论文部分内容阅读
针对典型跟踪微分器函数形式复杂、稳定性差和输出振颤明显的问题,设计了一种改进的高稳定性快速收敛非线性-线性跟踪微分器(MTD).首先通过引入非线性奇指数函数环节和线性函数环节构造MTD的跟踪函数,然后利用李雅普诺夫直接法和系统等价性证明MTD的全局渐近稳定性,最后通过对参数物理意义和参数变化对跟踪输出精度影响的分析得到MTD参数整定规则.跟踪过程中,当状态与平衡点距离较远时,MTD以非线性环节为跟踪函数主体驱动状态向平衡点快速收敛,以提高系统输出的跟踪速度;当状态与平衡点接近时,MTD以线性环节为跟踪函数主体驱动状态平稳逼近平衡点,以抑制系统输出振颤.仿真表明,MTD参数容易整定,与典型跟踪微分器相比,MTD在系统稳定性、收敛速度和输出平稳性方面具有优势,且具有滤波功能.
Aiming at the problem of complex, poor stability and obvious output chatter of the typical tracking differentiator function, an improved high-stability fast convergence nonlinearity-linear tracking differentiator (MTD) is designed.Firstly, by introducing the nonlinear singular exponential function And MTD tracking function is constructed by linear function, and then the global asymptotic stability of MTD is proved by using Lyapunov direct method and system equivalence. Finally, MTD parameters are obtained by analyzing the influence of the physical meaning of parameters and the variation of parameters on tracking output accuracy Tuning rule.In the tracking process, when the state is far away from the equilibrium point, the MTD converges quickly to the equilibrium point by tracking the main driving state of the function in a non-linear way to improve the tracking speed of the system output. When the state is close to the equilibrium point, The MTD is used to track the steady-state equilibrium of the driving state of the main body in the linear part, so as to restrain the output chattering of the system. The simulation shows that the MTD parameter is easy to set. Compared with the typical tracking differentiator, MTD achieves good performance in terms of system stability, convergence speed and output smoothness Has advantages, and has a filtering function.