On the Control of Three-Degree-of-Freedom Wave Energy Converters

2017 ◽  
Author(s):  
Shangyan Zou ◽  
Ossama Abdelkhalik
Keyword(s):  
Wave Energy ◽  
Degree Of Freedom ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Wave Energy Converters ◽  
Control Comparison ◽  
Quadratic Optimal Control ◽  
Pseudo Spectral Method ◽  
Three Degree Of Freedom ◽  
Pseudo Spectral

The control of a three-degree-of-freedom (3-DOF) wave energy converter (WEC) is considered in this paper. Recently, several methods have been developed in the literature for this problem. This paper is a comparison between three methods: the non-linear model predictive control, the pseudo-spectral method, and the time-variant linear quadratic optimal control. Comparison between the three methods is presented in terms of the harvested energy.

Numerical Analysis and Parameter Optimization of a Portable Two-Body Attenuator Wave Energy Converter

2021 ◽  
Author(s):  
Joseph Capper ◽  
Jia Mi ◽  
Qiaofeng Li ◽  
Lei Zuo
Keyword(s):  
Drag Coefficient ◽  
Wave Energy ◽  
Degree Of Freedom ◽  
Wave Energy Converters ◽  
Ocean Wave Energy ◽  
Significant Difference ◽  
Power Maximization ◽  
Study Power ◽  
Body Cross Section ◽  
Three Degree Of Freedom

Abstract Easily portable, small-sized ocean wave energy converters (WECs) may be used in many situations where large-sized WEC devices are not necessary or practical. Power maximization for small-sized WECs amplifies challenges that are not as difficult with large-sized devices, especially tuning the device’s natural frequency to match the wave frequency and achieve resonance. In this study, power maximization is performed for a small-sized, two-body attenuator WEC with a footprint constraint of about 1m. A thin, submerged tuning plate is added to each body to increase added mass without significantly increasing hydrostatic stiffness in order to reach resonance. Three different body cross-section geometries are analyzed. Device power absorption is determined through time domain simulations using WEC-Sim with a simplified two-degree-of-freedom (2DOF) model and a more realistic three-degree-of-freedom (3DOF) model. Different drag coefficients are used for each geometry to explore the effect of drag. A mooring stiffness study is performed with the 3DOF model to investigate the mooring impact. Based on the 2DOF and 3DOF power results, there is not a significant difference in power between the shapes if the same drag coefficient is used, but the elliptical shape has the highest power after assigning a different approximate drag coefficient to each shape. The mooring stiffness study shows that mooring stiffness can be increased in order to increase relative motion between the two bodies and consequently increase the power.

scholarly journals Convergence results for an averaged LQR problem with applications to reinforcement learning

2021 ◽  
Author(s):  
Andrea Pesare ◽  
Michele Palladino ◽  
Maurizio Falcone
Keyword(s):  
Optimal Control ◽  
Reinforcement Learning ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Current System ◽  
Numerical Test ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Lqr Problem ◽  
Quadratic Optimal Control

AbstractIn this paper, we will deal with a linear quadratic optimal control problem with unknown dynamics. As a modeling assumption, we will suppose that the knowledge that an agent has on the current system is represented by a probability distribution $$\pi $$ π on the space of matrices. Furthermore, we will assume that such a probability measure is opportunely updated to take into account the increased experience that the agent obtains while exploring the environment, approximating with increasing accuracy the underlying dynamics. Under these assumptions, we will show that the optimal control obtained by solving the “average” linear quadratic optimal control problem with respect to a certain $$\pi $$ π converges to the optimal control driven related to the linear quadratic optimal control problem governed by the actual, underlying dynamics. This approach is closely related to model-based reinforcement learning algorithms where prior and posterior probability distributions describing the knowledge on the uncertain system are recursively updated. In the last section, we will show a numerical test that confirms the theoretical results.

scholarly journals Two Inverse Problems Solution by Feedback Tracking Control

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 137
Author(s):  
Vladimir Turetsky
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Feedback Linearization ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Linear Quadratic Tracking ◽  
Ill Posed ◽  
Quadratic Optimal Control ◽  
Quadratic Tracking

Two inverse ill-posed problems are considered. The first problem is an input restoration of a linear system. The second one is a restoration of time-dependent coefficients of a linear ordinary differential equation. Both problems are reformulated as auxiliary optimal control problems with regularizing cost functional. For the coefficients restoration problem, two control models are proposed. In the first model, the control coefficients are approximated by the output and the estimates of its derivatives. This model yields an approximating linear-quadratic optimal control problem having a known explicit solution. The derivatives are also obtained as auxiliary linear-quadratic tracking controls. The second control model is accurate and leads to a bilinear-quadratic optimal control problem. The latter is tackled in two ways: by an iterative procedure and by a feedback linearization. Simulation results show that a bilinear model provides more accurate coefficients estimates.

scholarly journals A Hida–Malliavin white noise calculus approach to optimal control

2018 ◽  
Vol 21 (03) ◽  
pp. 1850014
Author(s):  
Nacira Agram ◽  
Bernt Øksendal
Keyword(s):  
Optimal Control ◽  
Diffusion Coefficient ◽  
White Noise ◽  
Backward Stochastic Differential Equation ◽  
Second Order ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Alternative Approach ◽  
Quadratic Optimal Control ◽  
White Noise Calculus

The classical maximum principle for optimal stochastic control states that if a control [Formula: see text] is optimal, then the corresponding Hamiltonian has a maximum at [Formula: see text]. The first proofs for this result assumed that the control did not enter the diffusion coefficient. Moreover, it was assumed that there were no jumps in the system. Subsequently, it was discovered by Shige Peng (still assuming no jumps) that one could also allow the diffusion coefficient to depend on the control, provided that the corresponding adjoint backward stochastic differential equation (BSDE) for the first-order derivative was extended to include an extra BSDE for the second-order derivatives. In this paper, we present an alternative approach based on Hida–Malliavin calculus and white noise theory. This enables us to handle the general case with jumps, allowing both the diffusion coefficient and the jump coefficient to depend on the control, and we do not need the extra BSDE with second-order derivatives. The result is illustrated by an example of a constrained linear-quadratic optimal control.

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