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This article presents an intelligent fuzzy logic controller (FLC) for controlling singlebody heaving wave energy converter (WEC) or what is widely known as “Point Absorber”. The controller aims at maximizing the energy captured from the sea waves. The power takeoff (PTO) limitations are addressed implicitly in the fuzzy inference system (FIS) framework. In order to enhance the WEC power capturing bandwidth and make it less susceptible to wave environment irregularities and the system parametric uncertainties, the controller is built to have a selfconfigurable capability. This also eliminates the need to repeatedly run
Wave energy is deemed to be one of the most promising renewable energy resources, with an estimated global potential of 2 TW [
Recently, an extensive research effort has been dedicated to the area of WEC control to maximize the exploited wave energy, while ensuring that the device is operating safely and within its physical and thermal limits. Falnes and Budal pioneered the efforts which led to the important principle of WEC maximum power absorption [
In this paper, an intelligent fuzzy logic based controller is proposed to control a point absorber WEC. This work is an extension of the preliminary results presented in [
In this work, the Uppsala University point absorber design is considered as shown in
The movement of the WEC oscillating body is governed by the forces resulting from the wavebody interactions and the forces applied by the PTO and mooring mechanisms. There is an array of forces that is experienced by the oscillating body and an equal number of reaction forces as stated in Newton's third law [
The wave excitation force,
The hydrodynamic radiation force,
The buoyancy stiffness force,
The drag force,
The mooring system force,
The restoring force,
The losses force,
The input force,
Several works have been conducted on how to handle the radiation convolution term [
To bring down the system's operating frequency to that of the most energetic wave frequencies (
Twoinput twooutput fuzzy controller is implemented. Fuzzy controllers have received great appreciation in industry recently [
Based on the principle of amplitude and phase control [
Without the input PTO force, the spring effect dominates the oscillating system intrinsic impedance. Therefore, by controlling the PMLG stiffness force, the velocity can be made less leading (or nearly in phase) compared to the excitation force, which results in higher excursions and more energy absorption. The opposite can be done to suppress the buoy excursions. Also if Δ
Due to the absence of systematic methods to determine the input and output MFs parameters, they have been chosen by trial and error; however that does not guarantee a decent performance of the WEC at diverse sea conditions. Therefore a method to continuously update the MFs to achieve optimum WEC operation is required. From here after, the developed FLC will be referred to as fixed structure FLC (FSFLC) in order to differentiate it from its selfconfigurable counterpart that is discussed next.
Much research work has been devoted to the subject of FLC online optimization [
PSO algorithms have been utilized in many engineering problems [
In this work, each particle contains the values of the inputs and outputs MFs parameters, namely the Gaussian MF mean and standard deviation. The PSO algorithm searches in a predetermined bounded searching space for the optimum solution that maximizes the absorbed real power. After initiating the particles with values within the specified boundaries, the goodness of the new particles are evaluated by updating the fuzzy controller and checking the WEC system response through computing a cost function. The dynamics of each particle is updated at every iteration using
The dimension of each particle in the swarm is 56, which is the total number of mean and standard deviation parameters that need to be tuned (
The control regime consists of two levels with separate time scales as shown in
To assess the proposed controller, numerical simulations are carried out using MATLAB/Simulink environment. Passive reactive control (PRC) regime is used as a simple and low cost strategy to further assess the developed fuzzy controllers. The PRC regime has been designed to maximize the captured power at only a single wave frequency. For this study, the PRC force is formulated similar to
The performance of the suggested PSOFLC is compared with that of a FSFLC and the PRC strategy. The hydrodynamic frequency domain analysis is carried out once before running the time domain simulations. The system design parameters are shown in
The PSO population size is set to 50 particles, while the total number of searching iterations is set to 80. Maximum number of search iterations is determined such that a good balance is achieved between reaching an optimum or nearly optimum solution and reducing the computational burden. Other parameters like
First, a polychromatic sea state of a significant wave height
The control strategies performance subject to varying wave frequency is presented in
The previous analysis is repeated for waves with larger heights (
Next, various irregular sea states were applied on the buoy. These sea states have been categorized based on the significant wave height
The sensitivity of the proposed controller towards parameter variations is assessed. Generally, controllers which are independent of the system mathematical model exhibit certain level of robustness, such as fuzzy logic controllers. However, a rigorous analytical approach is difficult to attain. Intuitively, the adaptive nature of the PSOFLC is expected to further make the controller less sensitive to uncertainties. To showcase the controller sensitivity to variations in the plant parameters, the mooring stiffness coefficient
In this paper, an intelligent fuzzy logic controller for single body heaving WECs is proposed. The suggested controller has the ability to update its internal structure by continuously modifying the fuzzy MFs using PSO algorithm. Several polychromatic sea states are applied to the system and the PSOFLC proved its superiority to FSFLC. The PSOFLC is capable of forcing the WEC system to absorb more energy regardless of the characteristics of the incoming waves. Also, the proposed controller can keep the system oscillations within reasonable bounded excursions, hence keeping the system stable.
It is obvious from the results that the PSOFLC strategy utilizes more control resource (
The robustness of the PSOFLC has been addressed through applying various perturbations to the system, which proved that robustness to parameter variations is function of the characteristics of the wave environment. It is important to mention that optimum operation of the WEC cannot be achieved; however, operating the system near the optimal condition as long as possible is conceivable. Also, due to the metaheuristic nature of the PSO algorithm, reaching to an optimal solution is not guaranteed. In this study, the design parameters of the PSO algorithm are kept constant throughout the simulations. A possible improvement, which will be the subject of future research, would be using an adaptive PSO algorithm, where the parameters that determine the searching behavior and convergence speed of the PSO algorithm can be updated online. Combining shortterm prediction algorithms to the current controller would probably alleviate the problem of realtime applicability, where enough time can be given to the PSO algorithm to optimize the fuzzy controller, these and other topics would be the scope of future work.
The authors declare no conflict of interest.
Heaving point absorber structure.
The Gaussian MFs updating principle.
Block diagram of the proposed PSOFLC controller.
The dynamics of the WEC buoy under different controllers (
The instantaneous absorbed power (black) along with the corresponding timeaveraged power (grey) (
The dynamics of the WEC PTO (
Comparison of the controllers performance for seastates with
Comparison of the controllers performance for seastate with
Jonswap wave spectrum of a seastate with
WEC power absorption at different seastate scenarios (
Controller sensitivity to variations in the mooring stiffness coefficient under a seastate of
Fuzzy rulebase.
IF  Δ 
THEN  
Δ 

Δ 

Δ 

Δ 

Δ 

Δ 

 
IF  Δ 
THEN  
Δ 

Δ 

Δ 

Δ 

Δ 

Δ 
Z: Zero; PS: Positive small; NS: Negative small; PM: Positive medium; NM: Negative medium; PB: Positive big; NB: Negative big.
Pseudo code of the PSO algorithm.


Update

Update

Adjust the controller FIS 
Evaluate the objective function 
( 
Determine the current best for each 
particle


Determine the current global best 
Output the final 
WEC design parameters.
Buoy radius ( 
5  m 
Buoy mass ( 
2.68 × 10^{5}  kg 
Water plane area ( 
78.54  m^{2} 
Submerged volume ( 
261.80  m^{3} 
Drag coefficient ( 
0.5   
Buoyancy stiffness coefficient ( 
7.89 × 10^{5}  N/m 
Restoring stiffness coefficient ( 
2 × 10^{5}  N/m 
Added infinite mass ( 
1.34 × 10^{5}  kg 
Resonance angular frequency ( 
1.56  rad/s 
Seabed depth ( 
80  m 
Losses resistance ( 
0.4 × 10^{5}  N.s/m 
Mooring stiffness coefficient ( 
1.5 × 10^{5}  N/m 
Mooring cable length ( 
4  m 