谐波减速器的非线性摩擦建模及补偿

Modeling and compensation of nonlinear friction in harmonic driver

针对带有谐波减速器的双框架控制力矩陀螺框架伺服系统中的非线性摩擦问题,提出了非线性摩擦建模及补偿方法。首先,根据框架伺服系统数学模型导出摩擦力矩与角加速度和电机电流的关系;然后,通过光电码盘测得的角位置计算角速率并设计估计器来估计电机端和负载端的角加速度,利用采样电流和估计的角加速度计算摩擦力矩,建立库伦+粘滞+Stribeck摩擦模型;最后,设计基于摩擦模型的前馈补偿控制器抑制非线性摩擦以提高系统控制精度。实验结果显示,与传统PID控制方法相比,伺服系统加入基于摩擦模型的前馈补偿之后,角速率误差曲线峰峰值减小28.2%,角速率误差均方值减小25.7%;表明通过基于摩擦模型的前馈补偿可以有效抑制非线性摩擦引起的角速率误差,提高伺服系统的控制精度。

To overcome the influence of the nonlinear friction on the gimbal servo-system of a double gimbal control moment gyro with harmonic drivers,the methods of modeling and compensation of the nonlinear friction are proposed.Firstly,the relationships between the nonlinear friction torque and the angle acceleration of a gimbal motor and the friction torque and the current of the gimbal motor are deduced according to the mathematical model of gimbal servo-system.Then,based on the angle position measured by encoders,the angle velocities of the motor and loader sides are calculated and an angle acceleration estimator is designed to estimate the angle accelerations of the motor and loader sides.Furthermore,the nonlinear friction torque is calculated and modeled as the Coulomb,viscous and Stribeck friction model.Finally,a feedforward compensation controller based on the model is designed to restrain the nonlinear friction and to improve the control precision.Experimental results indicate that compared with those of the conventional PID control method,the peak-peak value of angle velocity error curve has decreased by 28.2% and the mean squared error decreased by 25.7% after the feedforward compensation controller is added.It concludes that the feedforward compensation controller decreases the angle velocity error caused by nonlinear friction and improves the control precision of the servo-system.