IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 1, JANUARY/FEBRUARY 2005
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Neural Optimal Control of PEM Fuel Cells With
Parametric CMAC Networks
Paulo E. M. Almeida and Marcelo Godoy Simões, Senior Member, IEEE
Abstract—This paper demonstrates an application of the
parametric cerebellar model articulation controller (P-CMAC)
network—a neural structure derived from Albus’ CMAC algorithm and Takagi–Sugeno–Kang parametric fuzzy inference
systems. It resembles the original CMAC proposed by Albus in the
sense that it is a local network, i.e., for a given input vector, only
a few of the networks neurons will be active and will effectively
contribute to the corresponding network output. The internal
mapping structure is built in such a way that it implements, for
each CMAC memory location, one linear parametric equation
of the network input strengths. First, a new approach to design
neural optimal control (NOC) systems is proposed. Gradient-descent techniques are still used here to adjust network weights, but
this approach has many differences when compared to classical
error backpropagation algorithm. Then, P-CMAC is used to
control the output voltage of a proton exchange membrane fuel
cell (PEM-FC), by means of NOC. The proposed control system
allows the definition of an arbitrary performance/cost criterion to
be maximized/minimized, resulting in an approximated optimal
control strategy. Practical results of PEM-FC voltage behavior at
different load conditions are shown, to demonstrate the effectiveness of the NOC algorithm.
Index Terms—Control systems, fuel cells (FCs), neural networks,
optimal control.
I. INTRODUCTION
P
ARAMETRIC cerebellar model articulation controller
(P-CMAC) artificial neural networks (ANNs) were introduced very recently[1], as fast and efficient alternatives to
commonly used multilayer perceptron (MLP) networks for
applications like function approximation and signal processing.
P-CMAC architecture is based on the CMAC networks and on
Takagi–Sugeno–Kang parametric fuzzy systems (TSK-fuzzy
systems). CMAC networks were proposed in 1972 by Albus
[2], [3] to control robotic manipulators; however, the enormous
success of that algorithm in the control field has motivated
its utilization in some other important areas [4], [5], and even
some improvements in the original algorithm, to overcome
its limitations [6], [7]. In 1985, Takagi, Sugeno, and Kang
Paper MSDAD-A-04-20, presented at the 2003 Industry Applications Society
Annual Meeting, Salt Lake City, UT, October 12–16, and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Industrial
Automation and Control Committee of the IEEE Industry Applications Society.
Manuscript submitted for review October 15, 2003 and released for publication
July 7, 2004. This work was supported in part by the National Science Foundation and in part by the Brazilian agency CAPES.
P. E. M. Almeida is with the Federal Center for Technological Education
of Minas Gerais, 30.510-000 Belo Horizonte, Brazil (e-mail: pema@lsi.cefetmg.br).
M. G. Simões is with the Engineering Division, Colorado School of Mines,
Golden, CO 80401-1887 USA (e-mail: msimoes@mines.edu).
Digital Object Identifier 10.1109/TIA.2004.836135
proposed TSK-fuzzy systems [8], [9]. As shown by some
researchers, they present very good function approximation
features [10], [11]. A P-CMAC network retains the local data
flow properties of CMAC and implements parametric fuzzy
equations in a hidden layer inside the network, resembling
TSK-fuzzy systems.
We demonstrated in previous work that a P-CMAC works
in a reliable and robust way to approximate nonlinear arbitrary
mappings, starting from big and ill-conditioned data sources,
while other approaches had difficulties achieving good results
[4]. To illustrate this, a P-CMAC was successfully used to solve
a signal-processing problem at a mobile telephony field [12].
ANNs have often been used as basic and complementary tools
inside process control systems, mainly in cases where conventional control techniques cannot be applied or do not offer reasonable performance. Actually, process control researchers have
begun replacing these conventional solutions (which demonstrated inefficiency) with alternate algorithms that were based
on ANN and other similar techniques. For instance, some tasks
like function approximation, dynamic systems modeling, parameter identification, optimization, and process regulation are
being performed using such algorithms in a simpler, easier, and
more effective way, when compared to the old techniques used
before [13], [14].
This paper presents a process control approach, based on
P-CMAC networks, which approximates the behavior of an
optimal controller. Design (or offline training) and tuning (or
online training) steps are described in detail. This method is
based on some other techniques used to approximate optimal
control behavior in the literature [15]–[17]. However, there are
clear differences between our approach and these techniques,
as this paper will show. We named our approach neural optimal
control (NOC), to distinguish it from the existing architectures.
Here, a dynamic model of a proton exchange membrane fuel
cell (PEM-FC)—originally developed at the Federal University
of Santa Maria, Santa Maria, Brazil [18]—is adapted to run inside a control scheme. It was used as a test bed for the proposed control architecture, and its output voltage is controlled
by means of an NOC scheme. Presented results showed that the
P-CMAC worked very well and achieved the desired objectives.
This paper is organized into five sections. The fundamentals
of P-CMAC networks are briefly defined in Section II, where
NOC architecture is also introduced. Section III addresses the
adaptation of a dynamic PEM-FC mathematical model to simulate a closed-loop control system. Section IV shows results obtained with the proposed control algorithm. Section V concludes
the paper by analyzing obtained results and the NOC architecture performance.
0093-9994/$20.00 © 2005 IEEE
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Finally, the output layer executes weighted summations of the
neurons outputs
from the internal layer, as shown by (3),
and generates network outputs
(3)
B. NOC
Fig. 1. Parametric-CMAC network basic structure.
II. P-CMAC NETWORKS AND NOC
A. P-CMAC Architecture
P-CMAC networks aim to minimize the existing limitations
of Albus’ CMAC algorithm. Non-smooth response for smooth
inputs, and poor representation capabilities for complex systems
(due to binary behavior of CMAC receptive fields) are two of the
classical problems with those algorithms.
P-CMAC networks have an important modification in their
internal mapping when compared to CMAC. A CMAC internal
memory is implemented as a bit memory location connected to
the binary input activation functions. Fuzzy-CMAC networks
use real-valued memories, and each of them corresponds to the
membership grade of the input with respect to the fuzzy activation functions [4]. In a P-CMAC, these constant valued memories are replaced by parametric equations (in terms of the network inputs) and the membership grades of these inputs with
respect to fuzzy activation functions. Fig. 1 shows a schematic
diagram of the P-CMAC architecture.
In Fig. 1, the input mapping transforms input signals into
membership grades with respect to the fuzzy activation functions defined within input spaces. Equation (1) illustrates this
, considering a given input and a radial basis
mapping,
. In this equation,
activation function represented by
represents the radial function center and its curvature index
(1)
In the internal layer, the th neuron of a P-CMAC network
implements (2), where
are real-valued adjustable parameare the inputs to the network, and the operator repters,
resents a fuzzy conjunction operation between the membership
grades of the inputs that are connected to this neuron. This operation is represented in Fig. 1 by the legend “Nonlinear Mapping.” Here, we use multiplication
(2)
The main difficulty with using supervised training and ANN
to control dynamic systems is to acquire input–output data suitable for the controller network training phase. In the case of control systems, this is due to the desired controller output signals
not being explicitly known by the designer. Therefore, it is necessary to use an auxiliary algorithm to convert the known system
desired outputs into the corresponding controller outputs responsible for these systems outputs. Most of the approaches that
use neural networks to control dynamical systems employ the
backpropagation algorithm, or a variant of it, to obtain proper
values for controller training.
Starting from an ANN trained as a model of the physical
system to be controlled, the plant desired output is backpropagated through this model network and generates, at the network
input, a signal proportional to the control signal, which should
be applied to the plant to drive it to the desired state. One of
the first neural control approaches is the so-called direct-inverse
neural control [19]. In this case, one tries to teach an ANN to behave like the inverse model of the plant to be controlled. Connected in cascade with the physical system input, this network
should minimize the system dynamics and transfer the desired
states directly to the system outputs.
This approach can be considered a version of the classical
dead-beat controller adapted to the ANN paradigm. The advantages here are the online adjusting properties of the ANN, which
make the resulting control scheme much more resistant to physical variations in the controlled system. This was one of the key
problems limiting the employment of classical dead-beat controllers in actual control systems.
Common problems with direct-inverse control are the very
large control signal amplitudes that result from the controller
network [20, p. 246]. That leads to a control system which depends on a very large amount of energy to control the plant.
This occurs due to existing modeling errors, to imperfect poles
and zeros canceling, and to the introduction of high-frequency
poles in the closed-loop system. This last side effect causes
the resulting controller to generate highly varying control signals, which are not recommended in practical plants. As every
practical system has energy limitations, this approach cannot be
fairly employed in actual control systems.
A simple way to avoid the high amplitude and highly varying
control signals is to insert a reference model in the control loop.
Now, the ANN controller is trained to respond in closed loop,
as a linear system model chosen by the designer.
With these control schemes in mind, and starting from
popular dynamic optimization techniques discussed in [13],
here, an innovative control architecture is proposed to integrate
P-CMAC networks into an approximated optimal control
scheme. The resulting architecture is based on the reference
ALMEIDA AND SIMÕES: NOC OF PEM-FCs WITH P-CMAC NETWORKS
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C. ANN With Long- and Short-Term Memories
Fig. 2. NOC architecture diagram using P-CMAC networks.
model direct-inverse control approach; however, the training
algorithm has been improved. The designer can now define a
cost or performance criterion, and the controller network is
trained to simultaneously regulate the system and minimize
this criterion. An example of a typical cost criterion is shown
below in (4)
(4)
This criterion states that the error between the desired state
and actual state must be minimized and that, at the same time,
the resulting control signal must be minimized. The quadratic
function of control signal can be interpreted as the amount of
energy used to control the physical system. Thus, this criterion
is a tradeoff between output error and the total energy spent
to keep a low output error in the system. and parameters
can be adjusted to fine tune the performance of the resulting
controller.
The control architecture hereby proposed was named NOC
to avoid confusion with other similar schemes existing in the
literature. Although NOC is loosely based on the Werbos backpropagation of utility [17], which in turn culminated with the
proposition of neural dynamic programming (NDP) techniques
[15], NOC does not use the adaptive critic network concept as
NDP methods do. Moreover, NOC employs other tools, (like a
reference model and a second P-CMAC network trained as a direct model of the plant), to obtain desired control signals and
to adjust the controller network. Fig. 2 shows a diagram of the
NOC architecture.
In Fig. 2, system output is compared to a reference model
chosen by the designer. This offset signal is then fed back to the
cost criterion, together with the backpropagated desired control
signal from the direct model. The controller network is trained
to minimize this criterion, approximating the overall operation
to the operation of a conventional optimal controller.
In Fig. 2, can be a nonmeasurable, environmental, constructive, or random parameter. If of an environmental nature,
it can represent temperature variations that could have an influence on the control system. It can also represent nonmodeled
constructive aspects such as sensor and actuator nonlinearities.
In addition, it could take into account low-frequency noise existing in the process. Dust in connection pipes and equipment
long-term drifts are good examples of such kinds of low-frequency noise. At any rate, variation of will, from time to
time, determine different operating points; the control system
should work well despite the occurrence of any value for this
parameter.
In a sequence of technical papers, Lo proposed the ANN
with long- and short-term memories (LSTM), with application
to identification of dynamical systems [10], [21]. In his work,
the drawbacks of adaptive adjusting of an ANN to system identification are discussed. By adaptive adjusting, Lo means online
training of all weights in the model networks. These drawbacks
can be summarized as follows.
1) The existing algorithms to perform adaptive adjusting,
like backpropagation, Kalman Filters and others, spend a
lot of memory and CPU time and have very low convergence rates.
2) The criterion to be minimized, in the case of a whole network with nonlinear neurons, presents a quadratic function or high order. This implies the existence of poor
quality local minima. Online training allows neither multiple session optimization, nor employment of global optimization methods. Therefore, the probability of finding
and getting stuck on a poor local minimum is very high.
3) Online adaptation of all the network weights does not intelligently use available, large data sets. Because it does
not give priority to identify the system dynamics (or some
specific operation points of the plant), the resulting network is not a good approximation of the system to be modeled.
A natural way to avoid these drawbacks is to create an ANN
with two different kinds of weights: some related to a long-term
memory and others related to a short-term memory. The former
must be trained offline from a big data set, which in turn should
represent the system to be modeled for a variety of conditions
and operating points. The latter must be trained online to fine
tune the network response to the instantaneous operating condition.
In other words, long-term training is focused on getting
the main dynamics of the system modeled. After this offline
learning phase, the long-term weights or memories must be
kept constant, to preserve the grabbed information. The data
set used to train the long-term memories in an LSTM neural
network must include all operating points of interest and many
different values for the environmental parameter .
Now, let us consider different values for , given by
(5)
These are exemplary values of environmental, constructive,
and low-frequency noise referring to the system to be modeled.
For each one of these ’s, there should exist a subset with
input–output pairs, where each pair is
, in such a way
and represents a mapping between the
that
must be unisystem’s input and output signals. Input values
formly chosen inside the region of interest (or in a region slightly
larger than the actual region of interest), to allow for good approximation of its boundaries. It is important that the long-term
data set comprises input–output pairs covering the whole region
of operation of the plant.
The value of a long-term memory will be the same for all
values of , (i.e., long-term training is independent of the various
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considered in this training phase). This offline training of a
LSTM network can be based on a long-term criterion like
(6)
where
(7)
is a utility function that measures the error between the desired
and the actual output of the modeled system. During long-term
training, this criterion is minimized for all possible values of the
adjustable parameters . This is a soft-constrained optimization
problem to which many traditional methods can be applied and
can often achieve exact solutions.
On the other hand, weights related to short-term memory
should be trained online through a performance criterion based
on the capture of specific environmental/constructive parameters currently active in the plant or control system. Adjustment
of these weights will improve the controller performance for
these values of . For this specialized training, one assumes that
the value of varies over time in an unknown or random way.
However, there exists a number of input/output data measurements between two consecutive changes on it. This data set can
then be used to adjust short-term memories of the network so
that they take into account this unique value of now active.
From long-term training, a performance criterion can consistently be defined for specialized training, like the expression
(8)
where
(9)
are long-term memory values obtained during offline
and
training and is a forgetting factor which weights each instantaneous utility function based on its temporal proximity. In other
words, the older data will have less contribution during minicriterion.
mization of
If an ANN has only linear activation neurons at its output
layer, and the weights of this output layer are chosen to be the
short-term memories of this network, then short-term training
will be equivalent to a multiple linear regression algorithm.
Thus, there will be no local minima, and convergence of
training will imply that the global minimum of the short-term
criterion has been achieved.
In summary, an ANN with LSTM has: 1) a long-lasting or
long-term memory, reflecting basic features of the plant to be
modeled and ensuring that further training in other parts of the
network will not deviate much from the original knowledge captured during long-term training and 2) a short-term memory
with continuous or frequent adjustments occurring when environmental changes are detected, reflecting a response of the network to these changes, (i.e., an adaptation of the network to the
newly verified operation conditions).
Lo demonstrated that this approach leads to networks that
exhibit universal approximation properties as well as classical
MLP networks. With practical results, he showed that an MLP
network with LSTM has better performance than a classical
MLP network with the same number of neurons, and avoids
the training drawbacks just discussed [21], [22]. Considering
that P-CMAC networks are feedforward networks with features
similar to those of MLP networks, we assumed that those advantages observed with an MLP with LSTM would also be observed with a P-CMAC. Practical results shown in Section IV
confirm our expectations.
D. NOC Synthesis With P-CMAC and LSTM
Two P-CMAC networks with LSTM are employed to control
a dynamic system. The synthesis or training scheme is divided
into a design phase (when general training is performed), and
a tuning phase (when specialized training is performed). From
a topological point of view, there is no difference between a
conventional P-CMAC network and a P-CMAC network with
LSTM. From a training perspective, a P-CMAC with LSTM has
the following features.
1) The input activation weights and the parametric memories (i.e., the weights inside the parametric layer) turn
into long-term memories of the network. They are trained
during the control system design phase and, during the
tuning phase, their adjusting factors are zero.
2) The weights at the linear output layer turn into short-term
memories of the network. They are adjusted at the design
phase, together with long-term memories, and also at the
tuning phase.
Some differences between the training approach proposed by
Lo and the training approach hereby used are as follows.
1) Training Goal: Lo proposed an MLP with LSTM for dynamic systems modeling. Here, two P-CMAC networks
with LSTM are used to approximate optimal control behavior in a dynamic system. One step of this process does
include a model identification phase, but a control goal
should be considered an extension of a modeling goal.
2) Optimization Criterion: Lo used a quadratic error criterion in his work. Here, we synthesize a control system
capable of approximating its behavior from that of an optimal controller, based on an arbitrary performance or cost
criterion chosen by the designer.
An algorithm to synthesize an NOC system starting from
P-CMAC networks with LSTM is described in Table I.
III. DYNAMIC MODELING OF PEM-FC
A. Basic Functional Principles
An FC is an electrochemical device that converts chemical
energy of hydrogen gas (H ) and oxygen gas (O ) into electrical energy suitable for consumer applications. Today, there
are many different technologies associated with this type of energy conversion. The specific technology to be used depends
mostly on the adequate amount of energy used to drive an application (i.e., the power consumption of the application in mind).
For low-power domestic appliances, the most used technology
these days is the PEM-FC. A typical generation scheme based
on a PEM-FC is shown in Fig. 3.
ALMEIDA AND SIMÕES: NOC OF PEM-FCs WITH P-CMAC NETWORKS
TABLE I
NEURAL OPTIMAL CONTROL SYNTHESIS ALGORITHM
241
1) Nernst potential or open-circuit voltage: the basic reversible voltage generated inside an FC, coming from
the variation of the free Gibbs energy in the chemical
reactions occurring inside the cell;
2) ohmic over-potential: results from resistance to the
electrical transfers through the conductor plates and the
carbon electrodes, besides the electrical resistance of the
composite membrane;
3) activation over-potential: leakage caused by reduction in
the speed of chemical reactions in the electrodes surfaces;
4) concentration over-potential: mass transportation existing inside a FC affecting concentration of input gases
causes fluctuation in the partial pressures of them and
results in voltage drops in the output.
To the right in Fig. 4, one sees the section that models the
charge double layer (CDL)—an electrochemical phenomenon
that is responsible for the dynamic behavior of FC devices.
Because of CDL, output voltage exhibits a time constant after
load changes similar to the time constant of a first-order linear
system. Finally, in the upper right-hand corner of the same
figure, there is the section that calculates generation efficiency
of the FC and output power transferred to the electrical load.
IV. PRACTICAL RESULTS
Fig. 3. Context diagram showing input and output variables of a typical
PEM-FC generation system [26].
B. Simulink Dynamic Model of a PEM-FC
In the current literature, there exist various mathematical
models for evaluating the operation of a PEM-FC. Some are
based on curve-fitting experiments, starting from acquired data
[23]. Others are semi-empirical models that combine experimental data with parametric equations adjusted by comparison
with cells physical variables like pressure and temperature [24].
In both cases, the phenomenon of concentration over-potential is unfairly treated, because of the simplifications adopted by
some, or because of the static behavior of others. Concentration
over-potential is crucial in describing the dynamical behavior
of such systems. The work developed by Corrêa et al. [18], [25]
takes this effect into consideration, (inside a physical variable
modeling approach), and achieves a highly accurate model for
a real-world PEM-FC.
Starting from the electrochemical and thermodynamic representations of a PEM-FC, and from the approach described in
[26], a detailed dynamical model was created using the software
Simulink by The MathWorks Inc. This model will be used as a
test bed for the NOC architecture proposed in Section II. The
model is divided into six main sections according to the physical
phenomena described in the above-cited works. Fig. 4 shows a
Simulink diagram representing the adapted model.
On the left in Fig. 4, one can see the input gas pressures, temperature level, and electrical current imposed by the externally
applied load. Going right, the four main internal generation and
consumption sections are shown from top to bottom. They calculate the following potentials:
As a validation test to the described model, a simulation session identical to that presented by Corrêa et al. is performed
[18]. In that simulation, a PEM-FC starts running in an open-circuit situation (i.e., no load is connected to the output terminals).
Next, an electrical load that consumes 15 A of current is connected to the FC terminals for 10 s. In this case, the open-loop
response of an FC is a high-voltage drop until an equilibrium
level is reached between generated and consumed power. This
occurs because the input gas pressure is maintained constant
throughout the simulation time.
Comparison results are shown in Fig. 5. The response presented by the above-cited work is the cross-marked line, while
the response of the model described here is the circled-marked
line. By inspecting the graphics, one can see that the model responses are very similar.
To illustrate the synthesis of an NOC system using P-CMAC
networks, the PEM-FC Simulink model is employed. The gas
pressure loop is now closed and a control system is used to maintain output voltage constant for any load applied to the FC output
terminals.
A proportional–integral–derivative (PID) controller is used
to control the gas pressure loop for both input gases. As the
stoichiometric consumption rate for the two gases is constant
[13], only one controller is necessary in conjunction with two
independent gains, one for each gas line actuator. A Gaussian
additive noise with amplitude of 5% of the measured variable
(voltage between PEM-FC output terminals) is included in the
control sessions, representing inaccuracies in the acquisition
process. The resulting control diagram is shown in Fig. 6.
A typical result of a control simulation session is shown in
Fig. 7. Inspecting the graphics, one sees that the PID controller is
able to maintain a fairly constant value of the output voltage, for
various values of electrical load applied during the simulation
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Fig. 4.
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 1, JANUARY/FEBRUARY 2005
PEM-FC schematic model adapted to Simulink.
The cost criterion here has two parts. First, it weighs the difference between set-point voltage and actual output voltage of
the PEM-FC model. At the same time, it penalizes variations in
the control variable, gas pressure, allowing for extended operation periods and lower maintenance costs for the FC equipment.
This criterion, expressed by (10), is minimized during the spenetwork, as shown in
cialized training phase of the C
Fig. 8
(10)
Fig. 5. Comparison results of two PEM-FC models—the original developed at
Universidade Federal de Santa Maria, Santa Maria, Brazil, and the other adapted
to Simulink.
time. However, a considerable offset value is present at almost
all times, varying between hundreds of milivolts to a few volts
(depending of the specific load applied to the FC terminals).
This seems to be a limitation of the designed PID controller for
the operation conditions tested.
Next, input/output data of the PID controller, collected
during the control session just described, are used in the general
, which will function
training of the P-CMAC network C
as the controller network inside the NOC architecture (see
Fig. 2).
Fig. 9 shows a typical NOC session of a PEM-FC, using
P-CMAC networks with LSTM. This control system was
network,
obtained after both training phases of the C
general training (or design phase), and specialized training (or
tuning phase).
A comparison between the results achieved by the PID controller and NOC scheme shows that NOC is more accurate than
the PID controller. The calculated mean-squared error between
set-point voltage and actual output voltage is about 0.81 for PID
control sessions and about 0.78 for NOC control sessions. In the
case of NOC, minimization of the second part of the cost criterion resulted in much less variations in the control variable, as
expected. The calculated mean-squared derivative of the control variable is 0.99 for PID control sessions and 0.24 for NOC
scheme sessions, i.e., PID actuator variation is four times bigger
than NOC actuator variation. This difference can be observed
by inspecting gas pressure signals in Fig. 7 and in Fig. 9. This
result shows a clear advantage of the NOC algorithm over the
ALMEIDA AND SIMÕES: NOC OF PEM-FCs WITH P-CMAC NETWORKS
243
Fig. 6. PEM-FC PID pressure control diagram.
Fig. 8. Cost criterion minimization during specialized training.
Fig. 7. PEM-FC PID control: set point, output voltage, H pressure, O
pressure, and load current.
classical PID, as the designer can define proper cost criterion to
your particular needs and the resulting controller is synthesized
to minimize this criterion, in an automated way. During conditions where the load current is supported by the power capacity
of the FC, the error between reference voltage and actual output
voltage is very much around zero, in the case of the NOC architecture. This did not occur anywhere in the case of PID control,
possibly because of the expressive nonlinearities existing in the
control scheme.
Controller tuning is difficult to accomplish when the plant
under control is somewhat complex and exhibits nonlinearities. In that case, an immediate advantage of the NOC architecture, over traditional PID control, is that its tuning phase is
performed in an automated way, through the minimization of
(10) over time.
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to note that NOC synthesis assumes the existence of an initial
controller (which must be able to maintain the plant in stable
operation) as a starting point for its design. This assumption is
not always true and can limit the practical applicability of this
algorithm.
ACKNOWLEDGMENT
The authors are grateful to J. M. Corrêa for his help in modeling the PEM fuel-cell system used in the experiments.
REFERENCES
Fig. 9. PEM-FC neural optimal control—set point, output voltage, H
pressure, O pressure, and load current.
V. CONCLUSION
This paper has proposed a new architecture to synthesize approximated optimal control by means of ANN. The NOC architecture employs two simultaneous networks: one functioning as
a direct model of the plant under control, and the other functioning as the controller, generating control signals to be applied
to the plant. The ANN with LSTM approach (introduced by Lo
for MLP networks) was adapted for use inside the NOC architecture and P-CMAC networks. The advantages of using this approach are noticeable, in terms of both computational costs and
improved performance viewpoints. An algorithm for synthesis
of NOC systems was fully described on a step-by-step basis.
A control system of a PEM-FC was chosen as a test bed
for the NOC architecture. Starting from an existing model,
a dynamical model was adapted for use inside Simulink. An
NOC system was then synthesized (i.e., trained) to control the
PEM-FC output voltage. Obtained results suggest that NOC
works well, and has operation advantages when compared to
the design drawbacks and worse performance exhibited by a
typical PID controller. Specifically speaking, automatic tuning
capability and the choice of the control goals by the designer
grant to the NOC architecture great versatility, flexibility, and
operation robustness.
Offline synthesis efforts and the reliable maintenance of
needed topology during execution are NOC architecture bottlenecks not yet analyzed in this work. In the case of complex
nonlinear plants that are difficult to control, and for systems
that need accurate regulation behavior, the NOC architecture is
absolutely justifiable. For simpler control problems that do not
require a high degree of performance and cost control, conventional techniques can continue to be used. It is also important
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Paulo E. M. Almeida received the B.E. and M.Sc.
degrees in electrical engineering from the Federal
University of Minas Gerais, Belo Horizonte, Brazil,
in 1992 and 1996, respectively, and the Dr.Eng.
degree from São Paulo University, São Paulo, Brazil.
He is an Assistant Professor at the Federal Center
for Technological Education of Minas Gerais, Belo
Horizonte, Brazil. His research interests are applied
artificial intelligence, intelligent control systems,
and industrial automation. In 2000–2001, he was
a Visiting Scholar in the Division of Engineering,
Colorado School of Mines, Golden, where he conducted research in the
Mechatronics Laboratory.
Dr. Almeida is a member of the Brazilian Automatic Control Society. He received a Student Award and a Best Presentation Award from the IEEE Industrial
Electronics Society at the 2001 IEEE IECON, held in Denver, CO. He is also the
recipient of the Third Prize Best Paper Award from the Industrial Automation
and Control Committee of the IEEE Industry Applications Society (IAS) at the
38th IAS Annual Meeting, held in Salt Lake City, UT, in October 2003.
245
Marcelo Godoy Simões (S’89–M’95–SM’98)
received the B.S. and M.Sc. degrees in electrical
engineering from the University of São Paulo, São
Paulo, Brazil, in 1985 and 1990, respectively, the
Ph.D. degree in electrical engineering from the
University of Tennessee, Knoxville, in 1995, and the
Livre-Docência (D.Sc.) degree from the University
of São Paulo in 1998.
He joined the faculty of the Colorado School of
Mines, Golden, in 2000 and has been working to establish research and education activities in the development of intelligent control for high-power electronics applications in renewable and distributed energy systems.
Dr. Simões is a recipient of a National Science Foundation (NSF)—Faculty Early Career Development (CAREER) Award, which is the NSF’s most
prestigious award for new faculty members, recognizing innovative research
of young teachers/scholars. He is serving as the IEEE Power Electronics Society Intersociety Chairman, as Associate Editor for Energy Conversion, as well
as Editor for Intelligent Systems, of the IEEE TRANSACTIONS ON AEROSPACE
AND ELECTRONIC SYSTEMS, and as Associate Editor for Power Electronics and
Drives of the IEEE TRANSACTIONS ON POWER ELECTRONICS. He is the Program Chair for PESC’05, the IEEE Power Electronics Specialists Conference,
to be held in Brazil. He has been actively involved in the Steering and Organization Committee of the IEEE/DOE/DOD 2005 International Future Energy
Challenge.