控制力矩受限的卫星姿态有限时间鲁棒控制算法

为了解决在卫星姿态控制问题中经典滑模控制器所存在的收敛速度慢、指数收敛的缺陷,同时为增强控制器对外部干扰与系统不确定性的鲁棒性,提出了一种对系统模型具有鲁棒性的快速收敛有限时间控制算法.针对传统滑模面角速度下降过快导致的收敛速率慢的缺陷,基于Lyapunov方法设计了一种具有三段式结构的有限时间滑模面,提升收敛速率并保证稳态精度,同时利用欧拉轴的特性消除有限时间控制中的奇异性问题;通过引入符号函数项,解决系统转动惯量的不确定性与外部干扰力矩问题;通过放缩控制律中的比例项解决控制力矩受限的问题;通过Lyapunov函数证明本文提出的控制律的有限时间稳定性,同时给出系统收敛的时间估计.理论分析与仿真结果均表明,提出的控制算法能够在大幅提升收敛速率的同时保证稳态精度.同时也表明了提升系统性态的关键是规划姿态角速度,即通过合理设计滑模面与期望角速度曲线可以实现提升系统收敛速率与鲁棒性的目的.

Robust finite-time control algorithm for satellite attitude control under control torque saturation

To improve the convergence rate of standard sliding mode control whose convergence rate is exponential, a robust finite-time control algorithm for satellite attitude stabilization under control torque saturation is presented. A three-stage structure finite time sliding mode with better convergence rate and steady accuracy is developed based on the Lyapunov method, and the issue that severe descent of angular velocity leads to convergence rate decline of attitude quaternion is avoided. The singularity issue is solved by using the property of Euler axis. By limiting the proportional term in control law, the control torque constraint is added into the control law. The known disturbance torque and inertia matrix uncertainty is solved by introducing the sign function. The finite-time stability is proved by a Lyapunov function, the convergence time estimation is given, and the property that the proposed controller could largely improve the convergence rate and maintain the high accuracy at steady stage is demonstrated by theoretical analysis and simulation results. This paper proves that planning angular velocity is the key to improve system performance, and the convergence rate and the system robustness could be improved by properly designing sliding mode and desired angular velocity.