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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=1∏n

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)G−HlG(Tm−Ta)

−LHt(Tm−Tf)

(2)

ρfCfAf

∂Tf

∂t+ρfCfq∂Tf

∂x=LHt(Tm−Tf)(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 Kgm−3

C Speciﬁc heat capacity JK−1kg−1

ACross Sectional Area m2

T(x,y)Temperature K,°C

q(t)Oil ﬂow rate m3s−1

I(t)Solar Radiation W m−2

cos(θ)Geometric efﬁciency Unitless

Kopt Optical efﬁciency Unitless

GCollector Aperture m

Ta(t)Ambient Temperature K,°C

HlGlobal coefﬁcient of thermal loss W m−2°C−1

HtCoefﬁcient of heat transmission metal-ﬂuid W m−2°C−1

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

f−0.811Tf+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(k−1),T(k−1),T(k−2),I(k−1)],

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+j−1)]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(k−1)is the increase in control action. Np

and Ncare known as prediction horizon and control

horizon, respectively.δ,λ∈Rare 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+j−1)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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