Limited realization time of the spectra

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

22

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.

23 4.5. Discussion

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,

24

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.

25

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

26

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

27

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.].

28

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.

29

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

30

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

=1.31 s

t

=0.84 s 0.9

0.1

D=0.02

<0.02

t

=1.41 s

31

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

 development of the non-invasive, contactless, and maintenance-free ultra-sound