新型固定时间收敛多幂次趋近律

Novel fixed-time convergent multi-power reaching law

中文关键词  多幂次趋近律  滑模控制  固定时间  收敛速度  稳态误差界

英文关键词  multi-power reaching law  sliding mode control  fixed time  convergence rate  steady-state error bound

中文摘要

      针对现有文献中最新幂次滑模趋近律自适应性弱、全论域收敛速度慢、初始点处存在奇异性等不足, 本文 提出一种兼顾固定时间收敛和有限时间收敛的新型多幂次滑模趋近律. 该趋近律在现有幂次趋近律基础上引入变 底函数, 结合了幂次函数和指数函数的组合函数, 提升了滑模在不同趋近阶段自适应能力及收敛速度, 且满足无抖 振约束. 理论证明了本文趋近律在除原点外的状态空间每一点处均快于现有文献中的新型幂次趋近律, 并进一步推 导了与初始误差无关的固定收敛时间上界和稳态误差的解析式. 最后, 仿真结果表明在大扰动和大初始误差条件 下, 本文方案相对现有3种趋近律总误差分别减小了约74.7%, 59.9%以及54.1%. 状态反馈信号存在30 dB噪声干扰 的情况下, 本文方案相对3种趋近律总误差分别减小了约73.4%, 57.8%以及51.7%. 仿真均验证了本文提出趋近律的 优越性与有效性.

英文摘要

      Aiming at the shortcomings of the latest power sliding mode reaching law, such as weak adaptability, slow convergence speed of the whole domain and singularity at the initial point, a novel multi-power sliding mode reaching law considering both fixed-time convergence and finite-time convergence is proposed. Based on the existing power approach law, the approach law introduces a variable base function and a combination function combining power function and exponential function, which improves the adaptive ability and convergence speed of sliding mode in different approach stages, and satisfies the chattering free constraint. It is proved theoretically that the approach law in this paper is faster than the latest power approach law in the existing literature at every point in the state space except the origin, and the analytical expressions of the fixed-time upper bound of the convergence time and the steady-state error independent of the initial error are further derived. Finally, the simulation results show that the proposed scheme reduces the total errors of the three approach laws by about 74.7%, 59.9% and 54.1% respectively under the condition of large disturbance and large initial error. When the state feedback signal is interfered with by 30 dB noise, the total error of the proposed scheme is reduced 73.4%, 57.8% and 51.7% respectively compared with the three approach laws. These simulations have verified the superiority and effectiveness of the approach law in this paper.