Abstract
Parafoil trajectory directly affects the power generation of a high-altitude wind power generation (HAWPG) device. Therefore, it is particularly important to optimize the parafoil trajectory and then to track it effectively. In this paper, the trajectory of the parafoil at high altitudes is optimized and tracked in a comprehensively parameterized manner. Both the complex dynamic characteristics of the parafoil and the dexterous demand of the high-altitude controller are considered. Firstly, the trajectory variables and control signals are parameterized as Lagrange polynomials in terms of the corresponding values at the selected nodes. Then, the Radau pseudospectral method (PSM) is employed to reformulate the original dynamic trajectory optimization problem into a static nonlinear programming (NLP) problem. By doing so, the parameterized optimal trajectory, which has the maximum net power generation, can be obtained. To attenuate the strong nonlinear, multivariable and coupling characteristics of the flexible parafoil, a bandwidth parameterized linear extended state observer (ESO) is used to estimate and reject these dynamics explicitly in a unified way. Finally, the simulation results demonstrate the effectiveness of the proposed parameterized trajectory optimization and control strategies. The main contribution of this study is that complicated nonlinear parafoil dynamics with a complex trajectory can be well regulated by a PID-type linear time-invariant controller, which is appealing for practitioners.
Highlights
Wind power generation has a long history, and R&D in wind energy technology has never stopped [1,2]
The Radau pseudospectral method (PSM) is used to obtain the optimal parafoil trajectory with the maximum net power generation and the trajectory can be realized with 41 LGR sampling points, which can meets the microchip requirement
The parameterized extended state observer (ESO) is used to estimate and reject the uncertain dynamics of the parafoil, such that accurate tracking can be achieved in the absence of precise model information in the control design
Summary
Wind power generation has a long history, and R&D in wind energy technology has never stopped [1,2]. Williams [12] optimized the trajectory of the parafoil for power generation and obtained the relationship between cable tension and the wind. Jiang and Hamid developed adaptive laws by taking advantage of the lower and upper bounded slowly varying time-delay information for the unknown nonlinearities [24] These tracking strategies can be applied to the parafoil; the complexity of these. The Radau PSM is used to obtain the optimal parafoil trajectory with the maximum net power generation and the trajectory can be realized with 41 LGR sampling points, which can meets the microchip requirement. The parameterized ESO is used to estimate and reject the uncertain dynamics of the parafoil, such that accurate tracking can be achieved in the absence of precise model information in the control design.
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