基于非线性滑模的衍射薄膜自适应跟踪控制

Adaptive Tracking Control for Diffractive Film Based on Nonlinear Sliding Mode

设计了一种用于薄膜衍射成像系统的非线性滑模自适应控制器,以实现对大直径镜阵列中子阵列姿态的精确指向。通过推导基于误差四元数和角速度的运动学和动力学方程,设计衍射薄膜子镜阵列控制器进而实现精确指向。利用李雅普诺夫方法证明了控制器的全局稳定性。该控制器通过自适应地识别每个子镜系统的惯性矩阵,使其对有界扰动和惯性参数的变化具有鲁棒性。同时引入了连续反正切函数,有效防抖。仿真结果表明,在存在转动惯量矩阵不确定性和各种扰动的情况下,所设计的控制器能够保证各子镜中衍射膜的准确跟踪。

A nonlinear sliding mode adaptive controller for a thin-film diffractive imaging system is designed to achieve accurate pointing direction over the attitude of subarrays in large-diameter mirror arrays.The kinematics and dynamics equations based on error quaternion and angular velocity are derived,and a diffractive thin-film sub-mirror array controller is designed to point precisely.Moreover,the global stability of the controller is proved by the Lyapunov method.Since the controller can adaptively identify the inertia matrix of each sub-mirror system,it is robust to bounded disturbances and changes in inertia parameters.At the same time,the continuous arctangent function is introduced,which is effectively anti-chattering.The simulation results show that the designed controller can ensure the accurate tracking of the diffractive film in each sub-mirror in the presence of rotational inertia matrix uncertainty and various disturbances.