AN ADAPTIVE CONTROL OF THE WAVE IN A TOWING TANK

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FACULTY OF ELECTRICAL AND CONTROL ENGINEERING

The author of the PhD dissertation: Marcin Arkadiusz Drzewiecki Scientific discipline: Automation, electronics and electrical engineering

AN ADAPTIVE CONTROL OF THE WAVE IN A TOWING TANK

Supervisor:

Jarosław Guziński, D.Sc, Assoc. Prof.

Auxiliary supervisor:

Mohamed Amine Fnaiech, PhD

Gdańsk, year 2020

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FACULTY OF ELECTRICAL AND CONTROL ENGINEERING

Summary of PhD dissertation in Polish: W rozprawie przedstawiono system służący do adaptacyjnego sterowania falami, który został wdrożony w basenie holowniczym znajdującym się w Centrum Techniki Okrętowej S.A. Fale są generowane w celu odtwarzania warunków środowiska morskiego podczas badań modelowych. Badania tego typu wykonywane są na modelach obiektów w pomniejszonej skali, w celu prognozowania właściwości obiektów rzeczywistych. Dokładne modelowanie warunków środowiska morskiego ma zasadnicze znaczenie dla zapewnienia bezpieczeństwa ludzi i niezawodności konstrukcji morskich i przybrzeżnych.

Przeprowadzone badania wykazały, że dotychczasowe modele zjawisk hydromechanicznych związanych z generowaniem fal w basenie holowniczym CTO nie zapewniają wymaganej dokładności. Z tego powodu należało wdrożyć rozwiązanie automatyki, które umożliwi modelowanie warunków środowiska morskiego z wymaganą precyzją. W oparciu o przeprowadzone badania teoretyczne i eksperymentalne, opracowany został nowy system sterowania adaptacyjnego. Opracowane rozwiązanie zostało zrealizowane z wykorzystaniem systemu wbudowanego, wykorzystującego wysokowydajny mikrokontroler, komunikujący się z aplikacją komputerową. Wdrożone rozwiązanie zostało zweryfikowane eksperymentalnie i przyjęte przez CTO do generowania fal o oczekiwanym widmie z wymaganą dokładnością, przy niskich kosztach realizacji oraz w sposób przyjazny dla eksperymentatora, przy jednoczesnym pominięciu złożonych i nieadekwatnych modeli hydromechanicznych. W rozprawie rozważono również model wywoływacza fal z zaawansowanym wysokowydajnym napędem elektrycznym w miejsce aktualnie stosowanego napędu hydraulicznego.

Ponadto, podczas prowadzonych badań opracowano urządzenie ultradźwiękowe do pomiaru profilu fali na powierzchni cieczy, wykorzystujące nowatorski sposób pomiaru profilu fali na powierzchni cieczy, które są przedmiotami Polskiego oraz Europejskiego zgłoszenia patentowego.

Summary of PhD dissertation in English: The dissertation presents the system for adaptive control of waves, implemented in the in the towing tank located in the Maritime Advanced Research Centre, CTO S.A. The waves are generated to model the environmental conditions during hydromechanical model tests. The tests are performed on scaled models to predict the properties of full scale objects. Therefore, accurate modelling of the environmental conditions is essential to secure the human safety and reliability of naval and offshore structures.

The research carried out, showed that current models of hydromechanical phenomena related to wave generation in the towing tank do not provide the required accuracy.

Therefore, it is expected to solve the problem through the automatic approach in order to model the environmental conditions with required accuracy. In scope of the dissertation, the new adaptive control system with a fuzzy-logic controller has been developed on the basis of the studied theory, established conception and the research carried out.

Developed solution has been implemented using the embedded system with the high- performance microcontroller. The embedded system communicates with the computer application. The solution has been experimentally verified and accepted by the CTO to generate expected wave spectra with required accuracy at low realization costs and user- friendly manner with omission of complex and inapplicable hydromechanical models.

Additionally, the model of the wave maker with an advanced and high performance electric drive, instead of the currently used hydraulic drive, has been successfully considered. Moreover, as part of the work performed, the method and the ultra-sound device for a wave profile measurement on the surface of liquid, have been developed.

The method and the device developed are the subject of a Polish and an European patent application.

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1. INTRODUCTION, OBJECTIVES AND AIMS OF THESIS

1.1. Introduction

An experiment is of paramount importance for the design and operation of naval and offshore structures. Especially, due to the impact of survivability of these structures on human life and safety. Two types of experiments are possible: on real objects and on reduced models. The experiments carried out on the real objects are the most valuable but often impossible to be implemented due to their complexity, costs or risks. Therefore, the physical model tests being carried out in hydromechanics laboratories, occupy a privileged position when predicting the properties of objects such as ships, oil rigs or wind turbines.

Fundamentally, the model tests carried out at model scale, allow to predict the properties of the naval and offshore, full scale objects, to improve the human safety and survivability of constructions.

Moreover, from a scientific and research point of view, a particularly important feature of physical model tests is the possibility of verification of the developed physical theories.

The naval and offshore objects, in their environmental conditions, are mostly affected by the wind and waves. The influence of waves is usually of far higher importance, than the influence of the wind, due to the amount of the wave energy as compared to the amount of the wind energy, resulting from the difference in water and air density. This influence can result in many undesirable phenomena, related to the objects, i.a.: flooding the deck, broaching of the propeller, dynamic load of the hull and equipment and transported goods, manoeuvrability deterioration and resistance increase. Mentioned phenomena can deteriorate facility’s economic performance and be unbearable for people located on these objects or even be destructive for the object and people.

Consequently, physical modelling of waves is an essential part of the process focus on Modelling of Environmental Conditions (MEC), specific to the working area of the naval or offshore object. The MEC process is carried out in hydromechanics laboratories worldwide, during model tests, that are called seakeeping tests which are performed in a reduced scale on the models of naval and offshore objects subjected to simulated marine conditions influence, i.a.: towed or free running ships (Fig. 1.1), anchored structures like oil rigs or bottom-mounted structures like wind turbines.

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Fig. 1.1. The example of seakeeping tests in a hydromechanics laboratory: free running model of a ship

For the needs of the seakeeping model tests, the waves are generated in a wave tanks equipped with wave makers. The movements of the wave maker actuators, generate waves in the wave tank. Two basic types of waves can be generated: regular and irregular. The regular wave is induced by monoharmonic movement of the wave maker actuator. The irregular wave is induced by multiharmonic movement of the wave maker actuator and is desired to contain the expected harmonics of Energy Spectral Density (ESD) to reflect the real environmental conditions in a model scale. The generated irregular waves are consistent with the States of Sea (SS) [2]

desired for seakeeping model tests scenarios.

Measurements carried out during the seakeeping model tests allow an experimental determination of full scale object properties, in order to improve the human and construction safety and sustainable development of naval architecture and offshore sectors.

1.2. Thesis and Objectives

The scientific objective of this doctoral dissertation is to solve the complex problem related to the generation of the waves on the water surface in a wave tank with a required accuracy, for the needs of the seakeeping model tests to improve survivability of naval and offshore constructions and therefore human safety.

Waves on the water surface in wave tank are generated as a result of the oscillatory movements of wave maker actuator. Unfortunately, there is no direct relationship between the ESD of the generated wave and ESD of movements of the wave maker actuator. This is due to hydromechanical phenomena, which complexity causes that hydromechanical models are not sufficiently general and robust. Finally, in order to obtain ESD of generated waves, that reflects the real environmental conditions with the required accuracy, it was necessary to manually and iteratively apply corrections to the input signal of the wave maker.

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Moreover, the widely used technique of wave profile measurement was based on the phenomenon of variable resistance or capacitance between two electrodes immersed into the water, while the resistance or capacitance depends on the depth of immersion. This common solution is a nuisance for the user, due to settlement that result in necessity of cleaning the electrodes and adjusting the amplifier before each use. In addition the probes immersed into the water were the source and receiver of hydromechanical disturbances, related to the measured waves.

Each of the hitherto way of generating and measuring the wave was a time-consuming, high-cost and non-automatic solution based on iteratively cycles of: preparation, generation, measurement, analysis and correction.

In the scope of this doctoral dissertation newer types of regulation of plant has been considered and the target one has been developed. The fuzzy-logic controller and the adaptation module have been implemented to a high performance embedded system with an intuitive computer application.

A new method and an ultra-sound device for a wave profile measurement have been invented for the needs of the developed system. The method and the device have been applied for a Polish patent [44] and, subsequently, for an European patent [45]. The method and device are based on contactless ultrasonic measurements and thus, it is non-invasive and maintenance- free.

The entire solution has been worked out and implemented in the hydromechanics laboratory in the CTO S.A. Maritime Advanced Research Centre. However, both the adaptive system and the ultra-sound device are a ready-made products that can be broadly implemented to others hydromechanics laboratories.

The implementation of the objective of the dissertation, solved the significant scientific and technical problem of MEC in hydromechanics laboratory during the model tests, carried out for needs of naval and offshore industries.

The novelty and the main contribution of the doctoral dissertation are:

 development of a new complete control system of the wave maker for a real towing tank;

 development of the fuzzy-logic controller to control the velocity and the position of the wave maker flap;

 development of the non-invasive, contactless, and maintenance-free ultra-sound system for measurement of the wave profile;

 development of the robust and sufficiently general method of adaptive wave control based on the wave spectrum-feedback;

 consideration of modern and advanced electric drive of the wave maker.

The thesis of the doctoral dissertation is formulated as follows:

“It is possible to control the energy spectral density of the generated irregular waves, in an automatic manner with omission of complex and often inapplicable and not robust hydromechanical models, with use of the adaptive controller.”

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Whereby “the pragmatic attitude that an adaptive controller is a controller with adjustable parameters and a mechanism for adjusting the parameters” [K. J. Åström and B. Wittenmark, 2013, p. 1], was taken.

The obtained results validated this assumption and brought a number of additional benefits described along the dissertation.

2. THEORY

2.1. Model of waves

The waves generated in the wave tank, model the SS in a reduced scale. It is done to reflect the marine conditions to which the real object will be subjected. The SS are selected according to statistical data for the sea area for which the tested object is dedicated. The specifying SS with significant waveheight Hs and modal period Tp are presented in Tab. 2.1 [2].

The Hs is an average of ⅓ of highest waves, while the Tp, widely called peak period, corresponds to highest value of the ESD. For the needs of the model tests, Hs and Tp are precisely determined, according to statistical data, obtained from meteorological office, depending on sea area considered.

Tab. 2.1. Significant Waveheights and Modal Periods corresponding to the Sea States in the North Atlantic and North Pacific [2]

SS North Atlantic North Pacific

- Hs [m] Tp [s] Hs [m] Tp [s]

0-1 0..0.10 - 0..0.10 -

2 0.10..0.50 3.3..12.8 0.10..0.50 3.0..15.0

3 0.50..1.25 5.0…14.8 0.50..1.25 5.2..15.5

4 1.25..2.50 6.1..15.2 1.25..2.50 5.9..15.5

5 2.50..4.00 8.3..15.5 2.50..4.00 7.2..16.5

6 4.00..6.00 9.8..16.2 4.00..6.00 9.3..16.5

7 6.00..9.00 11.8..18.5 6.00..9.00 10.0..17.2

8 9.00..14.00 14.2..18.6 9.00..14.00 13.0..18.4

>8 >14.00 18.0..23.7 >14.00 20

The ESD according to modelled SS is calculated using the spectral formulations calculated as a functions of the harmonic frequency f. It can be done in terms of the statistically defined parameters of the waves – Hs and Tp. The formulations and cases reflected therein, have been described by the Specialist Committee of the ITTC organisation [3]. Required accuracy of physical modelling allows discrepancies between nominal and measured Hs and Tp within ±5%

[4], [32].

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Mostly, two spectra formulations are used for seakeeping model tests: Pierson-Moskowitz and JONSWAP [2]. The examples of spectra: Pierson-Moskowitz and JONSWAP (γ=3.3), calculated for 8^th SS in North Atlantic (Tab. 2.1.) for model scale equal to 1:30, are shown in Fig. 2.1 and Fig. 2.2, respectively.

Fig. 2.1. Pierson-Moskowitz Spectrum for 8^th State of Sea in North Atlantic for Model Scale equal to 1:30 – the full scale values of Hs=9 m and Tp=14.2 s scaled into the model scale

values of Hs=30 cm and Tp=2.593 s

Fig. 2.2. JONSWAP (γ=3.3) Spectrum for 8^th State of Sea in North Atlantic for Model Scale equal to 1:30 – the full scale values of Hs=9 m and Tp=14.2 s scaled into the model scale

values of Hs=30 cm and Tp=2.593 s

2.2. Wave maker theory

Linear Wave Maker Theory (LWMT) was formulated by Havelock [5] and Biésel and Suquet [6]. This theory defines a relationship between the waves generated on water surface in wave tank and the oscillatory movements of wave maker actuator. The LWMT states that the amplitude of generated wave A11 in far field is depend on: wave maker stroke S(z), depth of water h, height of articulation of the wave maker actuator h0 and wave number k as it shown in general formulation (2.1) [6]. The far field is understood as test section of wave tank, where amplitudes of initial disturbances are reduced below one percent of A11. That reduction is obtained at the distance from the wave maker actuator at least x=3h [6].

= 2 sinh ℎ

(2.1)

Nonlinear Wave Maker Theory (NWMT) was developed to extend the accuracy of the wave generation in a 2D Wave Flumes [7]-[11] and for numerical simulation of nonlinear waves [12]-[20]. However, mentioned studies do not exhausted all phenomena which occurs while wave generation and propagation in the towing tank equipped with flap-type wave maker considered.

The LWMT covers the process of generating the linear components of waves in the wave tanks, including the towing tanks. The NWMT covers the process of generating the nonlinear

1/Tp 1/Tp

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components in a 2D wave flumes and numerical simulations. However, the nonlinear component resulting from the wave maker actuator construction has been theoretically derived [21]. Except the wave maker theories, the further nonlinear processes and secondary phenomena, can affect the wave generation and propagation in the wave tank considered. During the laboratory experiments the numerous processes and phenomena can be observed, i.a.: disintegration of wave profile, wave damping and wave reflections from the beach and from the structural elements of the wave tank. This affects the propagation and transformation of the generated waves. The synthesis of hydromechanical models of these processes and phenomena is too complex, not robust and not general enough for application.

Nonetheless, for the model tests carried out in the wave tank considered, accurately modelling of environmental conditions in scope of waving is required. Thus, correct handling of all these processes and phenomena is vital for proper realization of the MEC.

3. CONCEPTION

3.1. Wave generating facilities

The considered towing tank is of the 270 m length, 12 m width and 6 m depth. There are three sections along the towing tank: the wave maker section, the test section and the beach section. The longitudinal profile of the towing tank is presented in Fig. 3.1. It is equipped with the facilities submerged in water: flap-type wave maker, straighteners, side wave absorbers, rubble- mound beach. The wave profiles are generated and formed in the wave maker section, to propagate along the test section at the desired parameters. Ultimately the waves are damped in the beach section.

Fig. 3.1. Longitudinal profile of the deepwater towing tank equipped with a flap-type wave maker 1, straighteners 2, side absorbers 3 and rubble-mound beach 4

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10 3.2. Wave control system

The plant consists of wave generating facilities presented in subsection 3.1. Hitherto control system, described in [30], [35] and [22], allowed to control the flap movements. However, it did not use the wave maker theory, discussed in section 2.2 and it did not compensate the hydromechanical phenomena discussed there. Actually, it was a flap-control system, not a wave control system. The wave signal was being calculated outside the control system and then corrected using experience of the wave designer and wave maker operator to predict the control signal adequate for expected wave. Moreover, this solution causes the necessity to make corrections manually to compensate the hydromechanical phenomena. This solution was time- consuming and employee-involving and had to be replaced by the automation system that allowed for:

 control of the flap movements due to the wave maker theory,

 automatic compensation the effects of hydromechanical phenomena.

3.4. Conclusions

The experimental and simulation research had to be carried out in order to develop the control system that reduced the costs of model tests and improved the accuracy of modelling of environmental conditions.

Firstly, the control system had to be developed to provide the required control of the flap movements and apply the wave maker theory, presented and discussed in section 2.2. Then, the automatic compensation of hydromechanical phenomena had to be developed, to provide the accurate control of the waves.

The numerous hydromechanical phenomena in general in a towing tank, arises from the processes not covered by the wave maker theory. The particularly considered towing tank is a physical hydromechanical object located in a hydromechanics laboratory in the CTO S.A. It is equipped with facilities presented in section 3.1. From the wave propagation point of view, the facilities improve the properties of the towing tank on the one hand, but each of the facility is the individual plant, that generates the specific disturbances, on the other hand. Moreover, the facilities are not ideal but physical – the straighteners, side absorbers and rubble-mound beach reduce the transverse waves and reflections in the towing tank only to a certain extent. Actually, the towing tank and the facilities interact together with the nonlinear waves, that model physical nonlinear environmental conditions. As a result there are the interactions and phenomena with the elusive or inapplicable model. Despite this, it was necessary to capture the effects of those interactions and phenomena in an automatic way.

Designed control system had to be developed and implemented using a user-friendly computer system and subsequently validated.

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4. RESEARCH

4.1. Introduction

The research is related to the physical object – the towing tank equipped with the wave maker and other wave generating facilities, introduced in the section 3.1. The research technique combines the model simulation of work together with the experimental research performed on the object. The model simulation has been carried out in the Scilab/Xcos software. It has been performed for the model of object, experimentally identified and modelled in the section 4.2. The experimental research includes the measurements and analyses performed on the basis of the theoretical formulation derived in accordance with the section 2.2. The research has been carried out in accordance with the descriptions detailed successively in the current chapter. The results have been finally discussed in the section 4.5.

4.2. Identification and modelling of actuators

The wave maker consists of two modules of actuators:

 electrohydraulic servo valve and stroke piston – the flap velocity module;

 variable displacement electropump stroking mechanism and double-acting hydraulic cylinder with flap immersed in water – the flap position module.

The flap velocity module, consisting of the electrohydraulic servo valve and the stroke piston, is presented in Fig. 4.1. The flap position module, consisting of the variable displacement electropump stroking mechanism and double-acting hydraulic cylinder, is presented in Fig. 4.2.

Fig. 4.1. The module of the servo valve with stroke

piston controls the velocity of wave maker flap Fig. 4.2. The module of the variable displacement electropump stroking mechanism and double- acting hydraulic cylinder controls the position of

wave maker flap

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12 4.2.1. Linear model of the flap velocity module

The input and output signals of the flap velocity module were measured. The measured signals allow to derive the frequency response of the flap velocity module. It has been presented in Fig. 4.3. The plots had been drawn with asymptotes of the basic element – an integral term [40], to derive the parameters of the linear model. The kI1 is the gain factor of the integral term.

Fig. 4.3. Bode plot of the flap velocity module – measurement (red diamonds) and asymptotes of the linear model (green lines)

Based on the derived parameters of the integral term [40], the linear model of the flap velocity module has been identified as (4.1) with kI1=10.15.

1 =

_"^! (4.1)

The electrohydraulic servo valve is proportional [37]. The stroke piston, according to the working principle [39] was expected to be an integrator. Thus, identified model is justified and compatible with the physical object.

4.2.2. Linear model of the flap position module

The input and output signals of the flap velocity module were measured. The measured signals allow to derive the frequency response of the flap position module. It has been presented

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in Fig. 4.4. The plots had been drawn with asymptotes of the basic element – an integral real term with inertia [40], to derive the parameters of the linear model. The kI2 is the gain factor of the integral real term. The TI2 is the time constant due to the inertia of the element.

Fig. 4.4. Bode plot of the flap position module – measurement (red diamonds) and asymptotes of the linear model (green lines)

Based on the derived parameters of the integral real term with inertia [40], the linear model of the flap velocity module has been identified as (4.2) with kI2=2.48 and TI2=0.15 s.

2 =

^#

" "∙% # (4.2)

The cylinder is coupled with the wave maker flap submerged in water. The double-acting hydraulic cylinder, according to the working principle [39], was expected to be an integrator.

Further, the flap submerged in water was expected to be origin of inertia due to the significant mass of the flap and water [39]. Thus, identified model is justified and compatible with the physical object.

4.3. Implementation of model and design of controllers

The model derived in accordance with section 4.2, was implemented into the Scilab/Xcos simulation environment. It allowed to perform the simulation tests necessary to design the most

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reliable wave maker controller. The fuzzy-logic controller of the Mamdani type with the flap- position feedback and flap-velocity feedback was considered. It was chosen as the target one due to the prime robustness, greatest stiffness, finest stability and satisfying step-response parameters, investigated along the dissertation.

The fuzzy-logic controller FLS of the flap velocity and flap position, has been considered.

This type of controller is successfully applied for improving the control performance of various types of objects, including the electrohydraulic actuators [41]-[43].

The FLS applied to the wave maker actuators has been established with two inputs and one output. The structure uses the flap velocity signal AX1 and the flap position signal AX2. The structural diagram of the proposed control system is shown in Fig. 4.5. The first FLS input is the flap position error FPE, calculated as the difference between the reference flap position signal AX2r and measured flap position signal AX2. The second FLS input is the flap velocity error FVE, calculated as the difference between the reference flap velocity signal taken as FPE and the measured flap velocity signal AX1. The FLS output is the S signal, given to the input of flap velocity module (I1), that acts the flap position module (I2) to move the flap. The scaling of the input and output signals is implemented in hardware with use of the signal matching circuits. The scaling parameters were selected to match the range of the FLS process variables with the thresholds of the sensors and actuators.

Fig. 4.5. Structural diagram of the flap velocity and flap position fuzzy-logic control system

The following fuzzy sets for input variable FVE have been formulated: Negative Fast NF, Negative Medium NM, Zero ZO, Positive Medium PM, Positive Fast PF.

Afterward, the following fuzzy sets for input variable FPE have been formulated: Negative Large NL, Negative Medium NM, Zero ZO, Positive Medium PM, Positive Large PL.

Wherefore, the following fuzzy sets for output variable S have been formulated: Positive Large PL, Positive Large PL, Zero ZO, Positive Medium PM, Negative Large NL, Negative Medium NM.

The membership functions of the fuzzy sets: mu(FPE), mu(FVE), mu(S), determine the grade of membership with a fuzzy set formulated for given variable: FPE, FVE or S, respectively.

Flap position module Flap velocity module

Flap velocity and flap position fuzzy-logic controller

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The Λ-, Γ- and L-type membership functions of fuzzy set have been formulated in accordance with [27]. The singleton-type membership functions of fuzzy set have been formulated in accordance with [28].

The membership functions of the input variables – FVE and FPE – are graphically presented in Fig. 4.6 and Fig. 4.7, respectively.

Fig. 4.6. Graph of the membership functions: Λ-type, Γ-type and L-type, determined to grade the membership mu of the FVE input variable with the fuzzy sets: NF, NM, ZO, PM, PF

Fig. 4.7. Graph of the membership functions: Λ-type, Γ-type and L-type, determined to grade the membership mu of the FPE input variable with the fuzzy sets: NL, NM, ZO, PM, PL

The membership functions of the output variable S are graphically presented in Fig. 4.8.

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Fig. 4.8. Graph of the membership functions singleton-type, determined to grade the membership mu of the S output variable with the fuzzy sets: PL, PM, ZO, NM, NL

The Mamdani fuzzy inference system has been established with a rule base presented in the Tab. 4.1. The FLS was intended to real-time computing in the embedded system applied to the wave maker. Thus, the calculations had to be simple and fast. Consequently, the output membership function and all the operations, were selected to be a plain addition or multiplication, as follows. The fuzzy implication of the values of membership with the fuzzy sets is performed in accordance with the algebraic product method. The aggregation of the active rules is performed in accordance with the algebraic sum method. The defuzzification is performed in accordance with the output membership function shown in the Fig. 4.8 and with the centre of gravity (CoG) method [27].

Tab. 4.1. Table of the rules base of the fuzzy inference system

FVEFPE NL NM ZO PM PL

PF PM PM PM PL PL

PM PM PM PM PM PL

ZO NM NM ZO PM PM

NM NL NM NM NM NM

NF NL NL NM NM NM

The simulation of work has been run and the output control surface of the modelled fuzzy- controller has been plotted as shown in Fig. 4.9.

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Fig. 4.9. Output control surface of the fuzzy-logic controller considered

The stability of the proposed system has been examined in the Lyapunov sense. It has been done using the procedure of state variable trajectory tracking, that is recommended for fuzzy-control systems [27], [29]. According to this procedure, a system is stable, if the state variables tend to the origin from any start state on the phase plan. The examination in Xcos/Scilab environment has been carried out for the closed-loop system presented in Fig. 4.5. The origin for the system considered is coordinated as (0.5;0.5). The trajectories have been tracked for given initial states of FPE and FVE on the phase plan as presented in Fig. 4.10. According to the results presented in Fig. 4.10, the state variables tend to the origin from all given initial states – thus the proposed system is stable in Lyapunov sense.

Fig. 4.10. Trajectories for given initial states of FPE and FVE on the phase plane – simulation in Xcos/Scilab

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Finally, the quality of regulation has been verified for the model of the closed loop-system with the established fuzzy-logic controller, under the parameters of step response: rise time tn, setting time tN, settling time tR, overshoot D, oscillating d/D.

The step response is shown in Fig. 4.11. It has been registered for the model of closed- loop system (Fig. 4.5) with AX2r given as input signal and AX2 given as output signal scaled to launch the step of 1 m stroke of the flap X2.

Fig. 4.11. Step response of the closed-loop system with fuzzy-logic controller considered – simulation in Xcos/Scilab

The current model has been chosen as the most reliable due to fine time-parameters of the step response and acceptable overshoot with oscillating. The fuzzy-logic controller has been intended for implementation to the real plant.

4.4. The Transfer Function

4.4.1. Linear Transfer Function

The Linear Transfer Function has been investigated under the regular waves generated with the desired heights of the 5 cm and 10 cm. The desired heights have been generated with the basic harmonic frequencies from 0.3 Hz to 1.2 Hz with increment of 0.1 Hz. The results of theoretical calculation for linear model have been compared with the results of the experiment.

Consequently, the theoretical model has been reduced with a factor equal to 0.8. The dropped amount 0.2 reflects the flow damping that arises from frictions in straighteners and the pressure drops in slots between the wave maker flap and the towing tank walls [21]. The LTF reduced and validated for the wave maker considered is shown in Fig. 4.12 and Fig. 4.13. In the Fig. 4.12 it can be seen that the waves of very low steepness meets the reduced linear model – highly for

t

N

=0.61 s

t

n

=0.38 s 0.9

0.1 D=0.19

d=0.3 ּּ D <0.02

t

R

=1.84 s

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harmonics within 1 Hz and less for harmonics exceeding 1 Hz, while steepness increase. In the Fig. 4.13 it can be seen that the waves of moderate steepness meets the reduced linear model mostly for harmonics within 1 Hz while the discrepancies increase rapidly with increasing frequency and resulting steepness.

Fig. 4.12. Linear Transfer Function for regular

waves of 5 cm height Fig. 4.13. Linear Transfer Function for regular waves of 10 cm height

As proven in the experiment performed, the reduced linear model is applicable in terms of linear theory for the towing tank with the wave maker considered, within the regular waves of low steepness. According to the experimental research carried out in another hydromechanics laboratory [31], LTF was applicable for regular waves while it was not sufficient for irregular waves due to lack of the linearity.

The seakeeping model tests, predominantly requires the generation of the irregular waves with at least moderate steepness. Mostly, the spectral formulations of Pierson-Moskowitz or JONSWAP are applied [2]. Furthermore, the spectra are applied with limited realization time.

The investigation has been carried out for the mentioned spectra.

The selected results of the experiment performed for the Pierson-Moskowitz spectra and for the JONSWAP (γ=3.3) spectra, are presented in Fig. 4.14 and 4.15, respectively. It can be seen, that ETF does not meet the reduced LTF. Moreover, the ETF is not homogeneous for the spectra of generated and investigated waves.

Fig. 4.14. Empirical Transfer Function for irregular waves of Pierson-Moskowitz spectrum with desired Hs at Tp=1.667 Hz (red lines) versus reduced Linear Transfer Function (black line)

Fig. 4.15. Empirical Transfer Function for irregular waves of JONSWAP (γ=3.3) spectrum with desired Hs at Tp=1.667 Hz (red lines) versus reduced Linear Transfer Function (black line)

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The ETF shapes presented in Fig. 4.14 and Fig. 4.15 seem to be random. To some extent, the ETF shapes may arise from disturbing the LTF by nonlinear interactions and secondary phenomena. Besides, the limited realization time, had been suspected to influence the ETF. To develop the improvement concept, in-depth research had to be performed. All of the mentioned factors had to be investigated. It has been done in accordance with the descriptions in the following subsections.

4.4.2. Secondary phenomena

Among the secondary phenomena, observed during the seakeeping model tests, the following stand out: the wave reflections from the rubble-mound beach, the wave damping along the towing tank and the breaking and disintegration of wave profile. It can affect the wave profile and consequently the parameters of the irregular waves. Therefore, the secondary phenomena had to be experimentally investigated to evaluate this impact.

The investigation has been performed under the regular waves generated with the desired height of 10 cm and basic frequencies desired from 0.3 Hz to 1.2 Hz with increment of 0.1 Hz.

The reflection coefficient for the rubble-mound beach R, damping coefficient in the test section D and spectrum spread coefficient averaged for the test section s, are shown – respectively – in Fig. 4.16, Fig. 4.17 and Fig. 4.18.

Fig. 4.16. Reflection coefficient versus wave frequencies in the test section for the rubble-mound

beach

Fig. 4.17. Damping coefficient versus wave frequencies in the test section in the towing tank

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Fig. 4.18. The spectrum spread coefficient versus wave frequencies in the test section of the towing tank

Summarizing the performed investigation of the secondary phenomena, their impact on the wave profile generation and propagation is related to the frequency of the harmonics. The investigated phenomena: reflections, damping and spectrum spread, almost do not influence the harmonics within the frequency of 0.7 Hz – it is visible in the results in Fig. 4.16, Fig. 4.17 and Fig. 4.18, respectively. However, as the harmonic frequency increases, this impact increases.

According to the mentioned results, the harmonics of 0.8 Hz is moderately affected by the damping and spectrum spread deterioration, while the harmonics of frequency higher than 0.9 Hz are highly affected to be damped and deteriorated under the spectrum spread along the test section of the towing tank.

The results could justify the ETF shapes at the harmonics exceeding the frequency of 0.7 Hz, although the ETF investigated there are inconsistent with the LTF also in scope of the harmonics within 0.7 Hz (Fig. 4.14 and Fig. 4.15). Accordingly it was assumed that other factor also affect wave generation or propagation along the towing tank. Consequently, the limitation of the realization time influence on the realization of wave spectrum, has been investigated in the following subsection.

4.4.3. Limited realization time of the spectra

The spectra of the irregular waves, are realized in time using the Random Phase Method.

It is a deterministic technique of wave signal generation, that allows to realize the spectrum in the realization time Tr, according to the expectations. Limited length of the towing tank and expected reasonable number of measuring runs with model towed along, enforces the limitation of Tr to applying it as equal to 128 s. On the other hand, the limitation of Tr, causes the increase of Δf and, consequently, inferior discretization of the control signal [23].

The impact of the limited realization time of the spectra has been investigated. It has been evaluated under comparison of results obtained for the measured waves of the identity desired Pierson-Moskowitz spectra with Hs=15.0 cm and Tp=1.667 s, realized in two different realization

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times Tr of 128 s and 1024 s. The values of the Tp and Hs have been determined from the spectra of measured signals, shown in Fig. 4.19 and 4.20.

Fig. 4.19. The Pierson-Moskowitz spectrum of desired Hs=15.0 cm and Tp=1.667 s for the

realization time of 128 s – reference (red continuous lines) and measured (black bars)

Fig. 4.20. The Pierson-Moskowitz spectrum of desired Hs=15.0 cm and Tp=1.667 s for the

realization time of 1024 s – reference (red continuous lines) and measured (black bars)

The desired values of the Tp and Hs have been compared with the results of the measurement in the Tab. 4.2. The values with the N and M superscripts are the desired and measured, respectively. The δTp and δHs mean the relative differences between desired and measured values of the Tp and Hs.

Tab. 4.2. Summary of the examination results – realization of RA for two given Tr

Tr HsN TpN HsM TpM δHs δTp Fig. no.

s cm s cm % % % -

128 15.0 1.667 12.8 1.602 -14.7 -3.9 4.120

1024 15.0 1.667 14.5 1.738 -3.3 4.3 4.121

In the Tab. 4.2 it can be seen that the spectrum generated in Tr of 128 s does not meet the 5% required accuracy of the Hs value [4], [32]. The values of ESD shown in Fig. 4.19 are noticeably low and the shape of the spectrum is distorted. Meanwhile, the spectrum generated in the Tr of 1024 s, meets the required accuracy of the Tp and Hs and the values of ESD shown in the Fig. 4.19 is of the more identity with the desired.

The results justifies the ETF shapes presented above in Fig. 4.14 and Fig. 4.15 for the irregular waves generated with the realization time limited to 128 s. Apparently the limitation of the Tr results that the required accuracy of realization of spectrum is not met. On the other hand the Tr has to be sensible limited. Increasing the Tr from 128 s to 1024 s, would increase of time- consumption and cost of the seakeeping model test eight-fold, due to increased number of measuring runs with model towed along the towing tank. Consequently, the limitation of the realization time is indispensable to realize the seakeeping model tests in reasonable time and with acceptable costs.

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The flap movements control system was considered in a few structures and algorithms with the position-feedback and velocity-feedback, along the dissertation. Among the controllers established and according to the research carried out there, the fuzzy-logic controller has been chosen as the most reliable controller. The controller chosen, allows to obtain the best quality of regulation due to stability and the most reliable step response parameters, presented in section 4.3.

For the reliable control of the flap movements parameters: the velocity and position, according to the conception discussed in section 3.2, the fuzzy-logic controller established, had to be implemented and validated.

The ETF determined for irregular waves, significantly differs from the LTF calculated and validated for regular waves as investigated in the subsection 4.4.1. However, the nonlinear component does not occur in the spectra of the irregular waves as investigated along the dissertation. The observed differences between ETF and LTF result from the secondary phenomena for the harmonics of frequencies exceeding 0.7 Hz as investigated in the subsection 4.4.2 and from the limited realization time for the harmonics of entire frequencies as investigated in the subsection 4.4.3. Besides, the differences in the ETF and LTF, presented in Fig. 4.14 and Fig. 4.15, seem to be nondeterministic.

Even advanced control theories to date [33],[34], do not handle the effects of limited realization time as investigated along the dissertation for the multi-segmented flap-type wave maker with a force-based absorption.

For the automatic compensation of the undesirable effects mentioned, according to conception discussed in section 3.2, the solution in form of the adaptive wave spectrum controller and the non-invasive system for measuring the wave profile, essential for implementation the wave spectrum-feedback, had to be developed, implemented and validated.

The thesis of the doctoral dissertation assumed that this solution is applicable, as will be proven below.

5. SOLUTION

5.1. Black-Box Adaptation System (BBAS)

The solution in form of the adaptive control system with a Black-Box model has been proposed as a recommendation arising from the research carried out in Chapter 4. The Black- Box approach has been proposed due to the lack of the satisfactory hydromechanical models to compensate the differences in ETF to the LTF investigated in the subsection 4.4.1. Moreover,

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there are no satisfactory models to compensate the impact of the disintegration and random breakdown into adjacent frequencies in consequence of the deterioration of the spectrum spread, investigated in the subsection 4.4.2. Furthermore, even if the deterministic model would be developed with certain accuracy, it would be inapplicable due to limited Tr necessary to be applied. It results in the generated wave profile is out of the control theory due to deterioration of the frequency resolution, discussed and investigated in the subsection 4.4.3. Therefore, due to the lack of the robust and sufficiently general model, the well-known and widely discussed adaptation systems, such as the Model-Reference Adaptation System MRAS [25], [26] were inapplicable.

The proposed system combines the prediction of the feedforward signal, the control of the flap movement parameters and finally the adaptive control of the wave spectrum with a wave spectrum-feedback.

The control system – Black-Box Adaptation System (BBAS) with structural diagram presented in Fig. 5.1 – consists of the frequency-domain part and the time-domain part. The frequency-domain part includes the Prediction Mechanism (PM), that uses known amplitude characteristic of the closed-loop system and LTF, derived from LWMT. It allows to calculate the predicted feedforward control signal processed into proportional controller (P), that is scheduled with adjustment mechanism (AM). The time-domain part includes the fuzzy-logic controller (FLS) of the electrohydraulic servo valve (I1) and hydraulic cylinder (I2) with Black-Box model of the towing tank (BB). Both parts: the frequency-domain and time-domain are conjugated with the Fast Fourier Transform blocks: forward (FFT) and backward (IFFT). The BBAS acquires the desired wave spectrum HWr(ω) and processes the spectrum in PM and P, subsequently, into the spectrum of the control signal AX2r(ω). The AX2r(ω) is translated into its time-domain equivalent signal AX2r(t), that is processed to the input of FLS. The FLS controls the parameters of the wave maker flap movements: the velocity AX1(t) with the flap velocity-feedback from I1 and the position AX2(t) with the flap position-feedback from I2. The flap movements generate the waves HW(t) in the BB. The AM calculates the correction function C(ω) for the HWr(ω) acquired at the input of the BBAS and for the HW(t) translated into its frequency domain equivalent HW(ω) acquired with the wave spectrum-feedback from BB. The C(ω) is calculated as the ratio of the desired HWr(ω), divided by the measured HW(ω). It allows to compensate the impact of the secondary phenomena and to limit realization time to obtain the spectrum of the desired accuracy.

The BBAS approach is expected to solve the problem of the lack of satisfactory hydromechanical models [24] and limited realization time. It is expected to solve through the wave spectrum-feedback and adaptive compensation of the effects of all phenomena, that occur while the wave generation and propagation.

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Fig. 5.1. Structural diagram of the proposed Black-Box Adaptation System – the frequency-domain part:

prediction mechanism PM and proportional controller P with adjustment mechanism AM, conjugated via the FFT and IFFT blocks with the time-domain part: fuzzy-logic controller FLS that controls electrohydraulic servo valve I1 and hydraulic cylinder I2 with Black-Box model of the towing tank BB [23]

6. IMPLEMENTATION

The solution presented in Chapter 5, has been implemented into embedded system merged with a personal computer application. Implementation of the control algorithm into the personal computer application as well as the embedded system has been realized using .NET environment and C# programming language. The embedded system with a Graphical User Interface (GUI), communicates with the personal computer application. It also communicates with the wave non-invasive measuring system and with the wave maker sensors and actuators to acquire the feedback signals.

The solution has been implemented into consistent and user-friendly computer system, that allows for remote control and monitoring of the wave maker. The way of implementing the solution greatly reduces the costs due to limited time-consumption and employee-involvement.

Moreover, it allows to improve and streamline operations due to standardization of processes realized in accordance with the internal procedures of the CTO S.A. [46]-[48] developed by the Author of the dissertation.

In the next step, the system has been launched and validated under the generation of waves with required accuracy of ESD, described in section 2.1, due to automatic compensation the undesirable effects, discussed in section 4.5. It has been performed in accordance with descriptions in the following chapter.

Flap position module Flap velocity module

Fuzzy-logic controller Prediction

mechanism Black-Box model

Adjustment mechanism Proportional

controller Desired

wave spectrum

frequency-domain time-domain

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7. VALIDATION

7.1. Validation

Following the verification carried out in the last section, the operating area has been described at the ultimate parameters of the wave profiles. The ultimate parameters of the wave profiles have been chosen as meeting the required accuracy. The operating area described on the ultimate parameters of the wave profiles of Pierson-Moskowitz spectra, is presented in Fig. 7.1. The same operating area circumscribed on the ultimate parameters of the wave profiles of JONSWAP spectra, is presented in Fig. 7.2.

Fig. 7.1. The BBAS operating area circumscribed at the parameters of wave profiles of the Pierson- Moskowitz spectra modelled with the required accuracy

Fig. 7.2. The BBAS operating area circumscribed at the parameters of wave profiles of the JONSWAP spectra modelled with the required accuracy

The results presented above indicate that the operating area is limited around. The left side of the area is limited due to range of motion of the wave maker flap between the mechanical buffers. The right side of the area is limited due to the wave breaking exceeding the maximum

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steepness of the wave. The peak of the characteristic is flaten due to the inertia of the wave maker flap and hydrodynamic loads, as indicated in [36] and analysed in the further subsection 8.2.3.

Nonetheless, the BBAS operating area validated and presented above meets the present and future expected needs of the CTO S.A. under the seakeeping model tests.

The BBAS has been intended to finely and convenient control of the process of modelling of the environmental conditions in the towing tank. The validated solution has been successfully used to conduct of numerous seakeeping model tests for needs of the research and industrial projects, included navy vessels, special purposes vessels, passenger vessels, container vessels, gas carriers as well as fishing vessels.

8. FUTURE DEVELOPMENT

8.1. Electric drive conception

Presently, most of the wave makers worldwide are equipped with the hydraulic and electric driving mechanisms – 43.2% and 51.3%, respectively [1]. In line with the general trend of increasing the use of electric motors, the new implementations of the wave makers are based on the electric drives. Among the advantages of electric driven wave makers over hydraulic driven wave makers, the following can be mentioned:

 immediate ability to work without the need for time-consuming heating of the hydraulic oil,

 easier maintenance without the need for condition monitoring and periodic change of the hydraulic oil and elements of the hydraulic installation,

 more advanced control of the drives themselves using modern methods and communication interfaces.

Due to development of the electric drive techniques in recent years [38] and mentioned advantages, it was purposeful to consider the implementation of an electric drive for the wave maker in CTO S.A. towing tank. For needs of the current conception and in accordance with the description in the following sections, the models of drive, transmission and actuator have been derived and the simulation of work has been carried out. Finally, the system with the electric drive has been compared with the system with the hydraulic drive under quality of regulation criterion.

8.2. Implementation of model

The model has been implemented in C to the Dev-C++ integrated development environment. It has been done in accordance with the diagram presented in Fig. 8.1. The PMSM model with FOC has been considered as follows. The PMSM has been considered as powered from PWM inverter (INV.) with an impulse period of 0.157 ms and a DC power source of voltage uDC=1.72 [p.u.].

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The parameters of the id PI and iq PI controllers have been experimentally tuned as:

Kp=1,Ti=10 and Kp=10,Ti=10 – respectively. The parameters were chosen to obtain the minimum torque oscillations on the motor shaft with satisfactory system dynamics.

The flap velocity and flap position fuzzy-logic control system FLS has been implemented in accordance with description in section 4.3. The PMSM rotor velocity ωr is taken instead of hitherto flap velocity signal. The PMSM rotor position θr is taken instead of hitherto flap position signal. The ωr and θr are measured using an encoder E.

The FLS output value had to be translated with a scaling factor SF into the reference current vector on q-axis. The SF has been experimentally chosen as equal to 4.0 to obtain satisfactory dynamics of the system with an electromagnetic torque not exceeding of 300% of the rated value at the peak. The simulation results of the implementation and tuning are presented in section 8.3.

Fig. 8.1. Structural diagram of the flap velocity and flap position fuzzy-logic control system with the electric drive with FOC type of control method and PMSM type of electric motor powered from the PWM inverter

8.3. Simulation of work

The work of the model implemented in subsection 8.2, has been simulated. The results are presented in Fig. 8.2. The steps of reference stroke AX2r are given in 0.1 s, 2.5 s and 6.0 s to test the response of the tuned system. The steps of the thrust torque TR are given in 5.4 s, 5.6 s and 5.8 s to test the system robustness for distortions that may originate from the reflected waves. The AX2 is the measured flap stroke. The TR is the flap thrust torque reduced to the PMSM shaft. The W is the shaft velocity of the PMSM. The Te is the electromagnetic torque of the PMSM.

The usd and usq are the stator voltages on d-axis and q-axis of the PMSM, respectively. The isd

and isq are the current vectors on d-axis and q-axis of the PMSM, respectively.

The simulation has confirmed that the system provides the required dynamics and robustness while the measured values do not exceed the permissible values.

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Fig. 8.2. Simulation of work of the synthesized model with electric drive

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The quality of regulation of the fuzzy-logic system with electric drive has been checked under the parameters of step response. It has been registered for the closed-loop system with AX2r given as input signal and AX2 given as output signal scaled to launch the step of 1 m stroke of the flap X2. Thus, the value of the steps are equivalent for two compared systems: the system with electric drive and the system with hydraulic drive. The step response is shown in Fig. 8.3.

Fig. 8.3. Step response of the closed-loop synthesized model with electric drive – stroke values: desired (black line) and measured (red line)

8.4. Conclusion

The fuzzy-logic control system of the wave maker flap with the electric drive has been modelled and simulated. In accordance with the simulation, the system is satisfactorily dynamic and robust. In accordance with the step response, the system with the electric drive in relation to system with the hydraulic drive, ensures shorter settling time tR with significantly less overshoot D and without oscillating d/D. The rise time tn and setting time tN are longer but satisfactory.

The satisfactory results of simulation and numerous advantages of electric drive, testify that the implementation of the simulated fuzzy-logic system with the electric drive, should be considered as future solution.

9. SUMMARY AND CONCLUSIONS

The dissertation describes the complete cycle of research and development process, realized to improve the existing product: the flap-type wave maker in a model basin; and, finally, to improve the existing service: the seakeeping model tests carried out in hydromechanics laboratory. The demand to be supplied – the high-performance hydromechanics experiments realization to improve the maritime safety – was identified. The problem to be solved – the accurate modelling of waves specific to the type of sea and to the state of sea in a model scale –

t

R

=1.31 s

t

n

=0.84 s 0.9

0.1 D=0.02

<0.02

t

N

=1.41 s

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was formulated. The available resources – the facilities and the techniques – were conceptualized. The right research to be accomplished – the experiments and simulations carried out on the facilities and models – were realized and analysed. The solution hypothesized to develop and implement – the BBAS approach to modelling of the maritime environment conditions in a model scale with required accuracy – was fulfilled. Finally, the solution was validated. The future development conception – the use of high-performance electric drive – was considered and modelled with a great results.

The greatest achievements of the doctoral dissertation are:

 improvement of an existing product – the flap-type wave maker – through a development of a new complete control system with a wave spectrum-feedback (BBAS) for a real towing tank in the hydromechanics laboratory;

 improvement of an existing service – significant facilitate the seakeeping model tests – provided to the maritime industry to improve the maritime safety;

 development of the fuzzy-logic controller to control the velocity and the position of the wave maker flap, ready-made for broad distribution within BBAS to hydromechanics laboratories;

 development of the non-invasive, contactless, and maintenance-free ultra-sound system for measurement of the wave profile, applied for a patent and ready-made to broad distribution for a wave profile measurements;

 improvement of the Quality Management System of the Maritime Advanced Research Centre, CTO S.A.

The significant achievement of the doctoral dissertation is the supply of the complete control system that allow to model the environmental conditions with high accuracy in a time- efficient, low-cost, user-friendly and an automatic manner. It greatly contributes to perform the seakeeping model tests in the Maritime Advanced Research Centre, CTO S.A. It allows to determine accurately the properties of the naval and offshore objects to improve the human safety and survivability of the constructions. This unique solution has been already used in the research and commercial projects of different vessels for numerous clients – domestic and international.

The projects included navy vessels, special purposes vessels, passenger vessels, container vessels, gas carriers as well as fishing vessels.

Another significant achievement of the dissertation is that the control system developed, is a ready-made for broad distribution as a catalogue product of the Maritime Advanced Research Centre, CTO S.A to another hydromechanics laboratories. 61.1% of the wave makers in towing tanks worldwide are single unit and 43.2% are equipped with hydraulic driving mechanism [1], such as the one considered in the dissertation. The modernization of these research facilities can be low-costly carried out to make them the user-friendly, time-efficient and low employee-offload.

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Moreover, the implementation of the developed system to the control of the fully electric drive with a multi-segmented flap is easy to execute. This is of great importance due to the fact that 51.3%

of the wave makers in towing tanks worldwide are equipped with electric driving mechanism [1]

and the use of electric drives constantly increases.

The method and the ultra-sound device for a wave profile measurement on the surface of liquid, were developed and implemented within the works related to the dissertation. It is the subject of a Polish and an European patent application [44], [45]. The method and the device developed are the ready-made products for a wave profile measurements and can be also broadly distributed as a catalogue product of the Maritime Advanced Research Centre, CTO S.A.

The solution developed under the dissertation, enabled the Author to develop the procedures [46]-[48]. The procedures were incorporated as the internal documents included in the Quality Management System of the Maritime Advanced Research Centre, CTO S.A., certified under ISO 9001:2015. Hence, the works within the dissertation, also improved the Quality Management System of the research centre.

Besides, due to the resources available in the deepwater towing tank, the hydraulic drive was applied within the dissertation. From the point of view of the general trend, the PMSM is more worth considering as the wave maker drive. To date, the 51.3% of wave makers worldwide are equipped with the electric driving mechanism, versus the 43.2% equipped with the hydraulic one [1]. According to the trend the number of the electric drive applications is expected to increase.

Thus, within the future works it is recommended to apply the electric drive and insight into more advanced solutions for improvement of the model tests different than the typical seakeeping tests at a desired state of sea in a model scale.

Among the more advanced methods related to modelling of environmental conditions, the worthy of future consideration are:

 the active absorption of the waves to further shorten the time interval between subsequent realizations, needed to calm the water [1];

 multi-segmented flap for the active absorption of transverse waves instead of the straighteners to shorten the wave maker section and lengthen the test section of the towing tank;

 method to suppress the nonlinear components, that would be unintended while the monochromatic waves generation [21];

 sensorless drive to control the flap-velocity and flap-position at reduced costs and reduced maintenance [38].

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AN ADAPTIVE CONTROL OF THE WAVE IN A TOWING TANK