基于随机微分包含理论的风力发电机齿轮传动多体系统的稳定性分析及其控制

The gear transmission system of wind driven generator is a very complicated periodic time-varying multi-body system with strong nonlinear fluid-rigid-flexible coupling, and this system has complex random wind load boundary conditions. In view of the discontinuous state of the system under different working conditions, we established a stochastic differential inclusion mathematical model for gear transmission multi-body system of wind driven generator. Aim at tooth surface friction, tooth side clearance, lash, engaging force and torque in gear transmission, we designed set-valued mapping and the qualitative properties and stability of stochastic differential inclusions are studied by using the theory of set-valued analysis. The relative position of the trajectory of the solution to the Lipschitz surface is studied through set reachability and invariance. The relationship between dynamic evolution and system parameters of gear transmission multi-body system is studied by means of analytical analysis and numerical simulation, and the optimal matching law of system parameters is obtained. A design method of sliding mode controller based on global and non-global dependent cone conditions is proposed, and in view of the possible external disturbance, the influence of the random wind speed and the changeable working conditions, etc in the actual operation of the gear transmission multi-body system of wind driven generator. Then the multi-input multiple-output (MIMO) variable control method and fuzzy immune PID pitch control strategy is adopt to discuss the global stability of systems. And it provides the corresponding theoretical guarantee for the stability and reliability of the wind turbine system in the western region.

风力发电机齿轮传动系统是一个非常复杂的强非线性流-刚柔耦合的周期时变多体系统，具有复杂的随机风载边界条件。针对系统在不同工况条件下所表现出不连续的状态，建立风力发电机齿轮传动多体系统的随机微分包含数学模型。针对齿轮传动中齿面摩擦、齿侧间隙、冲击、啮合力、扭矩等设计集值映射, 运用集值分析理论研究随机微分包含系统的定性性质及稳定性。通过集合可达性和不变性研究解的轨迹同 Lipschitz 曲面相对位置，综合运用解析与数值模拟探讨齿轮传动多体系统的动力学演化与系统参数的关联关系，寻求系统参数的最优匹配规律。提出基于全局和非全局相依锥条件的滑模控制器设计方法，针对风力发电机齿轮传动系统中存在的外界扰动、随机风载以及工况多变等因素，我们采用多输入多输出(MIMO)变量控制方法以及模糊免疫PID的桨距控制策略，探讨系统的全局稳定性问题，为西部地区的风力发电机系统稳定性和可靠性提供相应的理论保障。

随着风力发电机组的大型化，维护成本的提高，对齿轮传动系统的稳定性要求也随之提高。作为风电设备的核心装置增速箱，齿轮传动系统已经成为各种机器和机械设备中应用最为广泛的动力和运动传递形式之一，但是由于风力发电机增速箱常年工作在恶劣环境，在复杂风况及叶轮转矩的作用下，由于风力的不确定性，载荷往往会在瞬间发生剧烈变化，导致塔架、齿轮箱体等的激振和弹性变形。同时还要考虑齿面摩擦、齿侧间隙、啮合误差、时变刚度等的影响，导致风电齿轮传动系统产生的复杂的强非线性振动，这种振动会对机械系统的工作性能和可靠性产生很大的影响。因此，需要针对风力发电机传动系统的多自由度、强耦合非线性特性，建立多体动力学模型，对其进行较全面的动力学分析和优化设计，以保障风力发电机增速箱的正常运行。. 项目组针对风力发电机齿轮传动系统在不同工况条件下所表现出不连续的状态，建立了随机风力发电机齿轮传动多体系统的数学模型。针对齿轮传动中齿面摩擦、齿侧间隙、冲击、啮合力、扭矩等设计集值映射, 运用集值分析理论研究了系统的定性性质及稳定性。综合运用多种数值模拟手段研究了该类非光滑动力系统的吸引子共存与分岔行为、系统的动力学演化过程与系统参数的关联关系，揭示了系统的动力学特性发生改变的机理，针对风力发电机齿轮传动系统中存在的外界扰动、随机风载以及工况多变等因素，提出了优化的控制策略，研究了系统的全局稳定性问题，为西部地区的风力发电机系统稳定性和可靠性提供相应的理论保障。. 在项目执行期内，项目组成员在国内外重要学术期刊上发表学术论文14篇。