In this paper, the maximum power point tracking problem of variable-speed wind turbine systems is studied. Both mechanical part and electromagnetic part of the wind energy conversion system are taken into consideration. In view of the different time scales between the mechanical part and electromagnetic part, singular perturbation theory is applied to model the system in order to cope with the stiffness caused by the two-time-scale characteristic. Then, linear parameter varying (LPV) model is developed to approximate the nonlinear singularly perturbed model. In consideration of data detection time of the state variables, in practice, the control inputs are dependent on the states with a small time delay. Therefore, a novel delay dependent H ∞ controller is designed to make the rotor speed track the reference rotor speed. Furthermore, it is proved that the closed-loop system under control is asymptotically robust stable using Lyapunov theory. In the end, an example simulation verifies the effectiveness and advantages of the developed method by means of comparison with optimal torque control.

中文翻译：

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基于奇异摄动理论的风能转换系统延迟相关 H∞ 控制

本文研究了变速风电机组系统的最大功率点跟踪问题。风能转换系统的机械部分和电磁部分都被考虑在内。针对机械部分和电磁部分的时间尺度不同，采用奇异摄动理论对系统进行建模，以应对由两时间尺度特性引起的刚度问题。然后，开发了线性参数变化（LPV）模型来逼近非线性奇异摄动模型。考虑到状态变量的数据检测时间，在实践中，控制输入依赖于具有较小时延的状态。因此，设计了一种新颖的延迟相关 H ∞ 控制器以使转子速度跟踪参考转子速度。此外，利用李雅普诺夫理论证明了受控闭环系统是渐近鲁棒稳定的。最后，通过与最优转矩控制的比较，实例仿真验证了所开发方法的有效性和优势。