Conference PaperPDF Available

Nonlinear Fuzzy Model Predictive Control of the TCP-100 Parabolic Trough Plant

Authors:
Nonlinear Fuzzy Model Predictive Control of the TCP-100 Parabolic
Trough Plant
Juan Manuel Escañoaand Antonio J. Gallegoaand Adolfo J. Sánchezaand Luis J. Yebraband Eduardo F. Camachoa
aDepartment of System Engineering and Automatic Control, Universidad de Sevilla, Seville, Spain.
jescano@us.es;agallego2@us.es;asanchezdelpozo@us.es;efcamacho@us.es
bPlataforma Solar de Almería CIEMAT, Tabernas, Spain. luis.yebra@psa.es
Abstract
Advanced control strategies can play an im-
portant role in improving the efficiency of
solar plants. In particular, linear model pre-
dictive control strategies have been applied
successfully when controlling solar trough
plants. However, if the control algorithm
uses a linear model associated only with one
operating point, when the plant is working
far from the design conditions, the perfor-
mance of the controller may deteriorate.
In this paper, a fuzzy model-based nonlin-
ear model predictive controller is applied
to the new TCP-100 solar facility. The
control strategy uses a fuzzy model of the
plant for predicting the future evolution of
the outlet temperature. This approach re-
duces the computational time of the nonlin-
ear model predictive control strategy and al-
lows to solve it much faster than using the
full nonlinear model.
Keywords: Control, Model Predictive Con-
troller, Fuzzy model, solar trough, Nonlinear
MPC.
1 Introduction
There is a pressing need to increase the use of renew-
able energy sources. The need to reduce the environ-
mental impact produced by the use of fossil energies is
a very important objective as stated by the International
Renewable Energy Agency, the European Commission
and the National American Academy [1, 2]. As far as
the renewable energy sources is concerned, solar en-
ergy is the most abundant renewable energy available.
In fact, wind and most of the hydraulic energies depend
on solar energy [7, 5].
Many solar energy plants have been built around the
world in the last 20 years using multiple technologies:
parabolic trough, solar power towers, Fresnel collec-
tor, solar dish, solar Furnaces etc. In this paper we fo-
cus on parabolic trough solar plants. Many examples
of solar thermal plants can be found in [19]. One of
the first operative solar trough plant was the ACUREX
field at the Plataforma Solar de Almería and many con-
trol strategies for solar systems have been tested here
[10, 29, 30].
The use of solar energy has to address two important
problems. The first is to make it economical and com-
petitive. This can be achieved by reducing investment
and operating cost and by increasing the overall perfor-
mance [6]. Advanced control and optimization tech-
niques play a decisive role dealing with those issues.
The control objective in this kind of plants is to regu-
late the outlet temperature around a desired set-point.
The application of control strategies to solar plants
faces two problems: a) the primary energy source, so-
lar radiation, cannot be manipulated acting as a distur-
bance and b) the highly nonlinear nature of the process
[16]. This produces that conventional linear model pre-
dictive control strategies do not perform properly when
working far from the design point. Nonlinear model
predictive control strategies can be used but the prob-
lem is that the computational effort is much higher than
solving the linear case and attaining the global opti-
mum is not ensured [26]. Several approximations to
solve the nonlinear problem can be found in literature
[3, 22, 24] but they do not solve the full constrained
nonlinear problem. One of the problems is that the
use of the full nonlinear model to predict the future
response is the computational time invested. One pos-
sible approach is using a fuzzy algorithm to learn the
evolution of the distributed parameter model and using
it as a prediction model.
Some examples of using fuzzy control strategies have
been used in control of solar energy plants [9]. In
Atlantis Studies in Uncertainty Modelling, volume 3
Joint Proceedings of the 19th World Congress of the International Fuzzy Systems Association (IFSA), the 12th Conference of the European Society
for Fuzzy Logic and Technology (EUSFLAT), and the 11th International Summer School on Aggregation Operators (AGOP)
Copyright © 2021 The Authors. Published by Atlantis Press International B.V.
This is an open access article distributed under the CC BY-NC 4.0 license -http://creativecommons.org/licenses/by-nc/4.0/. 235
[15], a fuzzy predictive controller was applied to the
ACUREX plant. The controller was tested on simula-
tion and compared to a classical MPC strategy. More
recently, in [8] a fuzzy algorithm was used to imple-
ment the selection of the operation mode for a solar
cooling plant. This approach avoided the need of solv-
ing a hard nonlinear optimization problem.
Thanks to the structure of fuzzy systems, there have
been several simplified ways of implementing Fuzzy
Model-based Predictive Control (FMPC). Although
with suboptimal solutions, FMPC presents better per-
formance than strategies based on linear models. Some
techniques take advantage of the structure of the
Takagi-Sugeno models, designing a linear MPC con-
troller uj(k)for each consequent, calculating the con-
troller output as
u(k) =
L
j=1
n
i=1µi j(k)
N
j=1n
i=1µi j(k)(k)uj(k)(1)
Where µi j(k)membership degree of input ito the
membership function defined by the rule jfor such in-
put. Nand nare number of rules and inputs respec-
tively. This technique and its variants can be seen in
[14, 18]. Although this technique is simple enough to
be implemented in industry, it presents a serious prob-
lem with increasing fuzzy model rules, when it is ac-
curate enough. In [13] a complexity reduction tech-
nique is presented to solve this issue. The global op-
timum is also not always found and the design may
not guarantee stability. In [25] an explicit formula-
tion of a Fuzzy Generalized Predictive Control (FGPC)
is obtained without restrictions, guaranteeing stabil-
ity. Some FMPC strategies linearize the fuzzy model
around an operating point, solving a linear MPC prob-
lem [4, 27, 31, 28].
Recently, MPC for Programmable Logic Controller
(PLC) have been presented [23], in which, using real-
time optimization function blocks, developed under the
IEC 61131 standard, allow the implementation of MPC
(with constraints) in PLCs. This, together with the ex-
istence of the IEC 61131-7 part, which standardizes
the fuzzy control language for PLCs, can allow a prac-
tical realization of the FMPC. In this paper, a fuzzy
predictive controller is designed and tested for the new
PTC TCP-100 research facility at the PSA, currently
under construction, is presented. The control strategy
is tested on the mathematical model of a loop described
in [17], because the plant is not operative yet. A non-
linear fuzzy model is obtained to predict the future
evolution of the plant. The main advantage of using
a fuzzy model instead of the full nonlinear model is
that the computation time is much faster.
The paper is organized as follows: section 2 describes
Figure 1: Lateral view of the first TCP-100 PTC in
the first loop at Pataforma Solar de Almería (PSA-
CIEMAT). It is composed of 8 modules of 12 meters
length. Courtesy of PSA.
Figure 2: Top view of the TCP-100 field at Plataforma
Solar de Almería (PSA-CIEMAT). Courtesy of the
PSA.
the plant TCP-100. Section 3 presents the mathemati-
cal model used in this paper to test the controller. The
fuzzy model of the plant is presented in section 4. Sec-
tion 5 describes the fuzzy model-based predictive con-
trol strategy proposed in this work and some simula-
tion results. Finally, a section providing some conclud-
ing remarks is included.
2 TCP-100 solar field description
The TPC-100 solar facility has been built at the
Plataforma Solar de Almería (CIEMAT) replacing the
old ACUREX solar trough plants which operated more
than 30 years. The new plant is designed to be an ex-
perimental plant to develop research in automatic con-
trol of parabolic trough solar field.
The new TCP-100 solar field is composed of three
North-South oriented loops of parabolic trough collec-
tors (PTC). Each loop consists of two PTCs of 96 m
long each placed in series. Fig. 1 shows the first PTC
in the first loop.
The PTCs in each loop are connected in the South ex-
treme, and the colder PTC will be always the first in
the row, placed at the right part of each loop in Fig. 2.
Some novel features are implemented in the new field
Atlantis Studies in Uncertainty Modelling, volume 3
236
compared to the old ACUREX plant. These aimed
at implementing novel advanced control techniques
which may use multiple measurements provided by all
sensors located at several places along the loop. Some
of these characteristics are:
Inlet and outlet solar field temperature sensors.
For each loop, inlet and outlet temperatures are
measured. Inside the loop, for each PTC: inlet,
outlet and middle point temperatures sensors are
located.
Volumetric flow rate for each loop.
Control valves in each of the loops to regulate
mass flow rate in each loop.
A more complete description can be found in [17].
3 Mathematical model of a parabolic
trough loop
The mathematical model of the parabolic trough loop
used in this paper is presented. Since the TCP-100 so-
lar facility is formed by 3 parallel loops, the whole
plant model can be implemented by connecting the
model loops in parallel.
Each of the TCP-100 loops consists of two eight mod-
ule PTCs suitably connected in series. Each collector
measures 96 m long and the passive parts joining them
(parts where solar radiation does not reach the tube)
measures 24 m long.
This sort of systems can be modeled by using a lumped
description (concentrated parameter model) or by a
distributed parameter model [11]. The approach used
here to simulate the plant is the distributed parameter
model as it describes better the system dynamics.
3.1 Distributed parameter model
The model equations are the same used in the
ACUREX solar field developed in [11] and [6]. The
model consists of the following system of non-linear
partial differential equations (PDE) describing the en-
ergy balance:
ρmCmAm
Tm
t=IKo ptcos(θ)GHlG(TmTa)
LHt(TmTf)
(2)
ρfCfAf
Tf
t+ρfCfqTf
x=LHt(TmTf)(3)
Where the subindex mrefers to metal and frefers to
the fluid. The model parameters and their units are
shown in table 1.
Symbol Description Units
t Time s
x Space m
ρDensity Kgm3
C Specific heat capacity JK1kg1
ACross Sectional Area m2
T(x,y)Temperature K,°C
q(t)Oil flow rate m3s1
I(t)Solar Radiation W m2
cos(θ)Geometric efficiency Unitless
Kopt Optical efficiency Unitless
GCollector Aperture m
Ta(t)Ambient Temperature K,°C
HlGlobal coefficient of thermal loss W m2°C1
HtCoefficient of heat transmission metal-fluid W m2°C1
Lwetted perimeter m
Table 1: Parameters description
The density and specific heat of the fluid depend on
the temperature. The coefficient of heat transmission
depends not only on the temperature value but on the
oil flow as explained in [20].
The heat transfer fluid (HTF) is Syltherm800. Its prop-
erties have been obtained using data in the datasheet.
The mathematical expressions are described in detail
in [17]. The density and the specific heat of the fluid
can be computed as follows:
ρf=0.00048098T2
f0.811Tf+953.65 (4)
Cf=0.0000001561T2
f+1.70711Tf+1574.2795 (5)
And the coefficient of heat transmission can be com-
puted using the equation (6):
Hv(T) = 2·(0.00016213T3
f+1.221T3
f
+115.9983Tf+12659.697)
Ht=Hv(T)q0.8(6)
The thermal losses coefficient depends on the working
temperature and the ambient temperature. It has been
estimated considering that the overall thermal losses
for 400 °C are about 265 W/m2as the design condi-
tions for the metal tube stated [17].
The optical efficiency, Kopt , takes into account fac-
tors such as reflectivity, absorptance, interception fac-
tor and others. The peak optical efficiency is about 0.76
according to the plant technical report.
The geometric efficiency, cos(theta), is determined by
the position of the mirrors respect the radiation beam
vector. It depends on hourly angle, solar hour, declina-
tion, Julianne day, local latitude and collector dimen-
Atlantis Studies in Uncertainty Modelling, volume 3
237
40 60 80 100
3
q(k-1) (m /h)
0
0.5
1
Degree of membership
300 400 500
Tf(k-1) (ºC)
0
0.5
1
Degree of membership
300 400 500
T(k-2) (ºC)
0
0.5
1
Degree of membership
0 200 400 600
2
I(k-1) (W/m )
0
0.5
1
Degree of membership
C1= -0.13·q(k-1)+1.22·T(k-1) -0.39·T(k-2)+0.02·I(k-1)+61.37
C2= -3.05·q(k-1)+1.78·T(k-1)-0.80·T(k-2)+0.01·I(k-1)+68.63
C3= -0.09·q(k-1)+1.64·T(k-1) -0.70·T(k-2)+0.01·I(k-1)+23.98
C4= 0.014·q(k-1)+1.72·T(k-1) -0.75·T(k-2)+0.01·I(k-1)+9.36
C5= -0.046·q(k-1)+1.38·T(k-1) -0.51·T(k-2)+0.01·I(k-1)+41.85
Figure 3: Membership functions and consequents re-
sults from SC over process data.
sions. The complex calculations needed for obtaining
these parameters are shown in [17].
4 Fuzzy model of a parabolic trough loop
For the design of the fuzzy inference system (FIS), the
data generated by the distributed parameter model de-
scribed above were used, with a sampling time of 25
s. Subtractive Clustering (SC) [12] is used to obtain
an initial structure with which, through the grouping
of data in areas of the input space, the membership and
consequent functions are obtained, ready to be subse-
quently trained. Observing the relationships between
the variables in equations 2 and 3 and considering sec-
ond order local models, the following vector of in-
puts is chosen: [q(k1),T(k1),T(k2),I(k1)],
where qis the oil flow rate in m3/h,Tis the outlet
temperature (in oC) and I, the Direct Normal Irradi-
ance (DNI) in W/m2.
Figure 3 shows the antecedents and the consequents af-
ter using SC. After obtaining the initial fuzzy system,
a data set with different values of steps in the input
flow rate and different days with irradiance perturba-
tions has been prepared. With this data set, a Particle
Swarm Optimization algorithm [21] has been used to
fit the membership functions of the initial fuzzy sys-
tem to the data. To avoid overfitting of the new ad-
justed FIS, validation data have been reserved sepa-
rately. Figure 4 shows the result of the training.
Figure 4 shows the antecedents and the consequents
after the optimization process. Using a validation data
40 60 80 100
0
0.5
1
Degree of membership
300 400 500
0
0.5
1
Degree of membership
300 400 500
0
0.5
1
Degree of membership
0 200 400 600
0
0.5
1
Degree of membership
3
q(k-1) (m /h) Tf(k-1) (ºC)
T(k-2) (ºC) 2
I(k-1) (W/m )
C1= -0.13·q(k-1)+1.22·T(k-1) -0.39·T(k-2)+0.02·I(k-1)+61.37
C2= -3.05·q(k-1)+1.78·T(k-1)-0.80·T(k-2)+0.01·I(k-1)+68.63
C3= -0.09·q(k-1)+1.64·T(k-1) -0.70·T(k-2)+0.01·I(k-1)+23.98
C4= 0.014·q(k-1)+1.72·T(k-1) -0.75·T(k-2)+0.01·I(k-1)+9.36
C5= -0.046·q(k-1)+1.38·T(k-1) -0.51·T(k-2)+0.01·I(k-1)+41.85
Figure 4: Membership functions and consequents final
result.
set for the resulting FIS, the root mean square error. It
should be noted that the model is auto-regressive, and
it uses its previous out to feed two inputs. Figure 5 de-
picts the difference between the actual temperature and
the model result.
5 Fuzzy model predictive control
strategy
The control scheme is shown in Figure 6. With the
current sampling k, the fuzzy model predicts the out-
put temperature value, if the system evolves forward
in time Np. An optimizer uses the fuzzy model to cal-
culate what sequence of flow rate values qshould be
taken to minimize the following cost function:
J(Np,Nc,δ,λ) =
Np
j=1
δhb
T(k+j|k)TREF (k+j)i2+
Nc
j=1
λ[q(k+j1)]2,
(7)
Where b
T(k+j|k)is the predicted outlet tempera-
ture given by the FIS, from time kforward jsam-
ples (chosen, due to model structure, 25 s). q(k) =
q(k)q(k1)is the increase in control action. Np
and Ncare known as prediction horizon and control
horizon, respectively.δ,λRare weights used to pe-
nalize each term. To improve the performance of the
optimizer, a half-scale constrained nonlinear optimiza-
tion algorithm, such as active-set, has been used. Once
Atlantis Studies in Uncertainty Modelling, volume 3
238
250
300
350
400
450
500
550
RMSE full model: 3.3187
Real data
Full model
0 100 200 300 400 500 600 700
samples
Teperature (ºC)
Figure 5: Comparison between real temperature output data and FIS output.
Optimizer
FIS
future errors
future inputs
past inputs
and outputs
cost
function
constraints
q < q < q
min max
predicted
outputs
reference
temperature
+
_
Figure 6: FMPC scheme
the q(k+j1)ahead sequence is solved, only the
first element q(k)of the sequence is applied on the
system and the optimization process is recalculated
again, after advancing an instant of time. Figure 2
shows the result of the FMPC control strategy us-
ing real irradiance data from a day with many irradi-
ance perturbations. The following values were chosen:
Np=12,Nc=6,δ=1,λ=25. It can be seen that the
performance of the controller is quite good following
references and rejecting disturbances.
Figure 8 shows a comparison between this strat-
egy and another one where the model is based on the
distributed parameters model (DPMPC) described in
equations 2 and 3. In fact, the IAE is similar but, as can
be seen in Table 2, the average computation time for
the calculation of the control action makes the FMPC
strategy suitable for plant control.
Table 2: Control strategies performance.
Control
strategy IAE Average
comp. time
FMPC 5,65oC0,43s
DPMPC 5,35oC29,72s
6 Conclusion
In this work a nonlinear predictive controller based on
a fuzzy model is applied to the new TCP-100 solar in-
stallation. The control strategy uses a Takagi-Sugeno
fuzzy model of the plant to predict the future evolu-
tion of the output temperature. The approach reduces
the computational time of the nonlinear model predic-
tive control strategy and allows it to be solved much
faster than using the full nonlinear model. The strat-
egy has been tested in simulation, using a concentrated
parameter model of the plant under construction and
real irradiance data. In addition, thanks to new devel-
opments in the use of MPC in mid-range PLCs and the
use of the IEC 61131-7 standard, the strategy can be
implemented in industrial controllers.
Acknowledgement
The authors want to thank the European Commis-
sion for funding this work under project DENiM.
This project has received funding from the European
Union’s Horizon 2020 research and innovation pro-
gramme under grant agreement No 958339. Also,
from the Advanced Grant OCONTSOLAR (Project
ID: 789051) and the Spanish Ministry of Science and
Innovation, project SAFEMPC PID2019-104149RB-
I00.
Atlantis Studies in Uncertainty Modelling, volume 3
239
11 12 13 14 15 16 17
Time (Local Hour)
340
360
380
400
Temperature (ºC)
Set-point
Tinlet+60
Tout Loop 1
11 12 13 14 15 16 17
Time (Local Hour)
400
600
800
1000
DNI (W/m2)
20
40
60
80
Oil Flow (m3/h)
DNI
Q
Figure 7: FMPC performance. Day with irradiance perturbations
12.5 13 13.5 14 14.5 15 15.5 16 16.5 17
Time (Local Hour)
340
360
380
400
Temperature (ºC)
Set-point
Tinlet+60
Tout1 Loop 1
Tout2 Loop 1
12.5 13 13.5 14 14.5 15 15.5 16 16.5 17
Time (Local Hour)
700
800
900
1000
DNI (W/m2)
45
50
55
60
Oil Flow (m3/h)
DNI
Q1
Q2
Figure 8: FMPC (Tout 1) performance Vs DPMPC (Tout 2)
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After decades of research and development, concentrating solar thermal (CST) power plants (also known as concentrating solar power (CSP) and as Solar Thermal Electricity or STE systems) are now starting to be widely commercialized. Indeed, the IEA predicts that by 2050, with sufficient support over ten percent of global electricity could be produced by concentrating solar thermal power plants. However, CSP plants are just but one of the many possible applications of CST systems. Advances in Concentrating Solar Thermal Research and Technology provides detailed information on the latest advances in CST systems research and technology. It promotes a deep understanding of the challenges the different CST technologies are confronted with, of the research that is taking place worldwide to address those challenges, and of the impact that the innovation that this research is fostering could have on the emergence of new CST components and concepts. It is anticipated that these developments will substantially increase the cost-competiveness of commercial CST solutions and reshape the technological landscape of both CST technologies and the CST industry. After an introductory chapter, the next three parts of the book focus on key CST plant components, from mirrors and receivers to thermal storage. The final two parts of the book address operation and control and innovative CST system concepts. Contains authoritative reviews of CST research taking place around the world. Discusses the impact this research is fostering on the emergence of new CST components and concepts that will substantially increase the cost-competitiveness of CST power. Covers both major CST plant components and system-wide issues.
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Preface.- List of figures.- List of tables.- Nomenclature.- Introduction.- Description and dynamic models of the plant.- Basic control schema.- Basic structures of adaptive control.- Model-based predictive control strategies.- Frequency-domain control and robust optimal control.- Heuristic fuzzy logic control.- Summary and concluding remarks.- References.- Index.