Establishing accurate dynamic models in a form that is suitable for integration with model-based control methods, is of great significance for further improving the dynamic motion control precision of ball-screw drives. However, due to the nonlinear time-varying factors such as position-dependent dynamics and nonlinear friction disturbance, it is difficult to model the dynamic characteristics of ball-screw drives accurately, concisely and efficiently. To overcome this challenge, a sparse identification method for ball-screw drives is proposed. Ball-screw drives are modeled as discrete-time linear parameter-varying systems under nonlinear friction disturbance, and two types of dictionary function libraries are designed to represent the position-dependent dynamics and nonlinear friction respectively. After constructing the regression form of the system model, a stepwise sparse regression policy is proposed to solve all the coefficients of dictionary functions. The proposed method is verified in both simulation and real environments. The results both show that by the proposed method, an accurate and linearizable dynamic model of ball-screw drives can be identified only using the data from only one global random excitation experiment covering the working stroke.

以适合于与基于模型的控制方法集成的形式建立准确的动力学模型，对于进一步提高滚珠丝杠传动的动态运动控制精度具有重要意义。然而，由于位置相关动力学和非线性摩擦扰动等非线性时变因素，很难准确、简洁和高效地对滚珠丝杠传动的动态特性进行建模。为了克服这一挑战，提出了一种用于滚珠丝杠驱动的稀疏识别方法。将滚珠丝杠传动建模为非线性摩擦扰动下的离散时间线性参数变化系统，并设计了两类字典函数库分别表示位置相关动力学和非线性摩擦。在构建系统模型的回归形式后，提出了逐步稀疏回归策略来求解字典函数的所有系数。所提出的方法在模拟和真实环境中都得到了验证。结果均表明，通过所提出的方法，仅使用一次覆盖工作行程的全局随机激励实验的数据，就可以识别精确且可线性化的滚珠丝杠驱动动力学模型。