scholarly journals Control of Three Degrees-of-Freedom Wave Energy Converters Using Pseudo-Spectral Methods

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Ossama Abdelkhalik ◽  
Shangyan Zou ◽  
Rush Robinett ◽  
Giorgio Bacelli ◽  
David Wilson ◽  
...  
Keyword(s):  
Optimal Control ◽  
Wave Energy ◽  
Parametric Excitation ◽  
Degrees Of Freedom ◽  
Closed Form Solution ◽  
Form Solution ◽  
Programming Approach ◽  
Wave Energy Converters ◽  
Pseudo Spectral ◽  
Three Degrees Of Freedom

Abstract This paper presents a solution to the optimal control problem of a three degrees-of-freedom (3DOF) wave energy converter (WEC). The three modes are the heave, pitch, and surge. The dynamic model is characterized by a coupling between the pitch and surge modes, while the heave is decoupled. The heave, however, excites the pitch motion through nonlinear parametric excitation in the pitch mode. This paper uses Fourier series (FS) as basis functions to approximate the states and the control. A simplified model is first used where the parametric excitation term is neglected and a closed-form solution for the optimal control is developed. For the parametrically excited case, a sequential quadratic programming approach is implemented to solve for the optimal control numerically. Numerical results show that the harvested energy from three modes is greater than three times the harvested energy from the heave mode alone. Moreover, the harvested energy using a control that accounts for the parametric excitation is significantly higher than the energy harvested when neglecting this nonlinear parametric excitation term.

Evaluation of 3-D Computational Model of Oscillating Water Column Converter with Constructal Design with Three Degrees of Freedom and Limited Chimney Height

2021 ◽  
Vol 407 ◽  
pp. 128-137
Author(s):  
Vinícius Bloss ◽  
Camila Fernandes Cardozo ◽  
Flávia Schwarz Franceschini Zinani ◽  
Luiz Alberto Oliveira Rocha
Keyword(s):  
Water Column ◽  
Wave Energy ◽  
Degrees Of Freedom ◽  
Numerical Study ◽  
Mechanical Energy ◽  
Ocean Waves ◽  
Response Surfaces ◽  
Oscillating Water Column ◽  
Promising Source ◽  
Three Degrees Of Freedom

Theoretically, ocean waves contain enough mechanical energy to supply the entire world’s demand and, as of late, are seen as a promising source of renewable energy. To this end, several different technologies of Wave Energy Converters (WEC) have been developed such as Oscillating Water Column (OWC) devices. OWCs are characterized by a chamber in which water oscillates inside and out in a movement similar to that of a piston. This movement directs air to a chimney where a turbine is attached to convert mechanical energy. The analysis conducted was based on the Constructive Design Method, in which a numerical study was carried out to obtain the geometric configuration that maximized the conversion of wave energy into mechanical energy. Three degrees of freedom were used: the ratio of height to length of the hydropneumatic chamber (H1/L), the ratio of the height of the chimney to its diameter (H2/d) and the ratio of the width of the hydropneumatic chamber to the width of the wave tank (W/Z). A Design of Experiments (DoE) technique coupled with Central Composite Design (CCD) allowed the simulation of different combinations of degrees of freedom. This allowed the construction of Response Surfaces and correlations for the efficiency of the system depending on the degrees of freedom (width and height of the chamber), as well as the optimization of the system based on the Response Surfaces.

Toward a Minimal Dynamic Model of a 6-DOF Parallel Robot

1997 ◽  
Author(s):  
L. Beji ◽  
M. Pascal ◽  
P. Joli
Keyword(s):  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Closed Form Solution ◽  
Parallel Robot ◽  
Form Solution ◽  
Lagrangian Formalism ◽  
Inverse Kinematic Problem ◽  
Geometrical Properties

Abstract In this paper, an architecture of a six degrees of freedom (dof) parallel robot and three limbs is described. The robot is called Space Manipulator (SM). In a first step, the inverse kinematic problem for the robot is solved in closed form solution. Further, we need to inverse only a 3 × 3 passive jacobian matrix to solve the direct kinematic problem. In a second step, the dynamic equations are derived by using the Lagrangian formalism where the coordinates are the passive and active joint coordinates. Based on geometrical properties of the robot, the equations of motion are derived in terms of only 9 coordinates related by 3 kinematic constraints. The computational cost of the obtained dynamic model is reduced by using a minimum set of base inertial parameters.

scholarly journals Nonlinear Optimal Control Law of Autonomous Unmanned Surface Vessels

2020 ◽  
Vol 10 (5) ◽  
pp. 1686
Author(s):  
Yung-Yue Chen ◽  
Chun-Yen Lee ◽  
Shao-Han Tseng ◽  
Wei-Min Hu
Keyword(s):  
Optimal Control ◽  
Closed Form ◽  
Closed Form Solution ◽  
Nonlinear Optimal Control ◽  
Form Solution ◽  
Control Law ◽  
Tracking Problem ◽  
Optimal Tracking ◽  
Surface Vessels ◽  
Marine Surface

For energy conservation, nonlinear-optimal-control-law design for marine surface vessels has become a crucial ocean technology for the current ship industry. A well-controlled marine surface vessel with optimal properties must possess accurate tracking capability for accomplishing sailing missions. To achieve this design target, a closed-form nonlinear optimal control law for the trajectory- and waypoint-tracking problem of autonomous marine surface vessels (AUSVs) is presented in this investigation. The proposed approach, based on the optimal control concept, can be effectively applied to generate control commands on marine surface vessels operating in sailing scenarios where ocean environmental disturbances are random and unpredictable. In general, it is difficult to directly obtain a closed-form solution from this optimal tracking problem. Fortunately, by having the adequate choice of state-variable transformation, the nonlinear optimal tracking problem of autonomous marine surface vessels can be converted into a solvable nonlinear time-varying differential equation. The solved closed-form solution can also be acquired with an easy-to-implement control structure for energy-saving purposes.

scholarly journals Adaptive Optimal Control of Wave Energy Converters

2018 ◽  
Vol 51 (29) ◽  
pp. 38-43 ◽  
Author(s):  
Siyuan Zhan ◽  
Bin Wang ◽  
Jing Na ◽  
Guang Li
Keyword(s):  
Optimal Control ◽  
Wave Energy ◽  
Adaptive Optimal Control ◽  
Wave Energy Converters ◽  
Energy Converters
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