. Historically known as salts, they are the
primary component in many humidity control systems. The performance of these systems depends on
the desiccant qualities as well as the interaction of the various pieces of equipment in the system. A
component that is critical in the performance of the humidity control system is the control algorithm,
or control relationship, that is used to regulate the temperature of air delivered by the system.
This thesis deals with the performance of different control algorithms as implemented in the
temperature control system of a liquiddesiccant dehumidification system. It presents the commonly
applied methods of controlling temperature in humidity control systems and compares their ability to
regulate the dehumidification process. Questions this study is concerned with are How quickly will
the dehumidifier respond to a change in the desired humidity level?, What effect will using a
different control algorithm have on the overall system performance?, and What control algorithm is
required to control humidity to a tight tolerance?
Field tests were conducted on the operation of the actual physical dehumidifier, and the data
collected was used to compare the performance of the various control algorithms at regulating
dehumidifier supply air temperature. Further comparison of the control algorithms performance was
conducted using frequency response analysis of a mathematical model of the system. A mathematical
model of the temperature control loop for the dehumidifier was developed in software and simulated
on a computer. The models parameters were based on the field test data.
1
The overall purpose in performing the field tests and computer simulations is to gain an
understanding of the dehumidifier operation. This information can then be used to predict its
performance and operation under other environmental conditions.
1.2 Reason for Choosing this Topic
I decided to write a thesis as part of the masters program because I w anted to have the
experience of completing personal research and analysis of a physical process. My education and
work have provided very challenging and stimulating problems to solve, but often defined much of
the project for me. I wanted to develop the knowledge and skills that would make me a resource to
others in controlling process dynamics when the project goals might not yet be well defined. The
thesis, because it can be real lest of ones personal analysis skills and perseverance, seemed the most
direct way to grow in this area.
The dehumidifier installation project at Coors Brewing Company was assigned to me in the
summer of 1997 while I was working at Behrent Engineering Company. As I began to study the
dehumidification process in depth as part of the project, it also became apparent that it would be an
excellent one for a thesis. The process presented a variety of heat and mass transfer control problems.
The timing of the project coincided with the need for me to choose a thesis topic.
~>
2. Principles or Humidity Control
Two fundamental principles underlie how a dchumidifier or humidity control system
operates. They are thermodynamics and psychrometrics. Thermodynamics is the process of changes
in temperature, or how things are heated or cooled. Psychrometrics is a less familiar term, and
according to the 1989 Handbook published by the American Society of Heating, Refrigeration, and
AirConditioning Engineers (ASHRAE), is known as the study or measure of the properties of moist
air [3], Websters Dictionary presents the origins of the word as the combination of the Greek words
pschein or psychros meaning to blow, breathe, or cool and the other Greek word metron which is to
measure [2], Psychrometrics draws together the study of how heat is transferred (thermodynamics)
with the qualities and movement of the air we breathe.
A simple explanation of humidity control is the natural phenomenon of weather. In one
process water is evaporated into the air from lakes and oceans and forms into clouds. The clouds
move by air currents. When the clouds encounter air temperatures cool enough to cause rain, the
water is redeposited on the earth. To complete the cycle this water returns to the oceans and lakes by
rivers and streams. Farmers and many other people have developed their livelihoods around the
cycles of humidity control or weather. Certain patterns of weather are depended on for growing
seasons.
The need for humidity control in industrial processes is similar to that required by fanners;
only a certain environment will yield good results in producing or storing a particular product. For
instance, plastic mylar film used to trace electrical connections on printed circuit boards is highly
sensitive to changes in its moisture content. Changes in the moisture content of the air around the
film can add or remove moisture from the film, drastically altering its size. The end results of these
changes are circuit boards that dont work when the electrical conductors are not aligned with
computer chips on the board during the manufacturing process.
In the storage of hops, which are used in the brewing of beer, the moisture content of the
hops must be maintained below a certain level to prevent molds from growing on excess moisture in
the hops. Facilities for hops storage utilize equipment that regulate the temperature and humidity of
the building environment to maintain the required conditions. Along with protection of the hops
comes protection of the building itself. A cold building, just like the outside of a glass of cold water,
is great place for moisture to condense when the weather is right. Moisture condensing on wood can
cause molds to grow, and moisture on steel, even painted steel, can eventually lead to rust. Often, the
humidity control system for a coldstorage facility must have provisions for protecting the building
itself as well as the stored contents.
In general, there are two driving forces in humidity control: water vapor pressure and
temperature. Water has what is known as a vapor pressure, and it is related to its temperature. This is
the pressure that the liquid water exerts on the air around it. It is, by the way, only a small fraction of
the atmospheric pressure. When the air around the liquid water has a similar vapor pressure to the
liquid water, it is considered saturated and it will not accept any more water into the air as vapor.
When the air around the liquid water has a lesser vapor pressure to the liquid water, water is
transferred to the air through the process of evaporation until the air is considered saturated.
A visual description of the moisture transfer process in our atmospheric weather patterns is
shown in Figure 21. Vapor pressure drives the transfer of water from bodies of water into the air,
eventually forming clouds. When saturated air is cooled, the vapor pressure of the air becomes
greater than the vapor pressure of liquid water at that temperature. When this happens, the vapor
condenses into water droplets and rain occurs. Another description of condensation is that the
temperature of the air falls below the dewpoint for that air. The dewpoint is the temperature (for air at
4
a certain temperature and relative humidity) at which moisture vapor turns to droplets and begins
condensation.
A higher air temperature means an increased capacity contains for absorbing moisture. For
instance, saturated air (100% relative humidity) at 68 degrees Fahrenheit can hold twice as much
water vapor as saturated air at 50 degrees Fahrenheit. This is because the greater the air temperature,
the greater the vapor pressure at saturation. In other words, the air needs to absorb more water to
reach saturation at higher temperatures than at lower temperatures.
Just as bodies of air or water with different vapor pressures seek to equalize themselves,
those same bodies seek to equalize their temperatures. Air at a high temperature near buildings will
cause the cooler surfaces of buildings to warm up until they are the same temperature as the air. The
warming of these surfaces also has a concurrent cooling effect on the air, so the temperature of
equality is somewhere in the middle of where the air and the surface temperatures started.
5
In this particular study, it is particularly important to understand how moisture is transferred
in the storage of hops. After the hops are harvested in the fields and baled, some of the bales are
transported to cold storage facilities for longterm storage. As the bales cooled down to the desired
storage temperature at the warehouse the moisture content of the hops falls until the water vapor
pressure in the hops matches the saturation vapor pressure of the cold air in the warehouse. Although
it is not often apparent, the moisture content of many food or grain items at particular temperatures
plays a role in deciding the optimum temperature for their storage.
To apply these concepts to the humidity control for a cold storage facility we need to provide
equipment that will maintain the air temperature and relative humidity by controlling air temperature
and vapor pressure.
6
3. Description of Liquid Desiccant Dehumidification Equipment
The dehumidification system studied in this thesis is considered a liquiddesiccant
dehumidifier. A liquid salt consisting of lithium chloride and water is used to remove moisture from
the air passing through the unit. In applications other than this particular installation, the solution can
also humidify the air when required. The entire dehumidification system consists of many pieces of
equipment. The essential components of the system will be briefly described here to give the reader
an understanding of how the system works.
The dehumidifier described in this thesis is manufactured by Kathabar, Incorporated of
Somerset, New Jersey. The particular model numbers are the 1200FV Conditioner and 1.5FP
Regenerator. The conditioner and regenerator are the core equipment responsible for transferring
moisture to and from the airstream, and are what the rest of the system is built around. Refer to
Figure 31 for a schematic of the dehumidifier system.
7
CONDITIONER REGENERATOR
LEGEND
BT Bubbler Tuba Used in conjunction with
LCP to pneumatically sense solution level
In the pump tank.
FM Flow Motor Measures ond controls the
tronsfer of concentrated solution from
the regenerator to the conditioner.
KV7 Conditioner Pump Out Volvo Receives
a modulating olr signal from LCP1 and
modulates the solution pumped to the
regenerator pump tonk.
LCP Level Control Panel Senses solution
level and provides on/off functions such as
high level, low level and water makeup.
Also provides modulating control to maintain
a constant solution level In the pump tank.
TC3 Conditioner Leaving Air Temperature
Controller Receives a proportional signal
from TT3 and sends a modulating signal
to operate coolont valve V3.
TT3 Conditioner Leaving Air Temperature
Transmitter Senses air temperature leaving
the conditioner and sends a proportional
signal to TC3.
V3 Conditioner Solution Cod* Valve 
Receives a modulating signoi from TC3
and modulates the coolant entering the
solution cooler.
V4 Regenerator Solution Hooter Vdve 
Receives a modulating signal from LCP2
and modulates the heating media entering
the solution heater.
V5 Water MakeUp Valve Receives an on/off
signal from LCP1 and ollows condensate
to enter the conditioner pump tank.
Figure 31 Dehumidifier System Schematic
8
3.1 Conditioner
The conditioner is essentially a section of rectangular ductwork constructed out of fiberglass
with sheets of cardboard inside it and several liquid spray nozzles. Refer to Figure 32 for a
schematic picture of this piece of equipment.
Air from the building flows into the bottom of the conditioner and then flows upward
between the PVC (polyvinylchloride) coated cardboard sheets. A liquid solution of lithium chloride
and water is sprayed over the top of the cardboard and runs down through the sheets, falling out the
bottom into a tank below the duct.
As moist air flows upward in the conditioner it comes in contact with the thin film of
solution running down the cardboard and water vapor is transferred from the air to the liquid solution.
The driving force for the transfer is the difference in vapor pressure between the air and solution. The
height of the conditioner is designed to allow enough length and time for the air to be at equilibrium
vapor pressure and temperature with the entering solution. This assures that the air leaving the
conditioner has the proper moisture content. A common term for the type of equipment that the
conditioner is grouped in is packed tower. The conditioner is responsible for removing excess
moisture from the air being circulated through it and the building. The excess moisture is held in the
salt solution. If the moisture content of the solution were allowed to continue to increase, the solution
would stop dehumidifying the airstream. To keep the moisture content at the proper level, water is
continually removed from the solution by the regenerator.
9
1
Figure 32 Photograph of Kathabar Conditioner and Pump Tank
10
3.2 Regenerator
The regenerator is a much smaller version of the conditioner and is similar to it, except that it
uses plastic packing that look like baseball whiffle balls instead of cardboard sheets. Refer to Figure
33 for a photograph of the regenerator. A small amount of the liquid solution being recirculated
through the conditioner is directed to the regenerator. Prior to being sprayed into the regenerator, the
solution is heated to between 150 F and 200 F. When the sprayed solution encounters the air flowing
through the regenerator, water evaporates into the air and the leaving solution contains less water than
when it entered. The air becomes humidified and is exhausted outside the building.
The overall effect of the dehumidification process is that moisture in the air inside the
building is removed by the conditioner, transferred to the regenerator, and exhausted in the air leaving
the regenerator to outside the building. Other equipment supporting this process are the conditioner
solution cooler, temperature control valve, regenerator solution heater, and liquid level control valve.
*
Photo courtesy of Kathabar, Inc. Used by permission.
Figure 33 Photograph of Kathabar Regenerator
12
3.3 Conditioner Solution Cooler
In addition to dehumidifying the air, the conditioner is also responsible for cooling it to the
desired temperature. To accomplish this, the salt solution is passed through the conditioner solution
cooler. This cooler is a heat exchanger, which uses ammonia as a refrigerant to cool the salt solution.
The heat exchanger is called a plateandframe type heat exchanger. It consists of a number of
parallel plates made of titanium. The ammonia flows between every other plate and the salt solution
Hows in between the remaining plates. Refer to Figure 34 for a flow schematic of the heat exchanger
and Figure 35 for a photograph of the heat exchanger.
(Diagonal flow distribution shown
for illustration purposes only)
Courtesy of ITTHeat Transfer. Used by permission.
Figure 34 Plate and Frame Heat Exchanger Flow Schematic (left)
Figure 35 Photograph of Plate and Frame Heat Exchanger (right)
When the cooled solution enters the conditioner it will remove moisture and cool the air as it
travels past the airstream. The temperature of the solution is controlled by regulating the temperature
of the ammonia in the heat exchanger. Since the cooling of the solution transfers heat to the
ammonia, the ammonia is heated, and in this particular case is boiled. Ammonia enters the heat
exchanger as a liquid and leaves as a vapor. This design allows ihe heat exchanger to be extremely
compact for the amount of heal being transferred. This is because boiling or condensing of any lluid
transfers between 50 and 1000 limes more heat than merely healing or cooling a lluid without a phase
change.
3.4 Temperature Control Valve
The temperature of air leaving the conditioner is adjusted with a microprocessorbased
controller. It modulates a control valve used to regulate the amount of ammonia boiled off in the
conditioner solution cooler. By controlling the ammonia pressure in the heat exchanger, the controller
regulates the amount of heal transferred from the solution and then to the air. The type of valve used
is a globestyle control valve. Refer to Figure 36 for a photograph of the complete valve assembly
with actuator. The globe is raised or lowered in the valve by the controller to modulate the How rate
of ammonia vapor leav ing the solution cooler.
Figure 36 Photograph of Globe Valve Assembly with Actuator
14
3.5 Temperature Controller
The temperature controller is a singleloop type controller capable of receiving one input
signal and delivering one output signal. The controller is a Honeywell Model UDC 3000 and a
picture of the controller display face can be seen in Figure 37. The input signal is supplied from a
leaving air temperature sensor and is converted to temperature units by the controller. The controller
can be programmed to adjust the output signal according to any of several control algorithms already
present in the controller memory. Algorithms available include OnOff, Proportional, Proportional +
Derivative with Manual Reset, Proportional + Integral, and Proportional + Integral + Derivative
control. The controller can also be set up to provide splitranging control, which is used when heating
and cooling equipment are controlled by a single controller. A more complete description of the
control algorithms will be provided in the Section 4 Control Schemes.
15
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Courtesy of Honeywell, Inc. Used by permission
Figure 37 Temperature Controller Display
16
3.6 Conditioner Pump Tank
The solution draining off the bottom of the conditioner cardboard packing is collected in the
conditioner sump and pump tank. Since the two are located close to each other, they are described
here as a single piece of equipment. The large volume of the pump tank gives the system a large
thermal and solution mass. This has the effect of making the solution respond more slowly to
increases in moisture content. The small amount of liquid solution traveling through the conditioner
at any one time and collecting water will not cause wide and rapid fluctuations in the overall solution
concentration.
3.7 Solution Level Controller
The solution level controller is a controller identical to the temperature controller, a
Honeywell UDC3000. This controller receives an input signal of the conditioner pump tank solution
level height. The controller uses this level to control the amount of heat added to the solution in the
regenerator solution heater, which directly affects the amount of moisture, boiled ofif from the
solution.
3.8 Regenerator Solution Heater
The solution heater uses steam to heat the solution from approximately 40 F to 150 F 200 F
before entering the regenerator. This heater consists of two heat exchangers. The primary heat
exchanger is a shellandtube type heat exchanger consisting of several smaller diameter 90/10
copper/nickel alloy tubes through which w ater flows. Surrounding this bundle of tubes is an outer
shell, made of a large diameter steel pipe. The area between the shell and the outer surface of the
tubes is where steam flows. In a manner just the opposite to the conditioner solution cooler, the steam
enters the shell and condenses on the tubes as it gives off its heat to the water flowing through the
tubes. The approximately 300 F steam condenses and drains out of the shell through a steam trap.
The water pumped through the tubes is heated. It then flows to a secondary heat exchanger, which
17
anslers the heal in the water into the solution. This seeondary heat exchanger is a plateandlrame
'pe and is identical, but smaller in size, to the conditioner solution cooler.
The reason for the primary and seeondary heat exchangers is that prior to installation there
as concern that the steam supplied to the heat exchanger would be at 450 F. This temperature is
>ovc the gasket rating for any plalcandframe type heal exchanger. To deal with this problem a
lellandtube type heat exchanger was used to transfer the steam heat to the water, and the water
;ed as an intermediate heat transfer fluid. The option of only using a shellandtube type heat
changer would have been more expensive than using the two separate heal exchangers. The shell
idtube heat exchanger w ould have been required to be manufactured out of titanium to handle the
irrosive properties of the solution and this w ould have been extremely expensive.
9 Supply Air Temperature Sensor
A temperature sensor mounted in the conditioner supply air stream provides measurement of
jair for the temperature controller. The sensor is an RTD (resistance temperature differential) type
18
sensor and has an extremely high accuracy of 0.1 F for temperatures in the 0300 F range. The sensor
is enclosed in a 12inch long, 3/8 diameter stainless steel sheath for insertion into the air stream.
19
4. Installation of Actual System in Plant
The dehumidification system analyzed in this thesis is installed as a part of the environmental
control system in a cold storage facility. This particular building is known as the Hop Storage Facility
at Coors Brewing Company in Golden, Colorado. A general arrangement of the building can be seen
in Figure 41.
Side View of ColdStorage Facility
Dehumidifier
4,h Floor 
j 1 3rd Floor <=p
i 1 2nd Floor
Is1 Floor <
Figure 41 Cold Storage Facility Dehumidification System Arrangement
20
4.1 Cold Storage Facility Dehumidification System Layout
Each of the four floors in the building are divided (not shown in figure 41) into 34
individual storage compartments which are separately controlled for temperature. Connecting these
compartments on each floor are corridors for forklift and personnel traffic. In addition to the
corridors, there is also a dock area on the second floor for loading and unloading of tractortrailer
trucks. It is only the corridors and dock area that are supplied with air the dehumidification system.
4.2 Installation Performance Criteria
Three criteria were established for determining the design requirements of the dehumidifier.
1. Prevent moisture condensation on corridor walls.
2. Provide moisture removal capacity to handle moisture loads from:
a. Infiltration of moist air through exterior doors.
b. Evaporation from hops.
c. Evaporation from personnel.
d. Evaporation from periodic floor cleaning with liquids.
3. Provide heat removal capacity to maintain corridors and dock area at desired temperature.
Cooling loads include:
a. Heat transmission through building walls to the corridors from exterior temperature
and solar radiation.
b. Infiltration of moist air through exterior doors.
c. Forklift electric motor heat, lights, and personnel.
The three criteria were quantified into numerical design requirements, which were then used
to select appropriately sized equipment for dehumidification. The numerical design requirements
were:
1. The coolest wall temperatures in the corridors are found at the walls separating the individual
storage compartments from the corridor. The compartments are maintained at a temperature
of 28 F. Allowing for the effects of wall insulation, the corridor wall temperature is
approximately 30 F. To prevent condensation on the walls, the corridor air must have a
dewpoint temperature lower than 30 F. After a few iterations, a maximum corridor air
temperature was selected. It is 44 F with a maximum of 60% relative humidity. This air has
a dewpoint of 29 F.
2. Total moisture removal load to handle normal infiltration and evaporate in a reasonable
amount of time the water from the periodic floor cleaning is 100 lbs/hr.
21
3. Total heat removal capacity to maintain the corridors at 44 F was determined to be 524,400
Btu/hr or 43.7 tons of cooling.
A flow diagram of the dehumidifier and its components selected to meet these criteria is
found in Figure 42
EXHAUST
PLENUM
Figure 42 Dehumidifier Design Criteria
5. Dehumidifler Temperature Control Loop Model
A general description of the physical components that comprise the temperature control loop
and the remainder of the dehumidifier was presented in Chapter 3. This chapter will focus on the time
response characteristics of the loop components. Using field data obtained during the tuning of the
control loop, a mathematical model of the components in the loop was developed. This model allows
analysis of the frequency response characteristics of the system and comparison of the performance of
the six control algorithms.
The frequency response analysis method is dependent on the Laplace transformation of
system information. What is known about the system in the time domain (i.e. how many seconds it
takes the temperature sensor to respond to a change in temperature.) is transformed into the frequency
domain using the Laplace transformation. With the system model in this form, modeling and
simulation software can be used to analyze the system further and provide frequency response and
phase information. The software used for this analysis is SystemBuild software interface of MatrixX
version 6.03 of Integrated Systems, Sunnyvale, California.
5.1 Loop Components
A flow diagram of the air temperature control process is shown in Figure 51. The actual
temperature of the air leaving the dehumidifler is measured by the air temperature sensor. The
difference between the temperature setpoint and the measured temperature is computed as the
temperature error. Based on the error the temperature controller adjusts the dehumidifler temperature
control equipment to match the actual temperature to the temperature setpoint. The regulation of
temperature also accomplishes the regulation of the supply air humidity. This is due to the
characteristic that the lithium chloride solution at a constant concentration will dehumidify the air to
the same relative humidity level regardless of the temperature. The absolute moisture content of two
different volumes of air at the same relative humidity but at different temperatures is different. The
control of the concentration of the lithium chloride solution is performed by the solution level
controller described in section 3.7. The dynamics of the solution concentration level control loop are
such that, under normal operation conditions, the concentration not will vary enough to affect
temperature or humidity control.
Figure 51 Temperature Control Loop Flow Diagram
Each of the three blocks that comprise the air temperature control loop (Figure 51) will be
discussed in depth. Section 5.2 will cover the Dehumidifier Temperature Control Equipment. Section
5.3 will handle the Temperature Sensor. Chapter 6 will be devoted to the six different control
algorithms that will be used in the Temperature Controller.
5.2 Dehumidifler Temperature Control Equipment
The Dehumidifier Temperature Control Equipment refers to the following pieces of
equipment: temperature control valve, solution cooler, and conditioner. This section will provide a
brief explanation of the process of obtaining a model for each of these components.
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5.2.1 Temperature Control Valve
This valve modulates ammonia vapor flow according to a control signal from the
temperature controller. The signal is converted from electrical current to pneumatic air pressure by a
currenttopressure transducer (IP). The air pressure is then used to modulate the position of the
valve by changing the pressure on the diaphragm in the positioner and moving the valve. The
conversion of the electrical signal into air pressure is relatively fast, occurring within 1/1 Os of a
second.
Changing the position of the valve is not nearly as rapid as the signal conversion from
electrical current to air pressure. Field measurements on this valve indicated that it takes
approximately 8 seconds from the time a position change is initiated at the controller to the time the
valve reaches its intended position. This elapsed time is called a lag. Two characteristics of the
control valve cause this to occur. First, the valve has a cavity above the diaphragm to hold air. When
an increase in signal air pressure is initiated, the pressure in the cavity will rise as the new higher
pressure air rushes in. Since the cavity size is large compared to the flow rate of air entering it, there
is an observable time for the pressure to catch up to the entering air pressure. Second, the flow rate of
air to the valve positioner is restricted by the air piping. The combination of the air flow rate and the
positioner cavity volume combine to create the lag.
The lag for the valve is termed a firstorder lag. It is sometimes also called an RC lag, a term
borrowed from electronics, because it is the result of the resistance and capacitance characteristics of
the component. [5] The restriction on the airflow rale to the valve is the resistance portion and the
positioner cavity air capacity would be the capacitance portion. It can be represented in the frequency
domain using the Laplace transformation as:
75 + 1
(Equation 51)
25
Where:
T= time constant in units of seconds
s = frequency variable for the Laplace transform
In the case of our valve the time constant is 1.7 seconds, which is exactly 1/5 of the total rise
time of 8 seconds for the valve response. An alternate representation of the lag is achieved by
rearranging equation 51 where we have entered 1/7" = 1/1.7 = 0.6.
MT 0.6
s + \/T s + 0.6
(Equation 52)
There is another component to the valve model called limiting or saturation. The valve
opening can only range between 0 and 100% open of the opening in the valve. This means that the
flow rate of ammonia vapor through the valve is limited on the upper end by the orifice opening size.
This limit must be included in the model or else the model simulation will assume that the valve can
be opened beyond 100% if the controller output signal goes high enough.
A short summary of the characteristics of the valve and other components is presented in
Figure 52. The actual mathematical model of the valve presented in block diagram form is shown in
Figure 53 along with the rest of the model for the other dehumidifier control equipment component
models.
26
CHARACTERISTICS CHARACTERISTICS CHARACTERISTICS
Valve positioner Ammonia liquid Rapid temperature
time lag time lag change of air no
Valve position Heat exchanger time noticeable lag
limits lag Air transport time
Solution transport time delay delay
Figure 52 Dehumidifier Temperature Control Equipment Component Characteristics
27
5.2.2 Solution Cooler
The solution cooler is affected by the modulating of the temperature control valve. As the
control valve changes position, the pressure of ammonia vapor in the solution cooler heat exchanger
can be varied. The temperature of the ammonia in the heat exchanger is directly proportional to the
pressure. The solution cooler heat exchanger can also be modeled using firstorder lags. The response
time of the heal exchanger is modeled as two firstorder lags in series. The first lag is the time for the
temperature of the ammonia liquid to change in response to ammonia pressure. The capacitance
portion of the lag is the thermal capacitance of the volume of liquid ammonia in the heat exchanger.
The resistance portion is the flow restriction of ammonia vapor leaving the heat exchanger due to the
control valve.
The second lag is the time for the Lithium chloride solution in the heat exchanger to respond
to a change in temperature of ammonia liquid. The capacitance portion of the lag is the thermal
capacitance of the mass of metal in the heat exchanger used to transfer heat between the ammonia and
the lithium chloride solution. The resistance portion is the thermal conductivity and convection rales
in the heat exchanger. The values for the two lags were not known beforehand. They were obtained
by comparing the step response of the complete model with the step response of the actual system.
The ammonia liquid response time constant is 100 seconds and the heat exchanger response time
constant is 3.3 seconds for this system.
5.2.3 Conditioner
The conditioner is a packed column in which air is cooled and dehumidified as it passes by
the cool lithium chloride solution. The incredibly high efficiency and high heat transfer rates present
in the conditioner make the temperature response lime very small. In this system, the response time is
so small that it does not require modeling. Including it in our model would have no effect on the
accuracy of the model in comparison with the actual system.
28
5.2.4 System Time Delay
The conditioner, as well as other parts of the system, has a time delay due to the transport
time for air to flow a given distance in a duct. Another delay is the time for lithium chloride solution
to flow the distance between two heat exchangers. These delays affect the systems speed of response
to changes in the temperature controller setpoint. Based on the information in the actual system step
response data, there appears to be a total of 12 seconds of pure time delay in our system. All of these
delays can be lumped together, since the model does not care what order they come in.
The time delay can be represented in the frequency domain using the Laplace transformation
as:
e~sT (Equation 53)
Where:
6 = natural log and is the Laplace transform notation for a time delay
T= time delay in units of seconds
s = frequency variable for the Laplace transform
For our case the time delay looks like this:
e~'~s (Equation 54)
5.3 Temperature Sensor
The resistance temperature differential (RTD) type temperature sensor can also be modeled
as a firstorder lag. The capacitance portion is the thermal capacitance of the mass of metal in the
stainless steel tube surrounding the temperaturesensing element. The resistance portion is the air heat
transfer convection coefficient at the tube wall. This coefficient is affected by the air velocity past the
tube and the amount of moisture present in the air. Increasing either the air velocity or the moisture
content of the air will increase the convection coefficient. The value for the lag was not known
beforehand. It was obtained by comparing the step response of the complete model with the step
response of the actual system. The temperature sensor response time constant is 3.3 seconds. The
block diagram model of this lag is shown in Figure 54.
29
Tejnperature Sensor
TT
0.09
= + 0.09
Figure 54 Temperature Sensor Block Diagram Model in Frequency Domain
5.4 System OpenLoop Frequency Response
Openloop frequency response analysis of the dehumidifier temperature control equipment,
or plant, and temperature sensor was performed. The temperature controller was not included in this
analysis. The results of the analysis are presented in Figure 55. Chapter 8 will present frequency
response data for the compensated system with the controller included. The frequency response
provides information on output signal versus input signal for a range of frequencies. Bandwidth is a
standard measurement of the range of frequencies under which a system can accurately be controlled.
It is defined as the frequency at which the gain, or output signal, is 0.707 times the input signal. This
results is a 3 dB (decibel) drop in gain. The bandwidth for our equipment is 0.01 radians/second.
The other measure of system performance is phase margin. Figure 55 also presents the
phase as a function of input frequency. The phase margin represents the systems stability. For any
system, the stability criterion is that the phase of the system stay above 180 degrees.[7] This, of
course, only applies to portions of the bandwidth where the gain is 1 or greater. Phase margin is
measured as the difference between the phase of the system at a particular frequency and 180
30
degrees. For our system, the phase is greater than 180 degrees for all frequencies less than the 0.01
radians/second bandwidth.
Figure 55
OpenLoop Frequency Response of the Uncompensated System
6. Temperature Control Algorithms
In this particular application, the dehumidification unit is responsible for cooling the air and
for moisture removal. The amount of moisture removal required is important, however, there is not a
tight tolerance required on the humidity level provided by the unit. The design tolerances for this
dehumidification unit were temperature of 25 F +/1 F and absolute moisture content of 7.5 grains +/
1.5 grains of water per pound of air (1 grain = 1/7000th of a pound). At 25 F the moisture content of
7.5 grains corresponds to a relative humidity requirement of 50% +/10%.
The controller installed on the temperature control loop for regulating the dehumidifier
supply airs temperature is a singleloop PID controller. The controller is capable of implementing
several different control algorithms. This study will compare the performance of 6 of these control
algorithms. The algorithms are:
1. OnOff Control with Deadband
2. OnOff Control without Deadband
3. Proportional (P) Control
4. Proportional + Derivative (PD) Control
5. Proportional + Integral (PI) Control
6. Proportional + Integral + Derivative (PID) Control
This chapter presents a brief description of each control algorithm. The algorithms will
provide better performance as we work our way down the list. We start with the worst performing
control algorithm so that it will be apparent how increases in performance are achieved by succeeding
algorithms.
Regulation of humidity levels in an airstream or building space is accomplished in a variety
of ways depending on the control accuracy required. Economics drive the choice of controls offered
by dehumidifier manufacturers. For a home with an evaporative or swamp cooler providing cooling
and humidification, the only control furnished is an OnOff switch for the fan and water pump.
Humidity will vary according to the heat load in the home and the amount of moisture being
introduced by the swamp cooler.
For an industrial electronics fabrication facility, the tolerance of the fabrication process for
changes in humidity and temperature might be 50% RH +/ 1% and 70 F +/ 1 F. The control for this
application most likely would be a cascade PID control loop. The loop would adjust the
humidification of the airstream based on the entering air humidity and temperature as well as the
room air humidity and temperature.
6.1 OnOff Control with Deadband
OnOff control regulates the process variable, in this case supply air temperature, by
turning the cooling system on and off. There is no modulation of the cooling system; the system
operates at full capacity until the setpoint condition is achieved and then shuts off. Usually a dead
band range is specified for the control system, which prevents the system from cycling from on to off
to on again to maintain a narrow setpoint range.
For a dehumidifier of this type the desired setpoint might be 25 F with an upper deadband
range of 27 F and lower deadband range of 23 F. These settings would turn the dehumidifier cooling
system on at 27 F and continue cooling until the units supply air temperature reached 23 F. The unit
would then shut off cooling and the supply air temperature would warm up over time due to the
process or building heat generation. When the air temperature reached 27 F, the units cooling system
would again turn on.
The disadvantage of this controller is the constant cycling of the system. The controller is
periodically banging the control valve open and later banging is shut. This is why this type of
controller is sometimes called a bangbang regulator.
This type of control is not a popular choice w hen a tight control of temperature is required.
This is because the temperature will vary according to the deadband settings. Attempts to reduce the
deadband range result in rapid cycling of the cooling system in order to maintain temperature. Motors
and valve actuators are often not capable of handling repeated starts in a short period of time. The
motors windings will tend to heal up and eventually open the motor thermal overload protection
relays which prevents electrical power from entering the motor.
OnOff control is popular where a significant dead band can be tolerated. Although most
people would appreciate having a constant temperature inside their home or office, the vast majority
live in homes or work in offices where the variation in temperature of 35 degrees F is something they
are used to. The Honeywell controller manual uses the term hysteresis to refer to the deadband
setting.
6.2 OnOff Control without Deadband
The same controller described in section 6.1 can achieve tighter control by simply reducing
the deadband to zero.
6.3 Proportional Control
The first control algorithm of a modulating type is the proportional controller. This
controller adjusts the dehumidifier cooling system output by modulating the position of the
temperature control valve. Instead of only opening and closing the valve like the OnOff control
algorithm, the proportional controller adjusts the valve position to increase or decrease cooling
according to a gain constant K. The controller gain K is the relationship between the error signal and
the valve position.
34
An offset, or steadystate error, will always be present when using a proportional controller.
This will mean that the actual temperature will be, say 35.5 degrees F when the controller setpoint is
35.0 degrees F. A simple relationship exists for calculating the steadystate error for a controller gain
K when the feedback signal has a gain of 1 (unity gain):
1
e  (Equation 61)
\ + K
where ess = steadystate error
The accuracy of the proportional control algorithm to maintain a setpoint is directly related to
the controller gain K. The higher the value for K, the less the controlled variable will deviate from its
setpoint. The longterm deviation is referred to as the steadystate error or offset. The steadystate
error ess could theoretically be reduced to almost nothing by increasing the gain K. Flowever,
increasing the gain also reduces the system stability. Above a certain gain value the system will
oscillate unstably and not be able to be controlled.
Pzoport iona.1 Control lez
Figure 61 Proportional Controller Block Diagram Model in Frequency Domain
35
6.4 Proportional + Derivative Control
The addition of derivative control increases the speed of response of the system to changes in
setpoint. The derivative algorithm acts only on the rate of change of the error and not the error
magnitude itself. This means that the derivative algorithm only contributes to controller performance
when there is a change in the error magnitude. It does not work to reduce steadystate error.
The derivative algorithm functions by effectively increasing controller gain when the error
change rate is high. For example, if the actual air temperature of this system were to rapidly drift
away from setpoint, the derivative algorithm would increase the controller gain above the level
dictated by only the proportional algorithm. This would be done in order to drive the temperature
back to setpoint. As the rate of change of the error decreased, so would the derivative algorithm
contribution.
Although derivative control does not have a direct effect on reducing steadystate errors, it
can help reduce them. Derivative control does make the system more stable, which results in a higher
proportional gain value to be used. As noted in section 6.3 on proportional control, increasing the
gain reduces the magnitude of steadystate error.
A block diagram model of the proportional + derivative controller is shown in Figure 62. It
can be seen that the proportional control gain has been increased from 2.6 to 3.5. The tuning
guidelines recommend the higher gain as a result of the stabilizing influence of the addition of
derivative control. The derivative control algorithm, or lead compensator, as it is often called, is
shown as a part of the control valve block. The lead compensator Laplace transform is:
5 + 0.069 (Equation 62)
The lead compensator cannot be implemented in the model without a denominator, or lag, of
at least similar order. This is due to the constraints of the modeling mathematics and software. Due
to this requirement, it has been grouped into the valve response block, which is a lag, as follows:
36
5 + 0.069 t 0,6 _g?(s + 0.069)
0.069 5 + 0.6 ~~ ' (5 + O.6)
(Equation 63)
The addition of the constant 0.069 in the denominator for the lead compensator is to keep the
block as a unity gain (gain of 1) transfer function.
Figure 62 Proportional + Derivative Controller Block Diagram Model in Frequency
Domain
6.5 Proportional + Integral Control
The control algorithms presented up to this point in this study have still not eliminated the
presence of a steadystate error. Adding integral control to the simple proportional control algorithm
allows the controller to reduce or eliminate steadystate errors. In terms of controller performance, it
tends to destabilize the system due to its introduction of 90 degrees of phase lag. This reduces the
phase margin and destabilizes the system. Therefore, tuning guidelines recommend a smaller gain be
used with the proportional controller to reduce the instability. In this case, the gain has been reduced
from 2.6 to 2.3, as shown in Figure 63.
37
Integration of the error is the function of the integral controller. Authors of controls books
have tried several methods of explaining this action. One of the clearer descriptions is by David St.
Clair. He describes the integral action on errors as resetting the gain to an increased magnitude
according to the magnitude of the integral of the error. [5] This idea goes along with the term reset
commonly used to refer to the integral controller.
A reasonable value for the integral algorithm setting in the controller might be 0.65 resets per
minute. This value corresponds to 0.65 resets/minute x 1 minute/60 seconds = 0.011 resets/second or
92 seconds per reset. When a step setpoint change occurs, assume that the magnitude of the controller
initial response is some amount M. After this initial response, the integral algorithm controller will
respond to the error signal by increasing the controller output by the same amount M over a period of
92 seconds. Another way of describing this is to say that the controller output will be reset every 92
seconds until there is no error.
The longer the time setting for the integral algorithm, the longer it will take for the controller
to respond to setpoint changes. The integral parameter does have limits to how fast it can react since
the use of integral action tends to destabilize the system. The integral algorithm is essentially written
as:
925 + 1
This can be rearranged to the more easily implemented form:
5 + 0.011
5
(Equation 64)
(Equation 65)
38
Figure 63 Proportional + Integral Controller Block Diagram Model in Frequency
Domain
Integral controllers can experience a problem known as integral windup or reset windup.
This can occur when the system is operating and the controller error signal cannot be reduced to zero
due to a limit in the control actuator. In this situation, the control algorithm continues to integrate the
error and the integral portion of the controller gain grows abnormally large. The problem occurs
when the setpoint is changed and the system then has to adjust itself to the new setting. The controller
will not respond in a normal manner until the error reduces to a small value for a period. Besides poor
initial performance, this can sometimes lead to system instability, which may result in damage to the
process.
Another time that this problem can occur is in starting up a process after it has been shut
down for a period of time. Often equipment is shut down but controllers are left operational. During
this time, the controller continues to try and control, but without success. The controller attempts to
reduce the large error sensed, and consequently, winds up the integral portion of the algorithm.
Controller manufacturers have developed methods of implementing integral control so that
windup does not occur. In digital controllers, it is common to see a feedback loop around the
39
integrating algorithm. This loop effectively reduces the error signal to the integrator to zero when
saturation occurs for the control actuator. The error signal to the proportional algorithm is unchanged,
but by zeroing the error to the integral algorithm during saturation, windup is prevented. [11]
6.6 Proportional + Integral + Derivative Control
The last algorithm to be studied combines all the characteristics of the controllers studied
thus far into one controller. The PID controller, as it is commonly referred to, exhibits the ability to
eliminate steadystate erTor, reasonably quick response, and a reduced overshoot. The combination of
the integral and derivative algorithms in the same controller yields a proportional gain setting higher
than could be used with stability on integral control, but lower than could be obtained with just
derivative control.
The effect on the phase margin is that the integral algorithm will reduce the phase margin in
the low frequency spectrum while the derivative algorithm will increase the phase margin in the high
frequency region. The phase margin for this controller ends up being 45 degrees, the same as for the
proportional + integral controller.
The block diagram model for the controller is shown in Figure 64. It is essentially the series
combination of the proportional + integral and proportional + derivative control algorithms previously
discussed. The derivative algorithm is still implemented in the valve response block.
40
Figure 64 Proportional + Integral + Derivative Controller Block Diagram Model in
Frequency Domain
41
7. Performance Testing of Control Systems on Dehumidifier
A series of step response tests were conducted to compare the regulating performance of the
six different control algorithms on the actual dehumidifier supply air temperature. This chapter
describes how the tests were carried out, the method used for tuning controller parameters, and the
frequency response analysis performed on the simulation model.
The step response test is one of the most commonly used measures of control system
performance. It yields graphs that illustrate a controllers ability to respond to changes in setpoint.
The step response test was performed on the system separately for each different control algorithm.
Additionally, the step response was generated for the simulation model of the dehumidifier
temperature control loop for each control algorithm.
Frequency response analysis was performed on the computer simulation model. This
analysis provides information on the compensated openloop system gain and its phase versus input
signal frequency. It is straightforward to correlate the frequency response of each control algorithm
with step response data. Frequency response data was not collected from the actual system due to the
expensive and complex equipment necessary to obtain the information.
7.1 ClosedLoop Tuning and Determination of
Controller Parameters
Prior to conducting step response tests, it was necessary to determine the parameters to be
used by the control algorithms. The process of finding these parameters is called tuning. Although
the type of controller used in this study w as originally developed with tuning guidelines for
determining the parameters, few personnel installing such controllers are aware of proper tuning
procedures. The resulting poor tuning often leads to processes that perform poorly and waste energy.
42
Most tuning guidelines published by manufacturers of controllers are a variation on the
classic paper written by Ziegler and Nichols in 1942 entitled Optimum Settings for Automatic
Controllers [1], This method of tuning yields satisfactory performance for most of the common
industrial process control applications. However, there are several unique types of processes that are
either not suited to this tuning scheme or even the type of controller used in this study. In this case,
the method is well suited to deliver reasonably fast and stable control. The product manual for this
controller, the Honeywell UDC 3000, recommends verbatim the ZieglerNichols tuning method.[4]
For this controller there are only 3 parameters that will be set in the tuning procedure.
The controller parameters were determined using a modified ZieglerNichols closedloop
tuning method. This method uses the critical controller gain and system natural period to determine
controller settings for the proportional band (gain), integral, and derivative parameters. The critical
gain and system natural period are obtained by first setting the controller integral and derivative
parameters to 0 or their OFF positions. Then, while the system is in operation, the controller gain is
increased (or in the case of proportional band is decreased) until steady oscillation of the controller
setpoint occurs. The minimum gain at which this occurs is considered the critical gain of the
system controller. The Honeywell UDC 3000 controller is designed to handle the change of setpoint
on its facemounted keypad.
According to the modified ZieglerNichols closedloop tuning method the proportional band
parameter of the controller is set to equal a constant times the critical gain for any controller. Settings
for the integral and derivative parameters are determined solely from the natural period. The integral
term has units of resets per minute. It is chosen as equal to a constant divided by the natural period.
The derivative term has units of minutes. It is chosen as equal to the natural period divided by a
constant. The exact constants used for choosing the parameters are shown in table 71.
Tuning accomplishes the same goal as selecting poles and zeros for a controller using a more
mathematically based approach. The advantage of the ZieglerNichols tuning approach is that it
43
requires only elementary school level math to calculate controller settings and is thus readily useable
by field personnel.
7.2 ClosedLoop Tuning Results
The tuning process was performed by programming the controller according to the tuning
instructions. After this was set, the controllers proportional band (or gain) parameter was decreased
(increased gain) until the supply air temperature readings began to oscillate. Experimentation with
various proportional band settings and observation of the result on temperature fluctuations led to the
selection of the critical gain. This is the gain at which the system oscillates without any damping.
A plot of the system temperature oscillation at the critical gain is shown in figure 71. The
natural period of the oscillations is marked on the plot as well as the critical gain value. The line has
been smoothed to make the sinusoidal nature of the oscillation easier to see.
Loop Tuning Temperature Oscillation at Critical Gain
Figure 71 Temperature Oscillation at Critical Gain during Tuning
44
Based on the critical gain and natural period determined during closedloop tuning of the
system, the controller parameter settings were chosen according to the Ziegler & Nichols tuning
method. The tuning guidelines and numerical values chosen are listed in Table 71.
Table 71_______Tuning Guidelines and Resulting Numerical Controller Settings
Parameter ZieglerNichols Tuning Guidelines by Control Algorithm f 11 Numerical Controller Setting Based on Tuning
Algorithm P PD PI PID P PD PI PID
Proportional Band (PB) 2 x PB 1.65 x PB 2.2 x PB 2.2 x PB 0.8 0.6 0.9 0.6
Integral (I) resets/minute OFF OFF 1,2/Pn 2/Pn OFF OFF 0.65 1.08
Derivative (D) Minutes OFF Pn/8 OFF Pn/8 OFF 0.24 OFF 0.24
The natural period of the system was converted from seconds to minutes for the calculations.
The control algorithm identifiers are as follows: (P) Proportional, (PD) Proportional+Derivative, (PI)
Proportional+lntegral, and (PID) Proportional+Integral+Derivative.
7.3 Step Response Tests on Actual System
After controller parameter setpoints were determined using the previously mentioned
modified ZieglerNichols approach, the dehumidifier was considered ready for step response testing.
The step change input to the system was made at the Dehumidifier Supply Air Temperature Controller
TC1. A step of 3 degrees Fahrenheit was input to the controller manually by entering a new setpoint
value on the display keypad. A timehistory graphing of the step change can be seen in chapter 8 for
each control algorithm along with the resulting step response. Entering the change took
approximately 1.5 seconds, which is acceptable for approximating a step input for a system with
similar dynamic characteristics of the dehumidifier. This is true of most large thermal systems. If this
had been a small, lightweight, motor control system, the step change input would have had to occur
much more quickly or instantaneously. In this case, the system response is so much slower than 1.5
seconds that it would not have mattered if the step change had occurred instantaneously or over a 10
second interval.
45
The remainder of the test consisted of collecting data from the instruments until the process
variable, dehumidifier conditioner supply air temperature, had stabilized at its final value in response
to the step change. A list of the control algorithms on which the step response test was performed can
be seen in Table 72.
Table 72 Control Algorithms Tested with Step Response
Test Number Test Type Control Algorithm
1 Step OnOff with Deadband
2 Step OnOff with no Hysteresis
3 Step Proportional
4 Step Proportional+Derivative
5 Step Proportional+Integral
6 Step Proportional+lntegral+Derivative
Each of the tests was initiated at a conditioner supply air temperature of 36 F and relative
humidity of 38.7% For the temperature control performance tests, the step changes were made by
lowering the setpoint to 33 F.
7.4 Step and Frequency Response Analysis of Simulation Model
The step response test and frequency response analyses were performed on the simulation
model of the temperature control loop compensated with each of the six different control algorithms.
The step response test was conducted to provide a visual method of comparing the response of the
model with the actual system response. The comparison demonstrates that the model is a good
approximation of the actual system characteristics. With this accomplished, the frequency response
analysis of the model can be assumed equivalent to frequency response analysis performed on the
actual system.
In the MatrixX SystemBuild software, the step response was performed using the
Simulation command. The simulation time window analyzed was 500 seconds with a time step of
10 seconds. The time step of 10 seconds was chosen to match the data collection rate of 10 seconds
46
used in the field testing of the actual system. The Variable KuttaMerson integration algorithm was
chosen for the software simulation.
The openloop frequency response analysis was performed using the OpenLoop Frequency
Response Analysis command. The loop signal input location was chosen as the controller input.
The loop output was chosen as the temperature sensor output, which is in the feedback path. This
provided analysis of all elements in the loop, but without closing the loop. The range of frequencies
chosen was 0.0001 to 0.1 radians/second. This range provided a wide enough frequency spectrum to
show the phase drop to 180 degrees while still providing good resolution for reading the gain values.
The step response plots and openloop frequency response plots showing gain and phase
versus frequency are found in Chapter 8.
47
8. Comparison of Control System Performance
The six control algorithms' performance characteristics are compared using step and
frequency response analysis methods. Results of the step response tests performed on the actual
dehumidification unit are reported in this chapter for each of the algorithms. The two OnOff type
algorithms are not compared using frequency response analysis, nor is the step response shown for a
simulation model of the algorithm. These two controllers are included in this study primarily to show
the advantage of modulating type algorithms over the OnOff type.
A detailed comparison of control algorithm performance is carried out on the four remaining
modulating type control algorithms. The actual system and simulation model step responses are
presented as well as openloop Bode frequency response plots of the model. Th comparison of step
response data is done for the actual system only. The simulation model step response is shown only
to confirm the relative accuracy of the simulation model in approximating the actual system.
8.1 OnOff Control with Deadband
The presence of a 0.5% deadband setting in the controller equates to a hysteresis in
temperature of 0.005 x 300 F = 1.5 degrees Fahrenheit (where 300 F is the range of the input signal
from the temperature sensor). This means that the controller will assume the temperature is at the
desired setpoint if it is less than half of the deadband or 0.75 degrees Fahrenheit different from the
actual setpoint.
This control algorithm yields the following performance:
Step Response (Refer to Figure 81 for a graph of the Step Response)
Time to reach step setpoint initially: 207 seconds
Period of oscillations: 230 seconds
SteadyState Error in degrees Fahrenheit: Oscillates with maximum deviation
from setpoint of 1.3 and total
amplitude of 2.3
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The controller rate of response is slow and the period of oscillation is slower than the system
oscillation period. The reason for the period being longer is that the controller does not act to control
the process when the error is less than 0.75 degrees F. This results in a longer oscillation time than
would normally occur without hysteresis. The steadystate error is periodic, and is high at 1.3 degrees
F for a maximum deviation. The total swing of 2.3 degrees F corresponds to an absolute humidity
swing between 10.3 and 11.3 grains of moisture/lb of dry air. That is a change of 9.3% in the absolute
moisture content in the air.
0 n O ff A lg ro rith m (with 0.5% H ysteresis) S tep Response
Time In Second*
Figure 81 OnOff Control (with 0.5% Deadband) Step Response Actual System
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8.2 OnOff Control with No Deadband
Setting the hysteresis value in the controller to zero means that the controller will only
assume the temperature is at the desired setpoint if it is at the actual setpoint.
This control algorithm yields the following performance:
Step Response (Refer to Figure 82 for a graph of the Step Response)
Time to reach step setpoint initially: 142 seconds
Period of oscillations: 120 seconds
SteadyState Error in degrees Fahrenheit: Oscillates with maximum
deviation from setpoint of 0.7
and total amplitude of 1.2
The controller rate of response is quick and the period of oscillation is only slightly slower
than the system oscillation period. The steadystate error is periodic, and is high at 0.7 degrees F for a
maximum deviation. The total swing of 1.2 degrees F corresponds to an absolute humidity swing
between 10.6 and 11.1 grains of moisture/lb of dry air. That is a change of 4.6% in the absolute
moisture content in the air.
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Temperature In F
O n Off Alg ro rith m (w ith no H y s teres is) S tep Response
Figure 84 OnOff (with no Deadband) Step Response
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8.3 Proportional Control
The proportional band setting determined from the tuning process is 0.8. This control
algorithm yields the following performance:
Step Response (Refer to Figure 83 for a graph of the Step Response)
Time to reach step setpoint initially: Never reaches setpoint
Period of oscillations: 110 seconds
SteadyState Error in degrees Fahrenheit: Oscillates with average error of 0.8 and
maximum deviation from setpoint of
1.1 and total amplitude of 0.5
The controller rate of response is quick and the period of oscillation is same as the system
oscillation period. The system never reaches setpoint, but oscillates without damping about a
temperature that is 0.8 degrees F higher than the desired setpoint. The average steadystate error is
0.8 degrees F. This is high and corresponds to a deviation in absolute humidity of 0.6 grains of
moisture/lb of dry air. That is a deviation of 5.6% in the absolute moisture content in the air. The
total swing of 0.4 degrees F corresponds to an absolute humidity swing between 11.2 and 11.5 grains
of moisture/lb of dry air. That is a change of 2.8% in the absolute moisture content in the air.
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P ro p o rtio n a I A Ig ro rith m Step Response
Figure 83 Proportional Control Step Response Actual System
Ropcrticnai Algorithm Step Ffesponse StfnJdkn Mxlel
Time
Figure 84 Proportional Control Step Response Simulation Model
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Figure 85 Proportional Control Open Loop Frequency Response Simulation Model
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8.4 Proportional + Derivative Control
The proportional band setting determined by the tuning process is 0.6. The derivative setting
is 0.24 minutes.
This control algorithm yields the following performance:
Step Response (Refer to Figure 86 for a graph of the Step Response)
Time to reach step setpoint initially: Never reaches setpoint
Period of oscillations: 70 seconds
SteadyState Error in degrees Fahrenheit: Oscillates with average error of 0.6 and
maximum deviation from setpoint of
0.7 and total amplitude of 0.1
The controller rate of response is quick and the period of oscillation is shroter than the
system oscillation period. The system exhibits no overshoot of the setpoint or of the steadystate error
value. The system never reaches setpoint, but oscillates without damping about a temperature that is
0.6 degrees F higher than the desired setpoint. The average steadystate error is 0.6 degrees F. This is
high and corresponds to a deviation in absolute humidity of 0.4 grains of moisture/lb of dry air. That
is a deviation of 2.8% in the absolute moisture content in the air. The total swing of 0.1 degrees F
corresponds to an absolute humidity swing between 11.4 and 11.5 grains of moisture/lb of dry air.
That is a change of 0.7% in the absolute moisture content in the air.
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Temperature In F
Proportional + Derivative Algrorithm Step Response
Figure 86 Proportional + Derivative Control Step Response Actual System
Figure 87 Proportional + Derivative Control Step Response Simulation Model
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Figure 88 Proportional + Derivative Control Open Loop Frequency Response 
Simulation Model
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8.5 Proportional + Integral Control
The proportional band setting determined from the tuning process is 0.9. The integral setting
is 0.65 repeats per minute.
This control algorithm yields the following performance:
Step Response (Refer to Figure 89 for a graph of the Step Response)
Time to reach step setpoint initially: 140 seconds
Period of oscillations: 175 seconds
SteadyState Error in degrees Fahrenheit: Oscillates with average error of 0.0 and
maximum deviation from setpoint of
0.2 and total amplitude of 0.4
The controller rate of response is slower than the proportional and proportional + derivative
algorithms. The period of oscillation is longer than the system period of oscillation. The system
crosses the setpoint initially at 140 seconds and really starts to track it at 240 seconds. The initial
overshoot is 0.4 degrees F. It continues to oscillate with damping. The average steadystate error is
0.0 degrees F. The total swing of 0.4 degrees F corresponds to an absolute humidity swing between
11.2 and 11.5 grains of moisture/lb of dry air. That is a change of 2.8% in the absolute moisture
content in the air.
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P ro p o rtio n a I + In te g ra I A Ig ro rith m Step Response
Figure 89 Proportional + Integral Control Step Response Actual System
Figure 810 Proportional + Integral Control Step Response Simulation Model
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Figure 811 Proportional + Integral Control Open Loop Frequency Response 
Simulation Model
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8.6 Proportional + Integral + Derivative Control
The proportional band setting determined from the tuning process is O.6.. The integral
setting is 1.08 repeats per minute. The derivative setting is 0.24 minutes.
This control algorithm yields the following performance:
Step Response (Refer to Figure 812 for a graph of the Step Response)
Time to reach step setpoint initially: 165 seconds
Period of oscillations: Not able to discern period from data
SteadyState Error in degrees Fahrenheit: Oscillates with average error of 0.0 and
maximum deviation from setpoint of
0.2 and total amplitude of 0.4
The controller rate of response is slower than all the other algorithms. The period of
oscillation is not discemable from the data since it damps out quickly. The system crosses the
setpoint initially at 165 seconds and really starts to track it at 230 seconds. The initial overshoot is
only 0.3 degrees F. It continue to oscillate with damping. The average steadystate error is 0.0
degrees F. The total swing of 0.4 degrees F corresponds to an absolute humidity swing between 11.2
and 11.5 grains of moisture/lb of dry air. That is a change of 2.8% in the absolute moisture content in
the air.
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Temperature in F
Proportional + Integral + Derivative Algrorithm Step Response
Figure 812 Proportional + Integral + Derivative Control Step Response Actual System
Figure 813 Proportional + Integral + Derivative Control Step Response
Simulation Model
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Figure 814 Proportional + Integral + Derivative Open Loop Frequency Response 
Simulation Model
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9. Analysis of Control System Performance and Conclusions
Conclusions regarding the relative performance of the four modulating type control
algorithms were drawn based on five criteria. This chapter compares the algorithms according to the
five criteria of step response rise time, oscillation period, step response maximum overshoot, average
steadystate error, and bandwidth. The results of tests performed by Ziegler and Nichols for the same
types of controllers are presented alongside the field test data. Their data is shown to provide a
reference for how controllers operating in a laboratory environment behave compared to this system.
Following these comparisons is a brief discussion of the general characteristics of each control
algorithm as they apply to this system
9.1 Algorithm Step Response Rise Time
The speed of response for a controller is assessed by measuring its rise time response to a
step input change. The rise time is defined as the time required for the controlled variable to reach the
apex of its first oscillation, or the time to reach a plateau in the controlled variable. The rise time
values are shown in Table 91, along with the expected values presented by Ziegler and Nichols. The
proportional control exhibited a rise time of 115 seconds. Due to the rate action of the derivative
algorithm which is known for decreasing response times, similar, if not better performance was
expected from the proportional + derivative controller. Its response time was 110 seconds. The
proportional + integral control algorithm response time was 185 seconds. This was surprisingly
slower than expected when compared with ZieglerNichols findings. Both algorithms exhibited the
same time to reach 63% of the step change (reaching 34 F in 90 seconds). However, the proportional
algorithm significantly undershot the setpoint by 0.8 F while the proportional + integral algorithm
overshot by 0.4 F. The difference in time is really due to the extra travel in temperature that the
proportional + integral algorithm accomplished. The proportional + integral + derivative control
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algorithm response time was 190 seconds. A quicker response lime than the proportional + integral
control algorithm was expected due to the presence of the derivative in the algorithm. However, the
slower integral time parameter used in this algorithm dominated the response as the temperature
closed in on setpoint.
Table 91_____Comparison of Rise Time by Control Algorithm
Control Algorithm Rise Time (seconds) Expected Rise Time from ZieglerNichols [1] (seconds)
Proportional 115 Benchmark
Proportional + Derivative 110 No Comments
Proportional + Integral 185 Slightly longer than Proportional response
Proportional + Integral + Derivative 190 Slightly shorter than Proportional + Integral response
9.2 Algorithm Oscillation Period
The oscillation of the system after the initial rise time response to a step change influences
the time required for the system to damp out oscillation. The oscillation periods are shown in Table
92, along with the expected values presented by Ziegler and Nichols. The proportional control
exhibited an oscillation period of 110 seconds. Due to the rate action of the derivative algorithm
which again is known for decreasing oscillation times, similar, if not better performance was expected
from the proportional + derivative controller. Its oscillation period is 70 seconds. The proportional +
integral control algorithm oscillation period was 175 seconds. This was reasonably close to the
expected period when compared with ZieglerNichols findings. The proportional + integral +
derivative control algorithm oscillation period was not discemable. The system did not oscillate after
the fist return to setpoint following the initial overshoot. This algorithm rapidly damped out
oscillation
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Table 92_________Comparison of Oscillation Period by Control Algorithm
Control Algorithm Oscillation Period (seconds) Expected Oscillation Period from ZieglerNichols [1] (seconds)
Proportional 110 Benchmark of 110
Proportional + Derivative 70 No Comments
Proportional + Integral 175 Slightly longer than Proportional (range of 130170)
Proportional + Integral + Derivative Unable to discern from data 43% shorter than Proportional + Integral (100)
9.3 Algorithm Maximum Overshoot for Step Response
The maximum overshoot of the controlled variable in response to a step change is another
component to measuring the damping characteristics of the control system. The maximum overshoot
values are shown in Table 93, along with the expected values presented by Ziegler and Nichols. The
proportional control exhibited an undershoot of 0.8 F. This is reasonable for a proportional only
control algorithm, because it is expected to demonstrate a steadystate error. Since the proportional +
derivative algorithm is known for reducing overshoot, even more undershoot was expected from the
proportional + derivative controller. It undershot by the larger amount of 0.8 F. The proportional +
integral control algorithm is a slower responding and more unstable controller and demonstrated an
overshoot of 0.4 F. This was reasonably close to the expected period when compared with Ziegler
Nichols findings. The proportional + integral + derivative control algorithm was expected to
dramatically decrease the overshoot due to the derivative action when compared with the proportional
+ integral algorithm. Instead, the decrease in overshoot was minor w ith the overshoot being 0.3 F.
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Table 93_____Comparison of Maximum Overshoot by Control Algorithm
Control Algorithm Maximum Overshoot (degrees F) Expected Maximum Overshoot from ZieglerNichols [1] (degrees F)
Proportional Undershot by 0.6 Benchmark 0.6
Proportional + Derivative Undershot by 0.8 Similar to P
Proportional + Integral Overshot by 0.4 Slightly better than P
Proportional + Integral + Derivative Overshot by 0.3 71% smaller than P+I (0.1 based on P+I overshoot of 0.4)
9.4 Algorithm Average SteadyState Error
The average steadystate error measures the ability of the controller to provide accurate
control of a system. The average steadystate error values are shown in Table 94, along with the
expected values presented by Ziegler and Nichols. As expected, the proportional control exhibited an
average steadystate error of 0.8 F. This is reasonable for a proportional only control algorithm since
it is expected to demonstrate a steadystate error that is proportional to its gain. Since the proportional
+ derivative algorithm allows the proportional gain to be increased slightly, slightly less average
steadystate error was expected from the proportional + derivative controller. Its average steadystate
error was 0.6 F.
The integrating action of the proportional + integral control algorithm reduced to zero the
average steadystate error. This was as expected. Since the integrating action is also present in the
proportional + integral + derivative control algorithm, there was also no average steadystate error.
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Table 94 Comparison of Average SteadyState Error by Control Algorithm
Control Algorithm Average SteadyState Error (Degrees Fahrenheit) Expected Average Steady State Error from ZieglerNichols [1] (Degrees Fahrenheit)
Proportional 0.8 Benchmark
Proportional + Derivative 0.6 Slightly less than proportional
Proportional + Integral 0.0 None
Proportional + Integral + Derivative 0.0 None
9.5 Algorithm Bandwidth
The comparison of the bandwidth for the openloop compensated system was performed on
the simulation model. As shown in Chapter 8, the step response plots for the simulation model are
reasonably close to the actual system step response data. The bandwidth for this comparison was
defined as the 1.59 times the crossover frequency.[6] Refer to the Bode frequencyresponse plots
presented for each of the four algorithms in Chapter 8 for a more complete picture of system
frequency response.
The bandwidth is a measure of the systems speed of response. Faster responding systems
can handle higher frequency input signals satisfactorily as long as the phase margin is acceptable. The
bandwidth values are shown in Table 95. The proportional algorithm bandwidth was determined to
be 0.037 radians/second. The proportional + integral algorithm bandwidth is quite similar at 0.035
acceptable. The proportional algorithm bandwidth was determined to be 0.037 radians. This means
that the addition of the integral term does not have a significant effect on bandwidth for this system.
The addition of derivative control increases the bandwidth significantly to 0.054 radians/second for
the proportional + derivative algorithm and 0.059 radians/second for the proportional + integral +
derivative algorithm.
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Table 95_____Comparison of Bandwidth by Control Algorithm
Control Algorithm Crossover Frequency where Gain = 0 dB (radians/second) Bandwidth (radians/second)
Proportional 0.023 0.037
Proportional + Derivative 0.034 0.054
Proportional + Integral 0.022 0.035
Proportional + Integral + Derivative 0.037 0.059
9.6 Conclusions
Modulating type controllers exhibit characteristics such as reduced cycling time and the
elimination of a deadband that make their performance superior to OnOff type controllers. For
certain applications these advantages will quite desirable. However, even by choosing a modulating
type controller, the decision is not yet complete. Different modulating control algorithms will provide
varying performance with respect to step response rise time, oscillation period, step response
maximum overshoot, average steadystate error, and bandwidth. Depending on the requirements for
performance of the process being controlled, these performance criteria may be more or less important
to successful regulation of the process.
The four control algorithms compared in this study may be summarized as having the
following control characteristics as they were implemented on the dehumidification unit.
Proportional Algorithm rapid response time with short oscillation period, however, it
suffers from the inability to eliminate steadystate error.
Proportional + Derivative Algorithm decreased response time with decreased oscillation
period, however. It suffers from the inability to eliminate steadystate error, although it
reduces it beyond the proportional algorithm.
Proportional + Integral Algorithm slower response time with longer oscillation period, and
no steadystate error.
Proportional + Integral Algorithm similar response time to proportional + integral
algorithm, reduced overshoot, and no steadystate error.
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Different applications of these types of control algorithms may yield results different from
the data obtained for this system. Not all of the algorithms displayed the characteristics one would
expect from reading ZieglerNichols paper. In general, knowledge of the characteristics of each
algorithm will make selecting the appropriate controller for a process easier and help define
beforehand the performance expected of the system when it is in operation.
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References
[1] Ziegler, J.G., and N.B. Nichols, Optimum Settings for Automatic Controllers, Transactions
of the American Society of Mechanical Engineers, 64 (8), pp. 759768, 1942
[2] Websters New Collegiate Dictionary, 1979 Edition, G. & C. Merriam Company,
Springfield, Massachusetts.
[3] ASE1RAE Handbook, Fundamentals Volume, 1989 Edition, American Society of Heating,
Refrigeration, and Air Conditioning Engineers, Atlanta, GA.
[4] Honeywell UDC 3000 Universal Digital Controller Product Manual, Honeywell Industrial
Automation and Control, 1993.
[5] St. Clair, David W., Controller Tuning and Control Loop Performance, 2nd Edition,
StraightLine Control Company, Inc., Newark, Delaware, 1993.
[6] Van de Vegte, John, Feedback Control Systems, 2nd Edition, PrenticeHall, Englewood
Cliffs, New Jersey, 1990.
[7] Franklin, Gene F., Powell, David J., and EmamiNaeini, Abbas, Feedback Control of
Dynamic Systems, 3rd Edition, AddisonWesley Publishing Company, Reading,
Massachusetts, 1994.
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