为实现机器人关节在非线性摩擦和外界未知干扰力矩等因素影响下的精确和稳定控制，通过改进LuGre摩擦模型来描述系统的非线性摩擦特性，采用自适应算法进行摩擦补偿来逼近摩擦力的变化，并采用模糊神经网络逼近外界未知干扰力矩对系统的影响.引入正切障碍李雅普诺夫（Lyapunov）函数对输出信号进行约束，使误差被限制在给定范围之内.利用双曲正弦函数跟踪微分器解决了虚拟输入微分引起的“微分爆炸”和一阶滤波器精度差问题，将自适应控制方法与反步控制理论相结合，提出了一种带摩擦补偿的模糊自适应反步控制方法.利用Lyapunov判据证明了闭环系统的所有误差最终一致有界，并通过仿真得出本文所提出的控制方法相比于传统PID与神经网络动态面控制（Radial Basis Function Dynamic Surface Control，RBFDSC），位置跟踪误差分别提高了近7.5%和3%；当LuGre模型参数变化时，自适应算法也可以精确对摩擦力进行跟踪补偿，从而验证了本文所提出的控制策略的有效性和鲁棒性.
In order to achieve precise and stable control of the robot joint under the influence of nonlinear friction and unknown external disturbance moment, the LuGre friction model is modified to describe the nonlinear friction characteristics of the system, and an adaptive algorithm is used to compensate the friction to approximate the change of friction. The fuzzy neural network is used to approximate the influence of unknown external disturbance moment on the system. In this paper, the tangent barrier Lyapunov function is introduced to constrain the output signal, so that the error is limited within a given range. A hyperbolic sine function tracking differentiator is used to solve the “differential explosion” caused by virtual input differentiation and the poor accuracy of the first-order filter. A fuzzy adaptive backstepping control method with friction compensation is proposed by combining the adaptive control method with the backstepping control theory. Lyapunov criterion is used to prove that all the errors of the closed-loop system are uniformly bounded. Simulation results show that，compared with the traditional PID control and RBFDSC, the position tracking error of the proposed control method is improved by nearly 7.5% and 3%, respectively. Moreover, when the parameters of the LuGre model are changed, the adaptive algorithm can accurately track and compensate for the friction force, thus verifying the effectiveness and robustness of the proposed control strategy.
李俊阳 ?,赵琛 ,夏雨 ,甘来 .基于改进LuGre摩擦模型的机器人关节模糊自适应反步控制[J].湖南大学学报：自然科学版,2022,49(10):147~156复制