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Optimization of Bioreactor Controls using Model Predictive and Neuro Fuzzy Techniques
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5/28/2018 Optimization of Bioreactor Controls using Model Predictive and Neuro Fuzz...
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Optimization of Bioreactor Controls using ModelPredictive and Neuro Fuzzy Control Techniques.
Thesis submitted in partial fulfillment of the
Requirements for the degree of
Master of Science in Technology
in
Instrumentation EngineeringBy
(Signature)
NITHIN VARGHESE NINAN
(Register Number: 122539010)
Under the guidance of
(Signature)
Dr. R Suresh
HOD, Department of Chemical Engineering
R V College of Engineering
Bangalore
MANIPAL UNIVERSITY, MANIPAL
5/28/2018 Optimization of Bioreactor Controls using Model Predictive and Neuro Fuzz...
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Optimization of Bioreactor Controls using Model
Predictive and Neuro Fuzzy Control Techniques.
Thesis submitted in partial fulfillment of the
Requirements for the degree of
Master of Science in Technology
inInstrumentation Engineering
By
NITHIN VARGHESE NINAN
(Register Number: 122539010)
Examiner 1 Examiner 2
Signature: Signature:
Name: Name:
MANIPAL UNIVERSITY, MANIPAL
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CERTIFICATECERTIFICATECERTIFICATECERTIFICATE
Thisistocertifythatthisthesisworktitled
OptimizationofBioreactorControlsusingModelPredictiveandOptimizationofBioreactorControlsusingModelPredictiveandOptimizationofBioreactorControlsusingModelPredictiveandOptimizationofBioreactorControlsusingModelPredictiveandNeuroFuzzyControlTechniques.NeuroFuzzyControlTechniques.NeuroFuzzyControlTechniques.NeuroFuzzyControlTechniques.
Isabonafiderecordoftheworkdoneby
NITHINVARGHESENINANNITHINVARGHESENINANNITHINVARGHESENINANNITHINVARGHESENINAN
Reg.No.122539010
InpartialfulfillmentoftherequirementsfortheawardofthedegreeofMasterofMasterofMasterofMasterof
ScienceScienceScienceScience inTechnologyinTechnologyinTechnologyinTechnologyinininin InstrumentationEngineeringInstrumentationEngineeringInstrumentationEngineeringInstrumentationEngineeringunderManipalUniversity,
Manipalandthesamehasnotbeensubmittedelsewherefortheawardforany
otherdegree
(Signature)
GuideName:ShivajithCK
AssistantMangaerBiotechAutomation SartoriusStedimIndiaPvt.Ltd.
Bangalore
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ACKNOWLEDGEMENT
Under the esteem guidance of our project guide professor Dr. R Suresh, HOD
Department of Chemical Engineering, R V College of Engineering, Bangalore, a
detail study on Optimization of Bioreactor Controls using Model Predictive and
Neuro Fuzzy Control Techniques and its applications to various models has been
studied as well as simulation has been done. We are very thankful for his whole-
hearted co-operation without which this project could not have been completed.
I take this opportunity to express my sincere thanks and acknowledge the
support received from, Shivajith C K, Assistant Manager, Sartorius Stedim
Biotech Pvt. Ltd., for his valuable guidance and granting the permission to carry
out the project at Sartorius Stedim Biotech Pvt. Ltd.
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DECLARATION
I hereby declare that the entire work presented in this project was carried out by
me under the guidance of Dr. R Suresh, HOD Department of Chemical
Engineering, R V College of Engineering, Bangalore, and no part of it has been
submitted for any degree or diploma in any institution previously.
In keeping with the general practice of reporting scientific observations due
acknowledgements have been made wherever the work described is based on
the findings of other investigators. Any omissions, which might have occurred by
oversight or errors in judgment, are regretted.
Date: (Signature)
Nithin Varghese Ninan
Register Number: 122539010
Instrumentation Engineering, Batch 1
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Optimization of Bioreactor Controls using
Model Predictive and Neuro Fuzzy Control Techniques Nithin Varghese Ninan
Manipal Global Education Services Pvt. Ltd., Bangalore
Page | 1
Index
1. Abstract.................................................................................................................... 31.1 Problem Definition .................................................................................. 3
2. Introduction........................................................................................................... 52.1 Process Definition................................................................................................. 5
2.1.1 Activated Sludge Processes ................................................................ 92.1.2 Biological Nutrient Removal .............................................................. 10
2.2 First Order Plus Dead Time Modelling............................................................ 142.5 The BNR Process............................................................................................... 193. Literature survey................................................................................................ 243.1 Fuzzy Logic Control........................................................................................... 24
3.1.1 Fuzzy If-Then Rule ............................................................................ 243.1.2 Fuzzy Reasoning ............................................................................... 25
3.2 Artificial Neural Networks.................................................................................. 263.2.1 Multi-Layer Perceptron ...................................................................... 283.2.2 Back-Propagation Learning Algorithm ............................................... 30
3.3 Integration of Fuzzy Logic and Neural Networks........................................... 334. System Identification, Modelling and Simulation............................................. 36
4.2 Development of FOPDT Models ........................................................... 415.Fuzzy Logic Controller Design............................................................................. 44
5.1 Fuzzy Logic Controller Selection .......................................................... 445.2 Development of the Fuzzy Logic Controller .......................................... 44
6. A Brief History of Industrial MPC........................................................................ 476.1 Principle of MPC .................................................................................. 526.2 Constraints ........................................................................................... 536.3 The Receding Horizon .......................................................................... 546.4 Optimization Problem ........................................................................... 576.5 Models .................................................................................................. 58
7 Tuning of the MPC-controller............................................................................. 607.1 Sampling time T .................................................................................. 607.2 Prediction horizon P ............................................................................ 607.3 Control horizon M ................................................................................ 617.4 Weighting matrices of in- and outputs: u and y ............................. 61
8. The filter in MPC................................................................................................... 61
8.1 First order filter .................................................................................... 628.2 Kalman filter ....................................................................................... 638.3 Extended Kalman filter ....................................................................... 63
9. State of art of MPC for WWTPs......................................................................... 659.1 Linear MPC ........................................................................................ 659.2 Nonlinear MPC ................................................................................... 66
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Optimization of Bioreactor Controls using
Model Predictive and Neuro Fuzzy Control Techniques Nithin Varghese Ninan
Manipal Global Education Services Pvt. Ltd., Bangalore
Page | 2
10. Dynamic Matrix Control..................................................................................... 6611. Implementation of MPC in MATLAB................................................................ 70
11.1 MATLAB code .................................................................................... 7011.2 OUTPUT IN MATLAB WINDOW ........................................................ 7511.3 INFERENCE ....................................................................................... 77
12. Conclusions......................................................................................................... 7913. Bibiliography........................................................................................................ 80
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Optimization of Bioreactor Controls using
Model Predictive and Neuro Fuzzy Control Techniques Nithin Varghese Ninan
Manipal Global Education Services Pvt. Ltd., Bangalore
Page | 3
1. Abstract1.1 Problem Definition
The biological nutrient removal (BNR) stage of a wastewater treatment plant
is a biochemical system requiring regulation of the dissolved oxygen (DO)
concentration of the bioreactor. Typically, these processes are very slow and
incorporate nonlinearities, significant dead time and many sources of
disturbances, making them a challenge to control. Effective control of the
BNR process leads to better quality effluent that is eventually discharged into
bodies of water. In addition, significant energy is used by large air blowers
that supply process air to the bioreactors. Accordingly, a cost-savings can be
realized in achieving good control of the BNR process in the form of energy
conservation.
Due to the length of time it takes to observe changes in a BNR bioreactor,
system simulation is particularly well suited for developing a controller for the
process. The BNR process is highly complex from a first principles modelling
perspective, incorporating many variables of which some must be estimated,
in addition to nonlinearities (Brdys and Maiquez, 2002). A first order plus dead
time (FOPDT) modelling approach is proposed that drastically simplifies the
modelling of the bioreactor and is based on the results of step tests performed
on a subject bioreactor.
By reason of the large degree of uncertainty inherent in the BNR process,
a fuzzy logic controller (FLC) is proposed for the DO concentration in the
bioreactor, as fuzzy logic lends itself particularly well to these types of
systems. In addition, the FLC provides the capabilities of dealing with
nonlinearities and non-symmetry in the final control element, as well as being
able to be implemented as a simple lookup table.
This project thesis provides a brief overview of Model Predictive
Control (MPC).A brief history of industrial model predictive control
technology has been presented first followed by a some concepts like the
receding horizon, moves etc. which form the basis of the MPC. It follows the
Optimization problem which ultimately leads to the description of the
Dynamic Matrix Control (DMC).The MPC presented in this report is based on
DMC. After this the application summary and the limitations of the existing
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Optimization of Bioreactor Controls using
Model Predictive and Neuro Fuzzy Control Techniques Nithin Varghese Ninan
Manipal Global Education Services Pvt. Ltd., Bangalore
Page | 4
technology has been discussed and the next generation MPC, with an
emphasis on potential business and research opportunities has been
reviewed. Finally in the last part we generate Matlab code to implement
basic model predictive controller and introduce noise into the model. We
have also taken up some case studies like Swimming pool water
temperature control and helicopter flight control etc. by applying the MPC
controller on these models.
Originally developed to meet the specialized control needs of power plants
and petroleum refineries, MPC technology can now be found in a wide variety
of application areas including chemicals, food processing, automotive, and
aerospace applications Its reason for success is many, like it handles
multivariable control problems naturally. But the most important reason for its
success is its ability to handle constraints. Model predictive control (MPC)
refers to a class of computer control algorithms that utilize an explicit process
model to predict the future response of a plant. At each control interval an
MPC algorithm attempts to optimize future plant behavior by computing a
sequence of future manipulated variable adjustments. The first input in the
optimal sequence is then sent into the plant, and the entire calculation is
repeated at subsequent control intervals. The basic MPC controller can be
designed with proper restrictions on the prediction horizon and model length.
The prediction horizon has to be kept sufficiently larger than control horizon.
But after applying to many other applications we find as the complexity
increases then we need techniques other than DMC like generalized
predictive control (GPC) which are better.
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Optimization of Bioreactor Controls using
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Manipal Global Education Services Pvt. Ltd., Bangalore
Page | 5
2. Introduction2.1 Process Definition
In managed wastewater systems, wastewater is collected and routed through
sewer systems to wastewater treatment plants. These plants vary in size and
configuration but the function of all wastewater treatment plants remains the
same, which is to produce a wastewater stream that can be safely discharged
back into the environment and minimize the solid waste that is produced.
A process flow diagram for a typical wastewater treatment plant is given in
Fig. 2.1. As shown, wastewater enters the plant from the sewer where it is
coarsely screened and degritted. The effluent then flows to the primary
clarifiers to allow initial sedimentation to occur. The settled sludge, known as
primary sludge, is usually dewatered using centrifuges or sludge presses
before disposal or stabilization. Following primary clarification, the effluent
flows to the aeration cells, or bioreactors, where it is aerated and retained to
allow time for the biochemical reactions to take place which reduce
suspended solids through oxidation (Grady et al., 1999). Following aeration,
the effluent flows to secondary clarifiers where a second stage of
sedimentation occurs. The sludge that settles to the bottom of the secondary
clarifiers is known as activated sludge. Activated sludge is a concentrated
slurry (Grady et al., 1999), of which a portion is usually fed back to the
aeration cells and a portion is wasted. The sludge destined for the aeration
cells is referred to as return activated sludge (RAS) and the wasted sludge is
referred to as waste activated sludge (WAS). The final stage of wastewater
treatment is typically disinfection, either by ultraviolet light (UV) or chlorination.
It is known that waters containing a low concentration of DO produce
harmful aquatic effects. Wastewater effluent consists of a large portion of
soluble organic material (SOM), which serves as a nutrient source for aquatic
microorganisms that consume oxygen as part of their metabolic cycle,
reducing the available DO. Since these microorganisms can survive at lower
concentrations of DO than higher life forms, an ecosystem is developed which
distresses and precludes the latter. Wastewater also contains nitrogen and
phosphorous, which act as nutrients and lead to the proliferation of aquatic
vegetation in downstream bodies of water (Grady et al., 1999). This process is
known as eutrophication and also leads to a reduction in DO.
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Optimization of Bioreactor Controls using
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Manipal Global Education Services Pvt. Ltd., Bangalore
Page | 6
Fig 2.1: Process flow diagram for a typical wastewater plant.
There are four basic categories of pollutants in wastewater: soluble
organic matter (SOM), insoluble organic matter (IOM), soluble inorganic
matter (SIM) and insoluble inorganic matter (IIM). There are two basic types
of unit operations found at wastewater treatment plants: physical unit
operations and biochemical unit operations. Physical unit operations consist
of activities like screening, degritting and sedimentation. Biochemical unit
operations typically occur in a bioreactor where wastewater is exposed to
microorganisms, resulting in biochemical reactions.
In wastewater treatment, preliminary physical unit operations are usually
carried out first (screening and degritting) to remove large objects and IIM
followed by sedimentation (primary clarification). After sedimentation, the
remaining IOM settles to the bottom of the basin and exits as underflow for
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Optimization of Bioreactor Controls using
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Manipal Global Education Services Pvt. Ltd., Bangalore
Page | 7
further treatment and/or disposal. The effluent (overflow) then carries the
soluble material to the next stage of treatment. Wastewater, in general,
contains a very low concentration of reacting pollutants. As a result,
biochemical unit operations are used on the wastewater stream at this stage
as these types of operations are more efficient at low concentrations of
reacting constituents (Grady et al., 1999). During the biochemical operations,
the soluble material is converted into more benign forms such as gaseous
nitrogen and car-bon dioxide. Further, during growth, the microorganisms
capture the remaining IOM allowing it to be settled and removed during later
physical unit operations (Grady etal., 1999). The unit operations of a typical
wastewater plant are shown in Fig. 2.2.
In a bioreactor, the primary characteristic of the biochemical environment for
fostering microbial growth is the terminal electron acceptor (Grady et al.,
1999). The three different types of electron acceptors used are: oxygen,
organic compounds and inorganic compounds. If sufficient quantities of DO
are supplied to the bioreactor it is said to be aerobic. Anaerobic environments
are those in which the electrode potential is highly negative and the terminal
electron acceptors are the organic compounds carbon dioxide and sulfate.
Environments in which nitrites and/or nitrates are the primary terminal electron
acceptors are referred to as anoxic. In these environments, the electrode
potential is higher and growth is more efficient than anaerobic environments
due to the nitrite and/or nitrate contribution. However, aerobic environments
remain the most efficient for microbial growth. The biochemical environment
maintained in a bioreactor has a significant impact on the effectiveness of the
treatment and different types of wastewater warrant different applications of
biochemical environments.
There are many different bioreactor configurations and the physical
configuration of the bioreactor impacts the effectiveness of the operation. The
two major classes of bioreactors are suspended growth and attached growth.
The suspended growth type bioreactor requires sufficient mixing to maintain
suspension of the microorganisms, followed by a unit operation to remove the
suspended biomass. In attached growth type bioreactors the microorganisms
are grown as a biofilm solid surface. This discussion focuses on suspended
growth bioreactors as the process under study is of this type.
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Optimization of Bioreactor Controls using
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Manipal Global Education Services Pvt. Ltd., Bangalore
Page | 8
Fig 2.2: Unit operations of a typical wastewater plant.
Suspended growth bioreactors are implemented in several ways including
the continuous stirred tank reactor (CSTR), the sequencing batch reactor
(SBR) and the perfect plug-flow reactor (PFR). In a CSTR, the influent
wastewater continuously flows through the bioreactor. Sufficient mixing is
provided to maintain a well-mixed and uniform environment, which aids in
maintaining a constant average physiological state (Grady et al., 1999). Often
a sedimentation stage follows the CSTR and the underflow slurry (secondary
sludge) is recycled back to the bioreactor. CSTRs can be cascaded in series
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Manipal Global Education Services Pvt. Ltd., Bangalore
Page | 9
to achieve additional operational flexibility. In a SBR, the wastewater does not
flow continuously through the bioreactor. Instead a fixed volume of
wastewater is reacted to completion at a time. These types of reactors are
particularly flexible as the biochemical environment can be highly controlled to
suit the quality of the wastewater. In a PFR, the constituents of the fluid flow
through the bioreactor without mixing and in the same order in which they
enter.
2.1.1 Activated Sludge Processes
The ASP is a well-known and extensively deployed method of secondary
wastewater treatment that is capable of achieving a good quality effluent.
Activated sludge uses aerobic suspended growth of microorganisms to
remove SOM from wastewater. The ASP primarily consists of the bioreactor
and secondary clarification processes. The basic principle behind activated
sludge is that when microorganisms are exposed to SOM, they will consume
and reduce it. The microorganisms must be provided with sufficient DO, which
they require to survive and must be kept in a sufficiently suspended state to
achieve good results. Both of these goals are met by introducing process air
into the pre-treated wastewater stream. This can be done in a variety of ways
including diffused aeration, jet aeration and surface aeration.
Diffused aeration involves lining the bottom of the aeration basins with a
diffuser grid and forcing process air through the grid, usually utilizing large
blowers. This method diffuses air bubbles of varying sizes into the wastewater
stream. Jet aeration utilizes aspirating devices that require the wastewater to
be pumped through an ejector that mixes air into the pumped water stream.
Surface aeration operates by pumping water into the air, after which the falling
water contacts the water surface causing air to be mixed with the wastewater.
Generally, diffused aeration is suited for large, deep aeration basins,
whereas jet aeration is suitable for smaller tanks and surface aeration is
suitable for shallow aeration basins as the mixing is primarily concentrated at
the surface.
In ASPs, the aeration stage occurs in basins where the primary
biochemical operations take place. The effluent from the bioreactor is known
as mixed liquor. Following aeration, a clarification stage takes place, which
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Manipal Global Education Services Pvt. Ltd., Bangalore
Page | 10
allows for sedimentation of the microorganisms to occur. The settled
microorganisms can then be recycled in concentration (i.e., RAS) back into
the bioreactor and/or wasted (i.e., WAS). A schematic of the ASP is shown in
Fig. 2.3.
There are numerous configuration options for ASPs, which generally vary the
geometric characteristics of the bioreactor itself. The trade-offs between the
various configurations are usually driven by capital cost requirements,
efficiency and operational complexity. Two of the more popular bioreactor
configurations are called conventional activated sludge (CAS) and step-feed
activated sludge (SFAS). The geometric characteristics of these
configurations are shown in Fig. 2.4.
Fig 2.3: Simplified view of the activated sludge process. (Adapted from Grady
etal. (1999))
2.1.2 Biological Nutrient Removal
Much of wastewater is human waste, containing nutrients and bacteria. In
wastewater, the term nutrient generally refers to nitrogen and phosphorus, as
these elements when deposited in bodies of water provide nutrition to life-
forms present in the water. This process is also known as eutrophication. The
United States Environmental Protection Agency (EPA) offers the following
description of how eutrophication affects surface water:
Nitrogen and phosphorus are the primary causes of cultural
eutrophication (i.e., nutrient enrichment due to human activities) in
surface waters. The most recognizable manifestations of this
eutrophication are algal blooms that occur during the summer. Chronic
symptoms of over-enrichment include low dissolved oxygen, fish kills,
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Manipal Global Education Services Pvt. Ltd., Bangalore
Page | 11
murky water and depletion of desirable flora and fauna.
In addition, the increase in algae and turbidity increases the need to
chlorinate drinking water, which, in turn, leads to higher levels of
disinfection by-products that have been shown to increase the risk of
cancer. Excessive amounts of nutrients can also stimulate the activity of
microbes, such as Pfiesteria, which may be harmful to human health
(US Environmental Protection Agency, 2007).
Fig 2.4: Two types of activated sludge processes. (a) Conventional activated
sludge; (b) Step-feed activated sludge. (Redrawn from Grady et al.(1999))
Accordingly, a process that is capable of enhanced nitrogen and
phosphorus removal is highly desirable. This is the goal of the BNR process,
which uses the principles of the ASP, but through advanced bioreactor
configuration is able to achieve higher levels of nitrogen and phosphorus
removal.
The history of the BNR process is interesting and deserves a brief
discussion. Nitrogen and phosphorus removal technologies were developed
separately, but con-currently, in the 1960s. During this time, developers of the
processes were evaluating the use of various bioreactor zones and
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Optimization of Bioreactor Controls using
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Manipal Global Education Services Pvt. Ltd., Bangalore
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configurations and their effects on effluent quality. The bioreactor zones
under study were aerobic (sufficient oxygen), anaerobic (absence of oxygen
and nitrates) and anoxic (absence of oxygen with presence of nitrates).
Much research was dedicated to configurations that would yield good
nitrogen removal, however, due to the high costs, both capital and
operational, biological nitrogen removal processes received very little
commercial attention. Whereas biological nitrogen removal processes were
receiving much academic attention but little commercial attention, biological
phosphorus removal was a phenomenon that was actively being observed in
plugflow bioreactors that were uniformly aerated. This method of aeration
yielded low DO concentration levels at the front of the process creating
anaerobic zones which are now known to be crucial to biological phosphorus
removal. While it is now known that biological reactions are largely
responsible for the phosphorus removal, this was a point of controversy
during initial development of the process. These two processes have since
been integrated into a single process today which is referred to as biological
nutrient removal.
The framework for the BNR process was first introduced by Barnard
(1975), who purported the concepts which form the basis for BNR. The first
concept is that appropriate use of anoxic and aerobic zones as well as nitrate
recirculation form a single operational and cost-effective approach to nitrogen
removal.
The second concept is that sufficient removal of nitrate in the anoxic zone
results in phosphorus removal. Using these concepts, various bioreactor
configurations have been designed and implemented. The general BNR
process is depicted in Fig. 2.5.
The importance of the different zones in BNR is based on the terminal
electron acceptor. The terminal electron acceptor in the aerobic zone is
oxygen, in the anoxic zone it is nitrate-N and in the anaerobic zone where
neither oxygen nor nitrate-N are present, it is carbon dioxide and sulfate
(Grady et al., 1999). It is the alternating physiological environments created by
the BNR bioreactor configuration that provide
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Optimization of Bioreactor Controls using
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Manipal Global Education Services Pvt. Ltd., Bangalore
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Fig 2.5: Process flow diagram for the BNR process. (Redrawn from Grady et
al.(1999))
enhanced removal of nitrogen and phosphorus in the effluent. In general, the
aerobic zone provides SOM removal similar to the ASP, whereas the
anaerobic zone provides phosphorus removal and the anoxic zone provides
nitrogen removal.
Biological nitrogen removal requires the use of both nitrification and
denitrification processes. Nitrification occurs in aerobic zones where ammonia
is converted first to nitrites and then to nitrates. Denitrification occurs in the
anoxic cells when heterotrophic bacteria convert nitrate-N to nitrogen gas
using nitrate-N as the terminal electron acceptor as they oxidize SOM. The
nitrification and denitrification processes follow the nitrogen cycle, which is
depicted in Fig. 2.6.
Biological phosphorus removal involves the enrichment of the bioreactor
zone with phosphorus accumulating organisms (PAOs). In the anaerobic
zone, due to the lack of oxygen and nitrate-N, and the relatively short
retention time, oxidation of SOM by heterotrophic bacteria does not occur.
However, fermentation by these organisms will occur, resulting in the
production of volatile fatty acids (VFAs). The VFAs are then transported and
stored in the PAOs as polyhydroxyalkanoic acids (PHA) which are
then used in cellular growth and the reformation of polyphosphate from the
inorganic phosphorus found in the effluent. With the phosphorus trapped in
the PAOs it can then be settled and removed (Grady et al., 1999).
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Optimization of Bioreactor Controls using
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Manipal Global Education Services Pvt. Ltd., Bangalore
Page | 14
Fig 2.6: Graphical representation of the nitrogen cycle exploited in the BNR
process.
2.2 First Order Plus Dead Time Modelling
The response of a process to a step input provides a method of characterizing
and subsequently modelling the process. Step testing the process involves
inducing a step change in the process, usually performed by a setpoint
change, and observing the response. Many processes, when step tested in
this fashion, exhibit a first order response but with a time lag. The transfer
function of a first order process can be modified to include a time lag. This
type of model is known as a first order plus dead time (FOPDT) model. Many
processes can be modelled in this fashion. From the response of the process
to a step input, the three parameters that comprise a FOPDT model can be
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Optimization of Bioreactor Controls using
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Manipal Global Education Services Pvt. Ltd., Bangalore
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surmised. These parameters are the steady-state process gain K, dead time
TD and time constant . A graphical representation of the FOPDT model is
shown in Fig. 2.7.
The FOPDT model transfer function G(s) is expressed in the Laplace
domain as
where Kis the steady-state process gain Cs/m; Csis the ultimate process
response; mis the step input; is the time constant; and TDis the dead time
(Smith and Corripio, 1985).
When a process is step tested in this way, the response observed from the
feedback sensor represents the lumped response of the process, the actuator
and the feedback sensor
The model obtained can then be used in a simulation of the process and
provides the complete response of the system, including the dynamics of the
sensor, the actuator and the process itself.
2.3 Fuzzy Logic Control
Introduced by Zadeh (1965), fuzzy set theory is a form of mathematics that is
used to represent approximate knowledge. Contrary to crisp, bivalent logic,
where quantities take on values of one (true) and zero (false), fuzzy logic
provides a method of evaluating logical expressions where quantities can take
on continuous values between zero and one. This fuzzy as opposed to
crisp representation of the data lends fuzzy logic its power to evaluate
approximate reasoning. A brief introduction to fuzzy logic and its application to
control are provided as background to the proposed solution.
Fuzzy logic provides a method of utilizing approximate reasoning to solve
problems and is derived from the way that people approach problem-solving.
People generally think in fuzzy terms, i.e., a person might say the
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ep
m(t) m
rocess
esponse
(t)
Cs
0.632 Cst
C
0 TD t
Fig. 2.7: Graphical representation of a FOPDT model. (Adapted from Smith
and Corripio (1985))
temperature outside is veryhot, or the meat is slightlyundercooked. Fuzzy
logic affords the ability to use fuzzy descriptors or linguistic variables to define
the inputs and output of the fuzzy system. In the above examples, the terms
very and slightly are referred to as linguistic hedges and form part of the
linguistic variable. The linguistic variables are then used in the formation of a
rule base that is used to evaluate the output of the fuzzy system with respect
to fuzzy sets (fuzzy inputs and outputs of the system).
The way in which the linguistic variables are used to provide approximate
reasoning is through the use of membership functions. Membership functionsare used to define the degree of which a linguistic variable describes the state
of the fuzzy element under study. When the set of all possible values that a
fuzzy element can take on (i.e., the universe of discourse) is plotted,
geometric areas of the set are assigned to one of the linguistic variables.
Fuzzy logic operations are then used to evaluate the output of the fuzzy
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system with respect to the rule base and the linguistic variables.
Fuzzy rules generally take the form of an if-then statement, or an
implication. For example, if A and B then C, where A, B and C are fuzzy
objects, and where both A and B are conditions and C is the action.
Accordingly, a method of evaluating these types of fuzzy expressions is
required.
Fuzzy logic operations are analogous to bivalent operations. The fuzzy
operations complement, union and intersection correspond to the bivalent
logic operations NOT, AND and OR. In bivalent logic, the implication of one
set by another set is evaluated as the union of the first set with the
complement of the second set. Bivalent logic implication is also extended for
use in fuzzy logic. Implication, however, in the case of fuzzy logic, requires
that connectives be expressed in terms of the membership functions for the
corresponding sets. Fuzzy logic implication has been interpreted in several
ways including Larsen implication, Mamdani implication, Zadeh implication,
Dienes-Rescher implication and Lakasiewicz implication. The Mamdani
implication has been selected for this work due to its wide acceptance. The
expressions for fuzzy complement, union and intersection are given as
(Karray and De Silva, 2004)
A(x) = 1 A(x); x X;
A B(x) = max[ A(x); B(x)]; x X;
AB(x) = min[ A(x); B(x)]; x X;
respectively, where Xis the universe of discourse; xis the variable in X; Aand
B are fuzzy sets; Aand B are membership functions ofA andB, respectively;
Ais the membership function representing the fuzzy complement ofA;ABis
the membership function representing the union of A and B; and AB is the
membership function representing the intersection of Aand B.
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Fuzzy implication has been interpreted in multiple ways, however, since
Mamdani implication is selected for this work, the Mamdani implication is
provided which is given as (Karray and De Silva, 2004)
AB(x) = min[ A(x); B(y)]; x X; y Y; (2.2)
where Xand Yare the universes of discourse for Aand B, respectively; y is
the variable in Y; and AB is the membership function representing A implies
B.
The above equations can then be used to develop the compositional rule
of inference (CRI), which allows for the full evaluation of the if A and B then
C expressions making up the rule base. Since both the AND and implication
operations can be realized as min functions, and since the rules are joined
using OR connectives, the membership function of the entire rule base is
determined by (Karray and De Silva, 2004)
R(a; b; c) = max min[ Ai(a); Bi(b); Ci(c)]; (2.3)
i
where R is the overall membership function for the rule base; i is the rule
index; Ai, BiandCiare fuzzy sets;a,b andc are the variables inAi,BiandCi,
respectively; and Ai , Bi and Ci are membership functions of Ai, Bi and Ci,
respectively.
These equations are necessary for evaluating the fuzzy relationships that
form the system. Linguistic variables are assigned to the membership
functions making up the fuzzy set. The areas where the membership functions
overlap is what specifically characterizes fuzzy logic, where the boundary
between system states is not precisely defined and is partially composed of
multiple states. Typical fuzzy membership functions are shown in Fig. 2.8.
The figure depicts the membership function for a variable x. The linguistic
variables forx areHigh,Okay andLow. Areas A, C and E arethe parts of the
fuzzy set that are exclusively High, Okay and Low, respectively. However,
parts B and D are part Highand Okayand part Lowand Okay, respectively
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High Okay Low
1
(x)
A C E
X
0.5
B D
0
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
x
Fig. 2.8: Typical fuzzy membership functions.
illustrating the fuzzy relationships. Membership functions can be constructed
in several ways. Common types include Gaussian (as in Fig. 2.8), triangular
and trapezoidal, but others exist.
Fuzzy control is particularly well adapted to processes that are well
understood by an expert. The expert assists in the development of the fuzzy
rule base which describes in literal terms how the process is controlled. From
the fuzzy rule base, membership functions are developed that characterize
the relationships between the linguistic variables. Finally, fuzzy operations are
carried out to evaluate the fuzzy expressions. Utilizing the fuzzy logic
components described, a complete fuzzy inference system (FIS) can be
constructed.
2.5 The BNR Process
The particular wastewater process under study is the BNR stage. As
mentioned previously, BNR is an enhanced form of the ASP used in
wastewater treatment. These processes are microbiological in nature and
require regulation of the environment of the microorganisms contained in the
bioreactor.
The actual configuration of the bioreactor under study is show in Fig. 2.10.
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Fig. 2.10: Process flow diagram for the bioreactor configuration.
The process and instrumentation diagram (P&ID) for the process is shown in
Fig. 2.11. The P&ID shows the major components of the process control
system and their control signals to and from the industrial controller
(programmable logic controller). As shown in Fig. 2.11, a header pipe carries
the supply air to the FCVs controlling the airflow to each bioreactor cell. The
process air is supplied by a team of blowers operating in a lead/lag
configuration, whereby they are brought online sequentially as required. In
this scheme, the blowers have full voltage non-reversing (FVNR) motors and
the airflow through each blower is controlled by a FCV on its suction side. The
blower system operates to keep a constant air pressure in the supply header
through an independent control loop. The work in this paper focuses on
developing a controller for the bioreactor FCVs.
DO concentration of the aeration cells is a critical parameter in the overall
control of the BNR process. The organisms in the bioreactor require a
sufficient supply of oxygen to act effectively and there is a band of control
required. If too little oxygen is supplied the organisms are suffocated.
Conversely, if too much oxygen is supplied settling problems may occur later
in the treatment process, in addition to wasted energy (Turmel et al., 1998).
The dynamics that affect the DO inside of a bioreactor are complex and in
some models the number of parameters involved exceeds sixty (Brdys and
Maiquez, 2002).
BNR is a specialized form of the ASP. Many approaches to controlling
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Fig. 2.11: Bioreactor process and instrumentation diagram.
ASPs consider the entire process of which DO regulation is one
component. In attempting to control the entire ASP automatically, elaborate
mathematical models of the process must be constructed, which consist of
many variables that cannot be measured and must be estimated.
Furthermore, in many plants, certain parts of the ASP are controlled
manually by the plant operations staff that monitor critical parameters on a
daily basis. Samples of the wastewater are taken daily and analyzed in an
offline laboratory. Accordingly, as much of the information collected is of a
very coarse resolution, it does not lend itself to incorporation for automatic
control of the system. The DO concentration of the bioreactor, however, is
typically monitored continuously and it is highly desirable to be maintained at
a specified setpoint. Meeting this goal helps to produce a good quality effluent
and minimize operating costs. For this reason, this work focuses specifically
on controlling the bioreactor DO concentration without regard for the
remainder of the BNR process. Manual changes in the parameters of the BNR
process made by plant staff undoubtedly change the bioreactor dynamics,
however, the goal of this work is to characterize the bioreactor process and
develop worst-case conditions, which embody these potential changes in
dynamics and subsequently test the controller according to the range of
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process dynamics.
For the purpose of controller design and simulation, an actual BNR bioreactor,
is step tested and FOPDT models of the process are developed. The FOPDT
modeling approach allows the direct incorporation of experimental data
obtained from the actual plant into the simulation and design of the controller.
While this method has the drawback of relying only on a snapshot of the
process dynamics at a given point in time, it has the advantage of not having
to rely on elaborate mathematical models of the ASP, which incorporate many
assumptions and variables that cannot be measured.
To address the fact that only a snapshot of the process is being evaluated,
the bioreactor is tested under two separate conditions, a low wastewater flow
condition and a high wastewater flow condition through the bioreactor. The
objective of this experiment is to capture the dynamics of the process during
each event to observe the process dynamics under these conditions and
subsequently develop worst-case models for testing the controller
performance.
In wastewater plants, often, very little process instrumentation is available
to assist in the control decisions of a bioreactor. In addition, it is very desirable
to deploy a low maintenance, robust controller, that requires very little
operator intervention for long-term, sustained operation. With this in mind, the
work in this thesis focuses on developing a FLC for the bioreactor FCVs
requiring only feedback of DO concentration and returning the required FCV
stem position.
In addition, as the dynamics of each cell of the bioreactor are different, one
could develop individually tuned controllers for each cell, however, as
simplicity, robustness and low-maintenance are the ultimate goal of this work,
a single controller is developed that adequately controls each of the bioreactor
cells under wide ranging and proposed worst-case process conditions.
Finally, to ensure the controller is easy to realize in an industrial controller,
an algorithm is developed to approximate the control surface of the optimal
FLC as a lookup table. The lookup table can be implemented in any
programmable logic controller (PLC) and is ideal for fast computation.
The final result of this work is to be able to input one or more FOPDT pro-
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cess models and return a lookup table representing an optimal fuzzy control
surface, optimized for an individual system or several systems concurrently.
This technique can then be used to tune the controller optimally across its
entire operational range, providing that FOPDT models of the process at its
operational extremes can be obtained.
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3. Literature survey3.1 Fuzzy Logic Control
Based on Zadehs theory of fuzzy sets, the concept of fuzzy logic has been
successfully applied to the control of industrial processes particularly those
that are ill-defined but which can be successfully controlled by human
operators.
The basic idea of this approach is to incorporate the experience of human
operators in the design of the controllers. The value of the inputs and outputs
need not be numerical and may be expressed in natural language. Most
commonly, a fuzzy logic model includes a mapping of input values to output
values using simple IF-THEN statements, such as IF room temperature is
high, THEN supply more cool air to the room. These types of mappings
permit the incorporation of expert knowledge with the fuzzy logic model.
3.1.1 Fuzzy If-Then Rule
Assuming there are two inputs, xand y, to the system and the output is z. An
example of a fuzzy if-then rule is:
If xis Aiand yis Bi, then zis Ci.
where x , y and z are linguistic variables, Ai , Bi and Ci are fuzzy sets
characterized
by membership functions.
Another form of fuzzy if-then rule, T-S type proposed by Takagi and Sugeno
(1985), has fuzzy sets involved only in the antecedent.
If xis Ai and yis Bi, then z= c0i+ c1ix+ c2iy
where the consequent of the rule is a linear function of the input variables.
A simpler form is extensively used, which is actually a zero order T-S
fuzzy rule. If xis Aiand yis Bi, then z= zi
where zi is a crisply defined number.
Through the use of linguistic labels and membership functions, a fuzzy if-then
rule can easily capture the essence of humans experience. Fuzzy if-then
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rules form the core of the fuzzy inference system to be introduced below.
3.1.2 Fuzzy Reasoning
Fuzzy reasoning is an inference procedure used to derive conclusions from a
set of fuzzy if-then rules and one or more conditions. The steps of fuzzy
reasoning performed by fuzzy inference systems are (Shaw, 1998):
Compare the input variables with the membership functions in the
antecedent to obtain the membership values of each linguistic label
(fuzzification).
Combine the membership values on the antecedent to get firing
strength (weight) of each rule.
Generate the qualified consequent of each rule depending on the firing
strength.
Aggregate the qualified consequent to produce a crisp output (defuzzification).
3.1.3 Fuzzy Inference System
Basically, a fuzzy inference system is composed of four functional blocks as
shown in Fig. 3-1 (Jang, 1993):
Knowledge Base
Input Output
Fuzzification
Data Base Rule Base
Defuzzification(Crisp)
(Crisp)
Decision-Making Unit(Fuzzy) (Fuzzy)
Fig. 3-1 Basic fuzzy inference system
A fuzzification interface which transforms the crisp inputs into
degrees of match with linguistic values.
A knowledge base which contains a number of fuzzy if-then rules and
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defines the membership functions of fuzzy sets used in the fuzzy
rules.
A decision-making unit, sometimes referred to as an inference
engine, which performs the interface operations on the rules.
A defuzzification interface which transforms the fuzzy results into crisp
outputs.
Depending on the types of fuzzy reasoning and fuzzy if-then rules
employed, fuzzy inference systems can be classified into different types:
Mamdani fuzzy inference system:
The overall fuzzy output is derived by applying max operation to the
qualified fuzzy outputs (each of which is equal to the minimum of firing
strength and the output membership function of each rule). The centroid of
area, bisector of area and mean of maximum are normally used to obtain the
final crisp outputs from the fuzzy outputs.
Takagi-Sugeno fuzzy inference system:
This system is applicable for Takagi-Sugeno type rules. The final outputs are
the weighted average of each rules outputs. When the consequent of rules
are crisp value, the overall outputs are the weighted average of each rulescrisp outputs.
The following features have effect on the performance of fuzzy logic
controllers (FLCs) (Pedrycz, 1989).
Scaling factors for input and output variables.
Membership functions of fuzzy sets.
Setting of fuzzy rules.
3.2 Artificial Neural Networks
One of the most important capabilities of an artificial neural network (ANN) is
that it can be trained to do a mapping between input and output variables by
adjusting a set of weights and thresholds of a connectionist model based on
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training examples. It attempts to achieve good performance through massive
interconnections of simple computational elements or neural units. An artificial
neural network model is characterized by its architecture, its processing
algorithm and its training algorithm. The network architecture specifies the
arrangement of neural connections while the type of units is characterized by
the activation function used. For a given architecture, the neural network is
used in two different modes: the processing mode and the training mode. In
the processing mode, the processing algorithm specifies how the neural units
compute the outputs for any set of inputs and for a given set of weights. The
training algorithm specifies how the neural network adapts its weights for all
training patterns (Haykin, 1999).
With respect to the architecture, four main types of neural networks can be
distinguished:
Layered feed-forward neural networks, where a layer of neurons
receive inputs only from the neurons from the previous layer, such
as multi-layer perceptrons.
Recurrent neural networks, where the inputs to neurons are the
nets previous outputs as well as inputs from external sources.
Laterally connected neural networks, which consist of feedback
input units and a lateral layer consisting of such neurons that are
laterally connected to their neighbors.
Hybrid networks, which combine two or more of the above features.
The training algorithms for neural networks can be classified into supervised
learning and unsupervised learning. In supervised learning, the networks are
presented with a set of example input-output pairs and trained to implement a
mapping that matches the examples as closely as possible. In contrast, for
unsupervised learning, the networks are presented with only the input
samples, and learned to group these samples into classes that have similar
feature.
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3.2.1 Multi-Layer Perceptron
The multi-layer perceptron (MLP) is the most used and studied artificial neural
network. According to the Kolmogorov theorem (Kolmogorov, 1957), a three-
layer perceptron can be trained to approximate any non-linear function. Thus,
the MLP can be a suitable tool for obtaining good approximate solutions in
complicated mapping problems.
A MLP is formed from interconnections of many basic neurons and are
typically of the structure shown in Fig. 3-2. As shown in Fig. 3-2, in addition to
the necessary input layer and output layer, there is also a hidden layer. This
structure is referred to as a three-layer network in this work because it has
three layers of nodes. However, it has only two layers of processing elements,
the hidden layer and the output layer.
Hidden Layer
Input Layer Output Layer
Fig 3-2 Simple architecture of a multi-layer perceptron
In these layers, each neuron in a layer is connected to neurons in the
previous and in the next layer, but it is not connected to any neuron in the
same layer. These connections between neurons have their adjustable
weights, which are adjusted during the training process. The inputs to each
processing neuron are multiplied by their corresponding weight and the
weighted sum is then acted upon by an activation function before the output.
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x0 =1
w0
wi yxi f ()
xnw
n
Fig. 3-3 Structure of a neuron
Fig. 3-3 shows the structure of a single neuron. The function of the neuron
can be described by:
=wixi (2-1)
y =f ()(2-2)
where yis the output of the neuron,
xi,i =0,K,n are then inputs to the neuron,
wi,i =0,K,n are the weights connecting the inputxi to the neuron, and
f () is the activation function which operates on the weighted sum of input, v .
Typically, in addition to the inputs, a bias input is also added. If x0 is used as
the bias input, it is normally set to a constant value of 1 and the bias is
adjusted during training through adjustment of the bias weight w0.
The following activation functions are commonly used:
Threshold function:
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1, 0
(2-3)f ()=
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connecting weights are adjusted to reduce the difference between the target
or desired outputs and the actual outputs of the network. The training set,
comprising many training pairs, is presented to the neural network repeatedly
until the error decrease below the desired level. Study of different learning
algorithms is always a very active area of the research in artificial neural
networks. To date, many algorithms have been developed, among which the
back-propagation (BP) algorithm is the most widely used.
Before the BP algorithm is derived, the following notations are introduced:
ylj(p) :output of the jth node in layer lfor the pth training example net
input to
net lj(p) : the jth node in layer lfor the pth training example
wlji(p) : weight connecting the ith node in layer l1 to the jth node in
layer lfor the pth training example
d j(p) :desired response of the jth output node for the pth training
example
lj(p) : local gradient for jth node in layer lfor the pth training example
Nl :number of nodes in layer l
L : number of layers
P : number of training examples
The nodes in the first layer only transmit the inputs to the second layer.
Referring to Fig. 2-3, the output of a node in layer l, for l2 , is given by
ylj(p)=f (netlj(p)) (3-6)
whereN
netlj(p)=l1 wli(p)yi
l1
(p) (3-7)i=0
For the special cases, we have
yi1(p) is the ith component of the input vector to the network
y0l1(p)=1, andwlj0(p)is the bias weight
f () is the activation function.
BP uses a gradient search technique to find the network weights that
minimize an objective function. The objective function to be minimized is
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usually the average squared error function:
1P
Jav
= J(p) (3-8)P p=1
where J( p) is the total squared error at the output layer for the pth example:
1 N
J (p)= L(dj(p) yLj(p))
2 (3-9)
2
j=1
where NLis the number of nodes in the output layer.
The weights of the network are determined iteratively according to:wlji(p +1)=wlji(p)+ wlji(p) (3-10)
wlji(p)=
J(p)
(3-11)w
lji(p)
where is a positive constant called the learning rate. To implement this
algorithm, an expression for the partial derivative of J( p) with respect to each
weight in the network is developed. For an arbitrary weight in layer l, this canbe computed using the chain rule:
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where the kth neuron in the l+1 layer is connected to the jth neuron. Finally,
the correction wlji( p) is defined by:
The above equations comprise the back-propagation learning algorithm. At
the beginning of the training process, all the connecting weights are usually
initialized to some small random values. The learning rate can be fixed oradaptively chosen in a number of ways. The process of computing the
gradient and adjusting the weights is repeated until the output error decrease
to some specified level. The multi-layer perceptron can be used as a universal
approximator, a classifier or a regression machine.
3.3 Integration of Fuzzy Logic and Neural Networks
Fuzzy logic and neural networks have been briefly overviewed in the previous
sections. Table 3-1 lists the characteristics of fuzzy logic and neural networks.It can be seen that fuzzy logic and neural networks have several
characteristics in common. For example, both are model-free function
estimators that can be adjusted or trained for improved performance.
However, each has its own advantages. The advantages of fuzzy logic over
neural network are its tolerance for imprecision and explicit knowledge
wlji( p) =lj( p) yi
l1( p) (3-17)
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representation. On the other hand, neural networks offer other advantages
such as the ability to learn and to generalize from these. In this regard, it is
believed that the integration of fuzzy logic and neural networks can leverage
the advantages of the two individual techniques.
Table 3-1 Characteristics of fuzzy logic and neural networks (Medsker, 1995)
Properties of intelligent systems Fuzzy logic Neural Networks
Function estimators
Trainable, dynamic
Improvement with use
Parallel implementation
Numerical
Tolerance for imprecision
Explicit knowledge representation
Adaptive
Optimising
Interpolative
Tolerance for noise
Research in the use of fuzzy logic with neural networks has been progressing
at a rapid pace during the last few years. The integration of fuzzy logic and
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Optimization of Bioreactor Controls using
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Manipal Global Education Services Pvt. Ltd., Bangalore
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neural networks can be viewed from different perspectives. In terms of
applications, numerous studies have been done on the improvement of
control systems, conventional or fuzzy, by use of the neural technology. Other
applications modify neural networks, supervised or unsupervised, with fuzzy
techniques to improve their performance. The main approaches to integration
of fuzzy logic and neural networks can be summarized as follows: fuzzy
connectionst expert system, neural networks for designing and tuning fuzzy
systems, FAM (fuzzy associative memory), FCM (fuzzy cognitive map) and
FNN (fuzzy neural networks).
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Optimization of Bioreactor Controls using
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4. System Identification, Modelling and SimulationThe bioreactor under study is relatively slow to respond and generally it is not
desir-able to develop the controller by experimenting with the actual process.
Therefore, in order to develop the proposed FLC and further optimize it,
modelling the system is necessary to facilitate simulation.
One of the objectives of this work is to develop a controller that is robust
enough to perform well for multiple process models, several of which are
modelled directly from raw process step testing data and two that represent
worst-case scenarios. If this objective can be met then the controller is likely
robust enough to provide good performance in spite of less than perfect
modelling. However, given the difficulty in tuning the proposed controller in
the field, several potential sources of error are incor-porated into the models
including a nonlinear FCV, continuous random disturbances and low-pass
filtering of the feedback signal.
4.1 Bioreactor Step Testing
As mentioned, FOPDT models provide a realistic approach to system
identification for the purpose of system modelling. Much of the previous work
in modelling a bioreactor for the purpose of DO control system simulation has
been con ducted using analytical models derived from mass-balance
equations. The analytical models attempt to incorporate the vast physical,
biological and chemical properties present in a bioreactor, but for practical use
often require several variables to be estimated. Development of FOPDT
models through step testing is chosen for this work due to the realistic nature
of the technique. Through step testing the actual bioreactor under study, the
response of the actual process to a step input is observed and characterized.
In FOPDT modelling, higher order systems are characterized by a first
order approximation plus a transport lag. The three parameters of the FOPDT
model (time constant, steady-state process gain and dead time) are actually a
lumping together of many of the actual parameters of the process. The
purpose is to fit the process response to a curve that is simpler to express. In
turn, this means that it is more difficult to capture the operational ranges of
the process to understand the process capability, since the parameters of the
model are an abstraction of the actual process parameters. One of the
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Optimization of Bioreactor Controls using
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Manipal Global Education Services Pvt. Ltd., Bangalore
Page | 37
drawbacks to FOPDT modelling through step testing is that the process
response is only observed under the operating conditions present during
testing, while the process may respond differently under alternative operating
conditions. Thus, in some cases it is advantageous to observe and
subsequently model the process response under multiple operating conditions
to understand the process.
In the case of the bioreactor under study, there are many process parameters
that affect the response of the system. These include but are not limited to the
physical dimensions of the bioreactor and its associated piping and
components, pressure in the process air header, flow rate of the wastewater,
quality of the secondary sludge, flow rate of the RAS, flow rate of the WAS,
OUR in the bioreactor, quality of the wastewater, temperature of the
wastewater, temperature of the process air, etc. There are many more but
these are examples of the actual process parameters that would need to be
considered in any analytical model of the bioreactor. By contrast, step testing
presents a simple, but effective method of obtaining a reasonably accurate
model. This is especially valid for large, slow processes that do not need to be
controlled precisely, but need to perform reasonably well over a wide range of
process conditions.
It was determined through consultation with the Operators of the bioreactor
that one of the most important factors in the performance of the bioreactor is
the rate of wastewater flow. During times of high flow, the wastewater does
not have the same retention time in the bioreactor and also the high flows
tend to change the dynamics of the organisms in the bioreactor. Therefore, in
order to characterize the process, two conditions are selected to provide two
types of models that establish a worst-case operational range of the system.
The process conditions selected for this purpose are when the bioreactor is
experiencing low or normal wastewater flow rates and when it is experiencing
high wastewater flow rates, such as during a storm or melt event. Therefore,
each of the three cells is step tested during both low flow and high flow
conditions, giving the following specific conditions: cell 1 low flow (C1LF), cell
2 low flow (C2LF), cell 3 low flow (C3LF), cell 1 high flow (C1HF), cell 2 high
flow (C2HF) and cell 3 high flow (C3HF). The experimental step testing data is
plotted in Fig. 4.1.
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Optimization of Bioreactor Controls using
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The process and instrumentation diagram (P&ID) for the bioreactor shown
in Fig. 2.11 depicts the team of blowers which supply process air to a
common header. The common header is shared between two bioreactors and
it makes a constant header pressure available to the cells of the bioreactors
through a modulating, electrically actuated valve. The team of blowers
operates in such a way that blowers are brought online and taken offline
according to the demand for air, as sensed by a pressure transmitter on the
common header. One important point to consider in this test scenario is that if
the system dynamics change significantly and a blower needs to be brought
online or taken offline during the test, it could potentially cause a significant
undesirable disturbance to the system and compromise the test data.
The blower control system is not part of this work, however, it is important to
understand how it works in order to appreciate how the step testing is carried
out. The blowers are full-voltage non-reversing (FVNR) motors. The airflow
through each blower is controlled by modulating an electrically actuated valve
on the suction side of the blower. The operational regime of the blower
system is such that if the demand for process air is reduced beyond a certain
threshold, then blowers must be taken offline or they will automatically shut
down due to electrical current limitations, possibly causing an undesirable
disturbance. Hence, if the bioreactor FCVs are closed for step testing, it will
cause this very situation and as the valves are opened, and demand for
process air increases, blowers will be brought online causing step changes in
the header pressure.
6 45
4.8 36
a
n
ow
DO
(mg/L)
3.6 27
2.4 18
1.2 9
30 60 90 120
Time (min.)
(a)
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Optimization of Bioreactor Controls using
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1.5 75
1.2 60
PlantFlow
(MLD)
DO(mg/L)
0.9 45
0.6Cell 1
30
0.3Cell 2
15
Cell 3
Plant Flow
30 60 90 120Time (min.)
(b)
Figure 4.1: Plant flows during bioreactor step testing. (a) Low flow condition;
(b) High flow condition.
In addition, if the blowers are brought online, and then are taken offline again,
they have a ten minute restart inhibit period before they can be brought online
again.
The situation described above is mitigated by testing only one of the two
bioreactors and utilizing the second bioreactor to assist in manually controlling
the conditions of the process air header to ensure that blowers are not
brought online or taken offline during testing. It is noted that this method inconjunction with the existing blower control loop produces a very stable
header pressure. The step testing data is plotted with the header pressure in
Fig. 4.2, showing a header pressure setpoint of 55 kPa being tracking very
tightly.
The step testing is completed by first closing the FCVs for the selected
bioreactor. Each cell is then tested individually by opening the FCV to 100%.
The response of the DO concentration in the bioreactor is measured by DO
transmitters and is recorded in the supervisory control and data acquisition
(SCADA) system. The step test results are shown in Fig. 4.1 and 4.2. Fromthe results it can be generalized that when the flow is low, the process has a
higher gain.
An important characteristic of a system where multiple processes are present
is whether the processes interact. Interacting processes typically require a
decoupling mechanism for the controllers to avoid fighting each other. In the
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case of the bioreactors in this work, they are designed such that wastewater
flows in one direction and there are baffles between the aeration cells that
allow only a few inches of water to flow over to the next cell. This design
minimizes the backflow of oxygen from downstream aeration cells.6 60
4.8 48
Pressure(kPa)
DO(mg/L) 3.6 36
2.4 24
1.2 12
30 60 90 120Time (min.)
(a)
1.5 60
1.2 48
Pre
ssure(kPa)
DO
(mg/L) 0.9 36
0.6Cell 1
24
0.3Cell 2
12
Cell 3
Pressure
30 60 90 120Time (min.)
(b)
Fig. 4.2: Header pressure during bioreactor step testing. (a) Low flow
condition; (b) High flow condition.
The step testing is completed in the order of the most downstream cell to
the least downstream cell. This means that once a cell is tested, because it
cannot interact with upstream cells, it can be returned to service. This is
demonstrated by the results in that during both tests, when cell 3 is tested in
isolation, no response is observed in cells 1 and 2. Since the DO does not
migrate to upstream cells, the cells do not interact.
One might presume that as the wastewater flows downstream it carries
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Optimization of Bioreactor Controls using
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Manipal Global Education Services Pvt. Ltd., Bangalore
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with it some DO, however, the test results do not indicate this. During the low
flow step testing, each cell is returned to service after it is tested. However,
during the high flow step testing, cell 1 and cell 3 are inadvertently returned to
service for a brief period while step testing cell 2. The results indicate that the
contribution of DO from cell 1 and cell 3 to cell 2 during this period is
negligible, and that very little DO flows upstream or downstream to adjacent
cells.
4.2 Development of FOPDT Models
From the step testing data, the values for the FOPDT model parameters for
each process are extracted. There are methods to characterize the response
graphically in a piecewise fashion by observationally extracting the dead time
and steady-state process gain and then deriving the time constant. However,
for the purpose of this work, in order to generate the models as accurately as
possible, the models are simulated and tuned to match the step test process
reaction curves as closely as possible. The FOPDT model step responses are
plotted with the actual step test process reaction curves in Fig.s 4.3 and 4.4.
While the data collected during step testing is not perfect due to the number of
disturbances inherent in the process, the FOPDT models produce step
response curves that match the actual process reaction curves very well. Two
proposed worst-case models are developed by inspecting the process models
obtained experimentally and the use of two assumptions. The two
assumptions are that increasing process gain leads to decreased stability and
that increasing dead time leads to decreased stability. The time constant of
the process is varied to provide two extremes, one when the time constant is
relatively fast and one when it is relatively slow. The largest time constant is
doubled and the smallest time constant is halved to create the two scenarios.
The other two parameters, process gain and dead time, are doubled for each
scenario to create the two worst-case scenarios at opposite extremes of the
operational range of the bioreactor. The selected values for the parameters of
the process and worst-case FOPDT models are shown in Table 4.1.
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