针对未知环境扰动影响下空间机械臂的关节轨迹跟踪控制问题,本文提出了一种基于固定时间干扰观测器的自适应固定时间滑模控制策略。首先,本文设计了一种用于估计未知环境扰动的固定时间观测器,该观测器可以使估计误差在不依赖干扰上界已知的前提下于固定时间内收敛,并可根据实际环境的变化调整观测器增益,从而提高观测器对未知环境的适应性;其次,本文构造了一种新型固定时间稳定系统,相比于传统方法,该系统具有更小的收敛时间上界。在此基础上,本文设计了一种非奇异固定时间滑模面,该滑模面不仅避免了奇异问题而且可严格保证滑模面及其导数的连续性;最后本文设计了一种结合自适应估计律的固定时间控制器,其能够对动力学方程中的复杂非线性项进行等效处理并对干扰估计残余进行抑制,使整个系统在固定时间内收敛并保证收敛精度,数值仿真实验证明了本文所设计控制策略的有效性。
To address the problem of high-precision joint trajectory tracking control for space manipulators under unknown environmental disturbances, this paper proposes an adaptive fixed-time sliding mode control strategy based on a fixed-time disturbance observer. First, a fixed-time observer is designed to estimate unknown environmental disturbances. The observer ensures that the estimation error converges within a fixed time without requiring strict assumptions such as known upper bounds of disturbances, and the observer gain can be adjusted according to changes in the actual environment, thereby improving the adaptability of the observer to unknown environments. Second, a novel fixed-time stable system is constructed, which features a smaller upper bound of convergence time compared with conventional methods. On this basis, a nonsingular fixed-time sliding mode surface is designed, which not only avoids the singularity problem but also rigorously guarantees the continuity of the sliding mode surface and its derivative. Finally, this paper designs a fixed-time controller combined with an adaptive estimation law, which can perform equivalent processing of complex nonlinear terms in the dynamic equations and suppress the residuals of disturbance estimation, enabling the entire system to converge within a fixed time while ensuring convergence accuracy. Numerical simulation experiments have demonstrated the effectiveness of the proposed control strategy.