university of brescia, brescia, italy, may 10-11, 2018 ...€¦ · university of padova, ... in...

IFAC PapersOnLine 51-5 (2018) 13–18

ScienceDirectScienceDirect

Available online at www.sciencedirect.com

2405-8963 © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.Peer review under responsibility of International Federation of Automatic Control.10.1016/j.ifacol.2018.06.192

© 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

10.1016/j.ifacol.2018.06.192 2405-8963

Modelling and Simulation of an ArtificialTide Generation System

Davide Tognin ∗, Mirco Rampazzo ∗∗, Martina Pagan ∗∗∗,Luca Carniello ∗, Alessandro Beghi ∗∗

∗ Department of Civil, Environmental and Architectural Engineering,University of Padova, Italy, e-mail: [email protected]

∗∗ Department of Information Engineering, University of Padova, Italy,e-mail: [email protected].

∗∗∗ I.R.S. S.r.l., Padova, Italy, e-mail: [email protected]

Abstract:In this paper we consider a small-scale experimental apparatus that allows to reproduce andunderstand phenomena in large-scale typical lagoonal environments and to draw inferencesabout channel network ontogeny and evolution. In particular, the device reproducing theartificial tide is the core of the experimental apparatus and it is controlled in real-time tosatisfactorily reproduce the natural phenomena. The experimental apparatus has an intrinsiccomplexity and it represents an example of a multi-domain physical system (electrical,mechanical, and hydraulic). In order to design and to asses suitable control strategies, we developa Matlab-based simulation environment which is able to reproduce the behaviour of the artificialtide generation system. In particular, we use a hybrid modelling technique which integratescasual and acausal approaches. Finally, the dynamic model is calibrated and validated by usingreal experimental data. The developed model represents a good trade-off between accuracy andcomplexity and it is useful for control system development purposes.

Keywords: Artificial Tide, Causal and Acausal Modelling, Simulation

1. INTRODUCTION

Tidal systems are fragile and interesting environmentsbased on a delicate balance between sediment transport andhydrodynamics. Understanding the main processes thatunderlie the formation and development of tidal networksis necessary to address issues of conservation of thesehabitats, exposed to the effects of climate changes andhuman interference. In a tidal system the primary externalforcing is represented by the tide. The greatest differencebetween tidal networks and their fluvial counterpart isthat they are forced by a bidirectional flux. Indeed, thevelocity is direct towards the land during the flood andtowards the sea during the ebb. Therefore a differencebetween the velocity experienced during the two phasesof the tide has an important influence on the morphologyof a tidal environment. This difference is referred as tidalasymmetry and can be described using the ratio ps betweenthe flood peak and the ebb peak of the cross-sectionallyaveraged velocity (Tambroni et al., 2017). Towards thegoal of gaining further knowledge of some of the physicalprocesses responsible for tidal network development undercertain condition, in particular tidal asymmetries, we setup an experimental apparatus, schematizing a back-barrierlagoonal environment subject to tidal forcings (Stefanonet al., 2010).

It is worth highlighting that, the chance to conductmeaningful in-scale experiments relies significantly onthe behaviour of the artificial tide, that has to exhibitpredefined characteristics. To this aim, the height of the

artificial water wave has to be controlled in real-time.Nowadays, it is a common practice in the design of advancedcontrol systems, to make extensive use of Computer AidedControl Systems Design (CACSD) software tools (Chin,2017; Beghi et al., 2017). These tools allow to simulatethe relevant system dynamics, for a first assessment ofthe different control strategies. In order to setup a usefulsimulation-centric control system design project, there isa preliminary step to be taken into account, namely thederivation of a dynamic model (which translates certaininteresting properties of the real system into mathematicalequations) of the system to be controlled. In order todevelop an effective model we need to knowledge the domainexpert’s (i.e. the actual knowledge of the process and itsproperties) and the knowledge engineer’s (i.e. how theprocess functioning and its properties can be transferredinto a useful model) (Ljung and Glad, 1994).

It is worth noticing that, the considered artificial tide gen-eration apparatus is a non-trivial system from a modellingpoint of view. Basically, it includes a water pump and avertical sharp-edge weir, which oscillates vertically thanksto a stepper motor. The artificial apparatus represents anexample of a multi-domain physical systems (electrical,mechanical, and hydraulic). The system exhibits non-linearbehaviours with fast dynamics (e.g. the electro-mechanicalsub-system) and slow dynamics (the hydraulic sub-system),plus dead time (due to the water mass transport). On theother hand, new technologies provide new opportunitiesfor modelling and simulation. In this paper, we exploit the

1st IFAC Workshop on Integrated Assessment Modellingfor Environmental SystemsUniversity of Brescia, Brescia, Italy, May 10-11, 2018

Copyright © 2018 IFAC 13








1. INTRODUCTION














1. INTRODUCTION














1. INTRODUCTION














1. INTRODUCTION














1. INTRODUCTION







14 Davide Tognin et al. / IFAC PapersOnLine 51-5 (2018) 13–18

Fig. 1. Example of tidal meanders in the Venice Lagoon(Italy). The highlighted portions mark point bars,which are shifted seaward with respect to the apexof the meander.

potential offered by a hybrid approach that combine thetraditional causal (i.e. block-oriented) modelling approachwith the acausal (i.e. declarative) one (Kofranek et al.,2008). Beside this, these tools enable physical modelling ofmulti-domain physical systems. In particular, we developa Matlab-based simulation environment for the artificialtide generation system by means of Simulink causal blockdiagram and Simscape acausal components (Dingyu Xue,2013; Ramin S. Esfandiari, 2014). The model has beencalibrated by using real data which have been gained fromreal experiments in the physical model. Several tests havebeen conducted on the experimental apparatus which showthat the simulation tool is able to reproduce the relevantsystem dynamics.

The paper is organized as follows. In Section 2, theexperimental apparatus is depicted. Section 3 is devotedto the system modelling, and to the model calibration andvalidation. Examples of simulation are shown in Section 4.Some conclusions and remarks are drawn in Section 5.

2. EXPERIMENTAL APPARATUS

To reproduce a typical lagoonal environment we have useda large indoor apparatus, that is schematically depictedin Fig. 2. The system includes two adjoining basinsrepresenting the sea and a back-barrier lagoon (the plantview Fig. 2a). A section of the apparatus is shown in Fig. 2b,while Fig. 2c depicts the lagoon basin and the pantograph.The ultrasonic probe and the recirculating tank are shownin Fig. 2d. The lagoon basin is 5.3m long and 4.0m wide,while the much deeper adjacent sea basin is 1.6m longand 4.0m wide. The sea is separated from the lagoon bya barrier of wooden panels, which can be moved to createinlet with different shape and position and a shelf enable usto represent the gentle slope of the sea bed in front of thelagoon. During the experiments, the lagoon is covered witha layer of sediments made of cohesionless plastic grains.The tide is generated at the sea by the combined actionof a pump and a vertical sharp-edge weir, which is movedby a stepper motor and oscillates vertically. The water

continuously flowing over the weir is collected in a separatetank, where the pump recirculates the flow. The apparatusis equipped with two ultrasonic probes that provide ameasurement of the water level in the sea, a potentiometerto measure the position of the weir and a computer drivenpantograph to survey the bed elevation within the lagoon.It is worth highlighting that, the wave generated at theweir does not maintain its form during the propagation tothe lagoonal inlet, because of inertia. This is the reasonwhy the tidal wave cannot be imposed in the section of the

0.00

0.87

0.00SE

A

SH

ELF

L A G O O N

Probe 1

Inlet

Probe 3

Laser

Panto

gra

ph

Flow meterProbe 2

Pump 1.0 1.50.50 2.0m

PLAN

A

RE

CIR

CU

LA

TIN

G T

AN

K

A

Oscill

ating

weir

(a) Plan view: the rectangular tank, which is divided into the sea andthe lagoon basin, and the recirculating tank, in which the pump islocated.

1.0 m0.750.50.250

SECTION A-A

SEDIMENTS SEA

Oscillating weir Probe1-2

Laser Probe 3

Concrete

bottom

(b) Section A-A: the mechanism of water level variation and theoscillating weir.

(c) View from the right side: the lagoon basin and the pantograph(on the right).

(d) View from the left side: the ultrasonic probe on the sea basin(left), the recirculating tank (right).

Fig. 2. Experimental set-up.

IFAC IAMES 2018Brescia, Italy, May 10-11, 2018

14

Davide Tognin et al. / IFAC PapersOnLine 51-5 (2018) 13–18 15

Fig. 1. Example of tidal meanders in the Venice Lagoon(Italy). The highlighted portions mark point bars,which are shifted seaward with respect to the apexof the meander.

potential offered by a hybrid approach that combine thetraditional causal (i.e. block-oriented) modelling approachwith the acausal (i.e. declarative) one (Kofranek et al.,2008). Beside this, these tools enable physical modelling ofmulti-domain physical systems. In particular, we developa Matlab-based simulation environment for the artificialtide generation system by means of Simulink causal blockdiagram and Simscape acausal components (Dingyu Xue,2013; Ramin S. Esfandiari, 2014). The model has beencalibrated by using real data which have been gained fromreal experiments in the physical model. Several tests havebeen conducted on the experimental apparatus which showthat the simulation tool is able to reproduce the relevantsystem dynamics.

The paper is organized as follows. In Section 2, theexperimental apparatus is depicted. Section 3 is devotedto the system modelling, and to the model calibration andvalidation. Examples of simulation are shown in Section 4.Some conclusions and remarks are drawn in Section 5.

2. EXPERIMENTAL APPARATUS

To reproduce a typical lagoonal environment we have useda large indoor apparatus, that is schematically depictedin Fig. 2. The system includes two adjoining basinsrepresenting the sea and a back-barrier lagoon (the plantview Fig. 2a). A section of the apparatus is shown in Fig. 2b,while Fig. 2c depicts the lagoon basin and the pantograph.The ultrasonic probe and the recirculating tank are shownin Fig. 2d. The lagoon basin is 5.3m long and 4.0m wide,while the much deeper adjacent sea basin is 1.6m longand 4.0m wide. The sea is separated from the lagoon bya barrier of wooden panels, which can be moved to createinlet with different shape and position and a shelf enable usto represent the gentle slope of the sea bed in front of thelagoon. During the experiments, the lagoon is covered witha layer of sediments made of cohesionless plastic grains.The tide is generated at the sea by the combined actionof a pump and a vertical sharp-edge weir, which is movedby a stepper motor and oscillates vertically. The water

continuously flowing over the weir is collected in a separatetank, where the pump recirculates the flow. The apparatusis equipped with two ultrasonic probes that provide ameasurement of the water level in the sea, a potentiometerto measure the position of the weir and a computer drivenpantograph to survey the bed elevation within the lagoon.It is worth highlighting that, the wave generated at theweir does not maintain its form during the propagation tothe lagoonal inlet, because of inertia. This is the reasonwhy the tidal wave cannot be imposed in the section of the

0.00

0.87

0.00SE

A

SH

ELF

L A G O O N

Probe 1

Inlet

Probe 3

Laser

Panto

gra

ph

Flow meterProbe 2

Pump 1.0 1.50.50 2.0m

PLAN

A

RE

CIR

CU

LA

TIN

G T

AN

K

A

Oscill

ating

weir

(a) Plan view: the rectangular tank, which is divided into the sea andthe lagoon basin, and the recirculating tank, in which the pump islocated.

1.0 m0.750.50.250

SECTION A-A

SEDIMENTS SEA

Oscillating weir Probe1-2

Laser Probe 3

Concrete

bottom

(b) Section A-A: the mechanism of water level variation and theoscillating weir.

(c) View from the right side: the lagoon basin and the pantograph(on the right).

(d) View from the left side: the ultrasonic probe on the sea basin(left), the recirculating tank (right).

Fig. 2. Experimental set-up.


14

r PositionController

Stepper controller

uDriver Stepper

Motor

Worm Gear+

Leadscrew

Sharp edgeWeir

Electro-Mechanical Plant

Sea + Lagoon+

Water

Pump

Hydraulic Plant

y

Fig. 3. The electro-mechanical sub-system main components are: the driver and the stepper motor, the worm gear withthe lead-screw, and the sharp-edge weir. The hydraulic sub-system includes mainly: the sea, the lagoon, the water,and the water pump. The water level in the sea y is controlled by manipulating the stepper motor position u. Thestepper controller (highlighted by the red coloured dashed-line) is modelled by means the causal approach whilethe electro-mechanical and hydraulic sub-systems (highlighted by the blue coloured dashed-line) are modelled byusing the acausal approach.

weir but should be reproduced in front of the lagoon to besure of the characteristic of the wave.

The system should reproduce any tidal forcing, in particulartide characterized by ebb and flood dominance, whichcan be seen as sum of sinusoidal signals with a phase lag.Propagating from the weir to the lagoon inlet the wavemodifies because of inertia (i.e. it reduces the amplitude andexperiences a time delay). Therefore, the signal imposed atthe weir, does not overlap the signal in front of the lagoon.

A block diagram of the system is depicted in Fig. 3. Inbroad terms, the system can be outlined as two sub-systemsthat interact with each other in a structured manner:

• the electro-mechanical sub-system, which includes: thedriver, the stepper motor, the worm gear, the lead-screw, and the sharp-edge weir;

• the hydraulic side sub-system, which includes: thewater, the sea, the shelf, the lagoon, and the waterpump.

In order to conduct meaningful in-scale experiments, whichrelies significantly on the characteristics of tide, the waterlevel at the sea is controlled by manipulating the steppermotor position, which in turn, determines the sharp-edgeweir height position, while the water pump is set to a fixedflow rate.

3. MODELLING

In this paper, we design a model-based simulation environ-ment for the artificial tide generation system to preliminaryasses different control algorithms. To this aim, it is acommon practice to build a mathematical model of acomplex system like the considered experimental apparatusby aggregating sub-models of its constituent parts, i.e.by using a modular modelling approach. From this pointof view, two options are generally available: causal (orprocedural) approach and acausal (or declarative) one. It isworth highlighting that, the causality can explain the evo-lution which was in the past declared as the evolution fromblock oriented tools into object oriented tools. In the firstapproach, one assumes that a system can be decomposedinto block diagram structures with causal interactions, themodel is described in a form which is close to the numericalsolution algorithm and the interaction between the modelsis formalized in terms of input and output variables. In thisway, it is rather straightforward to simulate elementary andaggregate models. On the other hand, often a significant

effort in terms of analysis and analytical transformations isneeded to obtain a problem in this form (e.g. the equationswould be converted to ordinary differential equations,ODEs, form manually). Furthermore, the causal modelexhibits low re-usability and the corresponding code maybe difficult to read or modified a posteriori. Conversely, inthe acausal approach, the model is described by equationsin a context-independent form, without caring about theactual solution algorithm (equations are represented asacausal implicit differential algebraic equations, DAEs).It is worth noticing that, in nature real systems areacausal. Furthermore, the interaction between the modelsis formalized in terms of connection equations without anyspecification on causality. The acausal approach exhibitsboth high re-usability and high readability of the basicmodels. On the other hand, it is more difficult to go from themathematical model to the numerical simulation algorithm.It is worth highlighting that, each of the aforementionedapproaches has its intrinsic advantages and disadvantages.In this paper, we want to exploit the advantages providedby both approaches and so a mix of causal and acausalmodels are used. In particular, we develop a Matlab-basedsimulation environment for the artificial tide generationsystem by means of Simulink and Simscape components.In traditional Simulink block-oriented tools (causal), thesignals are transmitted through links between individualblocks and they serve to transfer values of individualvariables from the output of one block to the inputs ofother blocks. Input information is processed in the blocksto output information and the interconnection of blocksreflects both the structure of the modelled real system andthe calculation procedure (Perelmuter, 2017). Conversely,Simscape lets use and define components as textual files,complete with parametrization, physical connections, usingDAEs.

In the following, the main physical components of thesystems, such as the electro-mechanical sub-system andthe hydraulic one are modelled by means of Simscapeblocks, while the control systems are modelled by meansof traditional Simulink causal blocks.

3.1 Electro-mechanical sub-system

The experimental apparatus is composed by the followingmain electro-mechanical components: a driver, a steppermotor, a worm gear coupled with a lead-screw, and a sharpedge-weir.


15


By way of an example, we show the dynamic equationsmodel (1) that reproduce the behaviour of the electricmotor, where eA and eB are the back emfs induced in theA and B phase windings, respectively, iA and iB are the Aand B phase winding currents, vA and vB are the A and Bphase winding voltages, Km is the motor torque constant,Nr is the number of teeth on each of the two rotor poles. Ris the winding resistance, L is the winding inductance, Rm

is the magnetizing resistance, B is the rotational damping,J is the inertia, ω is the rotor speed, ϑ is the rotor angleand Td is the detent torque amplitude. The nominal valuesof the main parameters of the stepper motor are shown inTable 1.

eA = −Kmω sin(Nrϑ), (1a)

eB = −Kmω cos(Nrϑ), (1b)

diAdt

=(vA −RiA − eA)

L, (1c)

diBdt

=(vB −RiB − eB)

L, (1d)

Te = jdω

dt+Bω, (1e)

Te = −Km(iA − eARm

)sin(Nr, ϑ)+ (1f)

+Km(iA − eBRm

) cos(Nrϑ)− Td sin(4Nrϑ),

dϑ

dt= ω. (1g)

Fig. 4 shows different aspects in the electro-mechanical sub-system Simulink/Simscape modelling. Specifically, Fig. 4adepicts the topology and the typology of the hybrid model(causal and acausal). The diagram includes the causalposition controller for the driver stepper motor and theacausal electro-mechanical sub-system, which comprisesthe stepper motor driver, the stepper motor, the wormgear, the leadscrew, the mass, electrical and mechanicalreferences, and many sensor (e.g. load, position, velocityetc.). In particular, the position controller is developed bymeans of Simulink causal blocks, Fig. 4b, in which, thereference input defines the required motor angular positionin terms of the number steps. The stepper controllerprovides the pulse direction and the pulse train at theinput of the Stepper Motor Driver Simscape block. Itis worth highlighting that, the Simulink-PS Convertercyan colored blocks convert the input Simulink signalsinto a physical signals and, in this way, we can buildhybrid causal and acausal models. Moreover, by way ofan example, Fig. 4c shows the Simscape source code ofthe ideal mechanical translational mass block. It has onemechanical translational conserving port and the blockpositive direction is from its port to the reference point.This means that the inertia force is positive if mass isaccelerated in positive direction.

3.2 Hydraulic sub-system

The hydraulic components of the system can be describedusing the equation that govern the underlying physics. Theexperimental apparatus can be divided into two controlvolumes: Vc1, which represents the portion of the sea basin

ENA

REF

REV

A+

A-

B+

B-B-

B+

A-

A+

REV

REF

ENA

Stepper Motor Driver

A+

A-

B+

B-

R

CB-

B+

A-

A+

C

R

Stepper Motor

f(x) = 0

Solver

Configuration

theta

R

C

Load

Sensors

Ref

PWM

0v

REV

Position Controller

Stepper Controller

WGG W

Worm Gear

Mechanical

Translational

Reference

R

C

V

PP

V

C

R

Ideal Translational

Motion Sensor

SPS

PS-Simulink

Converter

Mass

SPS

PS-Simulink

Converter1

SNN S

Leadscrew

Reference

1

Step

Angle

[deg]

2

Velocity [mm/s]

3

Position [mm]

(a) Position controller and electro-mechanical sub-system: the hybridmodelling.

(b) Given a position reference, the stepper controller provides, byusing classical Simulink blocks, both the pulse direction and pulsetrain at the Stepper Motor Driver block.

(c) Simscape ideal mechanical translational mass source code.

Fig. 4. Position controller and electro-mechanical sub-systems: hybrid modelling.

between the weir and the deflector panels, and Vc2, whichincludes the lagoon and the remaining portion of the seabasin. For each of these control volumes, we can write a


16

Table 1. Main parameters of the stepper motor.

Name Value

Maximum supply voltage 230 VAC

Motor phase current 2 Arms

Nominal torque 4 NmRotor inertia 2.2 kg cm2

Step per revolution 200 stepWinding resistance 5.8 ΩCurrent time rise constant 9 m s

hchp hb

h0

hm

Vc2 Vc1

Qin

Qsf

AlAmAc

Qin

Qsf Bl LagoonSea

Qf

LagoonSea

B

Oscill

ating w

eir

Deflector

Fig. 5. Notation used for the hydraulic sub-system mod-elling.

continuity equation. For Vc1 it results as follows:

Acdhc

dt= Qin − (Qf +Qsf ) , (2)

where hc the water level, Ac the area of the control volume,Qin is the pump flow rate, Qf is the flow rate exchangedwith Vc2, and Qsf is the overflow rate from the weir;whereas, for the control volume Vc2, the continuity equationresults as follows:

Atdhm

dt= Qf , (3)

where At is the sum of the sea basin area and the lagoonbasin area and hm is the water level in this control volume.

We add two equation on the discharge flow

Qf = Af

√2g (hm − hc), (4)

Qsf = CqB√2g (hc − hp)

3/2, (5)

where Cq is the discharge coefficient, B the width of theweir and hp the weir crest height.

Similarly to what has been done for the electro-mechanicalsub-system, the hydraulic model has been implementedin the Matlab-based simulation environment by usingSimulink/Simscape blocks.

3.3 Models Calibration and validation

The aforementioned first-principle models include severalparameters which can assume different values and so mak-ing the shape of the equations flexible while maintaining

Fig. 6. Example of an experimental test. The input refer-ence signal is a triangular-wave, the system output isthe weir position.

-10 -5 0 5 10Target

-10

-8

-6

-4

-2

0

2

4

6

8

10

Out

put

DataOutput = Target

(a) Calibration: RMSE = 0.44 mm.

-10 -5 0 5 10Target

-10

-8

-6

-4

-2

0

2

4

6

8

10

Out

put

DataOutput = Target

(b) Validation: RMSE = 0.56 mm.

Fig. 7. Model calibration and validation steps.

their structure. The nominal model parameters are pro-vided from literature and technical data-sheet while othersparameter values can be guessed by expert knowledgeor can be estimated from real data. Anyway, in orderto obtain a suitable representation of the processes ofinterest that satisfies pre-agreed criteria (e.g. goodness-of-fit or cost function), certain model parameters needto be adjusted around their nominal values. Here, thecalibration procedure is carried out by comparing observedand simulated data. To this aim, an extensive experimentalcampaign has been carried out to obtain real data. In Fig. 6an example of experimental test is shown: the consideredinput to the system is a triangular-wave reference signal tothe driver while the considered output is the weir position.The data gained from the experimental tests have beensplit into a calibration dataset and a validation one. Byexploiting the first dataset, we adjust the values of modelparameters by solving offline an optimization problem thatminimize the Root Mean Squared Error (RMSE) betweenthe simulated output and the target one. Finally, thecalibrated model is validated, i.e. it is tested to checkits performances in the validation dataset. It is worthnoticing that, validation is always appropriate, in view ofthe uncertainty affecting the models and for this reasonit is appropriate to use different data for the calibrationand validation steps. By way of an example, Fig. 7 showsthe comparison between target and output data whenthe calibration of certain electro-mechanical parameters is


17

Davide Tognin et al. / IFAC PapersOnLine 51-5 (2018) 13–18 17

Table 1. Main parameters of the stepper motor.

Name Value

Maximum supply voltage 230 VAC

Motor phase current 2 Arms

Nominal torque 4 NmRotor inertia 2.2 kg cm2

Step per revolution 200 stepWinding resistance 5.8 ΩCurrent time rise constant 9 m s

hchp hb

h0

hm

Vc2 Vc1

Qin

Qsf

AlAmAc

Qin

Qsf Bl LagoonSea

Qf

LagoonSea

B

Oscill

ating w

eir

Deflector

Fig. 5. Notation used for the hydraulic sub-system mod-elling.

continuity equation. For Vc1 it results as follows:

Acdhc

dt= Qin − (Qf +Qsf ) , (2)

where hc the water level, Ac the area of the control volume,Qin is the pump flow rate, Qf is the flow rate exchangedwith Vc2, and Qsf is the overflow rate from the weir;whereas, for the control volume Vc2, the continuity equationresults as follows:

Atdhm

dt= Qf , (3)

where At is the sum of the sea basin area and the lagoonbasin area and hm is the water level in this control volume.

We add two equation on the discharge flow

Qf = Af

√2g (hm − hc), (4)

Qsf = CqB√2g (hc − hp)

3/2, (5)

where Cq is the discharge coefficient, B the width of theweir and hp the weir crest height.

Similarly to what has been done for the electro-mechanicalsub-system, the hydraulic model has been implementedin the Matlab-based simulation environment by usingSimulink/Simscape blocks.

3.3 Models Calibration and validation

The aforementioned first-principle models include severalparameters which can assume different values and so mak-ing the shape of the equations flexible while maintaining

Fig. 6. Example of an experimental test. The input refer-ence signal is a triangular-wave, the system output isthe weir position.

-10 -5 0 5 10Target

-10

-8

-6

-4

-2

0

2

4

6

8

10

Out

put

DataOutput = Target

(a) Calibration: RMSE = 0.44 mm.

-10 -5 0 5 10Target

-10

-8

-6

-4

-2

0

2

4

6

8

10

Out

put

DataOutput = Target

(b) Validation: RMSE = 0.56 mm.

Fig. 7. Model calibration and validation steps.

their structure. The nominal model parameters are pro-vided from literature and technical data-sheet while othersparameter values can be guessed by expert knowledgeor can be estimated from real data. Anyway, in orderto obtain a suitable representation of the processes ofinterest that satisfies pre-agreed criteria (e.g. goodness-of-fit or cost function), certain model parameters needto be adjusted around their nominal values. Here, thecalibration procedure is carried out by comparing observedand simulated data. To this aim, an extensive experimentalcampaign has been carried out to obtain real data. In Fig. 6an example of experimental test is shown: the consideredinput to the system is a triangular-wave reference signal tothe driver while the considered output is the weir position.The data gained from the experimental tests have beensplit into a calibration dataset and a validation one. Byexploiting the first dataset, we adjust the values of modelparameters by solving offline an optimization problem thatminimize the Root Mean Squared Error (RMSE) betweenthe simulated output and the target one. Finally, thecalibrated model is validated, i.e. it is tested to checkits performances in the validation dataset. It is worthnoticing that, validation is always appropriate, in view ofthe uncertainty affecting the models and for this reasonit is appropriate to use different data for the calibrationand validation steps. By way of an example, Fig. 7 showsthe comparison between target and output data whenthe calibration of certain electro-mechanical parameters is


17


0 250 500 750 1000 1250 1500t [s]

-10

-5

0

5

10

15

h [m

m]

(a) Tidal wave height hm: modelled (blue line) and measured (bluemarkers); position of the weir crest hp: modelled (red line) andmeasured (red markers).

0 250 500 750 1000 1250 1500t [s]

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

Q [l

/s]

(b) Flow rate exchanged between Vc1 and Vc2 (Qf ), flow rate of thepump (Qin), flow rate over the weir (Qsf ).

Fig. 8. Results of the hydraulic sub-system modelling.

carried out. Specifically, Fig. 7a refers to the calibrationstep: certain electro-mechanical sub-system parameters (e.g.the worm gear friction loss coefficient) have been adjustedby using an heuristic technique (Genetic Algorithms, Beghiet al. (2011)) that minimize the RMSE. Beside this, Fig. 7bis related to the validation step and we can see that theoutputs and the targets are sufficiently close each other,indeed the RMSE equals 0.56 mm.

4. SIMULATION RESULTS

We consider here certain relevant simulations, the resultsof which are shown in Fig. 8. In particular, the wave height(blue line, Fig. 8a) presents a time delay and an amplitudereduction compared with the position of the sharp edgeof the weir (red line), due to the propagation processesof the wave. The model output predictions restate that isnecessary to generate the desired wave directly in front ofthe lagoon in order to be sure of the wave characteristics atthe lagoonal inlet. A comparison between the model outputpredictions with the measurements of the ultrasonic probe,for the tide (blue markers), and of the potentiometer, forthe weir position (red markers), assesses the capability

of the model to correctly reproduce the real system. Inaddition to the wave height, the model can also predictthe flow rate, hence the velocity values, as presented inFig. 8b. When the flow rate Qf (blue line) exchangedbetween the two control volumes Vc1 and Vc2 is negative,the velocity is direct seaward and the sediments are erodedand transported from the lagoon to the sea basin.

5. CONCLUSIONS

CACSD software tools are very useful to simulate relevantsystem dynamics for a first assessment of the differentcontrol strategies. In this paper, we have developed andtested a Matlab-based simulation environment for the multi-domain artificial tidal wave generation system. In particular,we have used Simulink traditional block diagrams andSimscape components to integrate different causal andacausal sub-models in order to make them transparentto the users, to preserve their testability, and to gainthe necessary user confidence. Constructing models fora slice of reality and studying their properties has provedto be very useful. A comparison between simulations andreal experiments shows that the simulation tool is able tocorrectly reproduce the relevant system dynamics. Futuredevelopments will include the designing and testing ofdifferent control strategies, such as standard regulators andadaptive controllers.

REFERENCES

Beghi, A., Franceschetti, P., Rampazzo, M., Sisti, E.,Algarvia, C.A., and Lionello, M. (2017). Modelling andsimulation of a convective low temperature sludge dryerwith multilayer belt. In 2017 IEEE 3rd InternationalForum on Research and Technologies for Society andIndustry (RTSI), 1–6.

Beghi, A., Cecchinato, L., and Rampazzo, M. (2011). Amulti-phase genetic algorithm for the efficient manage-ment of multi-chiller systems. Energy Conversion andManagement, 52(3), 1650–1661.

Chin, C.S. (2017). Computer-Aided Control SystemsDesign: Practical Applications Using MATLAB andSimulink. CRC Press Taylor and Francis Group.

Dingyu Xue, Y.C. (2013). System Simulation Techniqueswith MATLAB and Simulink. Wiley & Sons.

Kofranek, J., Matejak, M., Privitzer, P., and Tribula, M.(2008). Causal or acausal modelling: labour for humansor labour for machines. In Technical Computing Prague,124–140.

Ljung, L. and Glad, T. (1994). Modeling of DynamicSystems. Prentice-Hall, Inc., Upper Saddle River, NJ,USA.

Perelmuter, V. (2017). Electrotechnical Systems: Simulationwith Simulink and SimPowerSystems. CRC Press.

Ramin S. Esfandiari, B.L. (2014). Modeling and Analysisof Dynamic Systems, Second Edition. CRC Press Taylorand Francis Group.

Stefanon, L., Carniello, L., D’Alpaos, A., and Lanzoni, S.(2010). Experimental analysis of tidal network growthand development. Continental Shelf Research, 30(8),950–962.

Tambroni, N., Luchi, R., and Seminara, G. (2017). Cantide dominance be inferred from the point bar patternof tidal meandering channels? Journal of GeophysicalResearch: Earth Surface, 122(2), 492–512.


18

university of brescia, brescia, italy, may 10-11, 2018 ...€¦ · university of padova, ... in...

Documents