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摘要: 针对一类具有模型不确定性和外部扰动的时变非线性系统, 基于模型参考控制方法, 设计了具有固定时间收敛特性的终端滑模控制器. 首先, 提出一种带有输入饱和限幅和补偿信号滤波的模型参考控制结构; 然后针对广义误差信号, 采用新型终端滑模面设计了补偿控制器, 较好地平衡靠近和远离平衡点的收敛速度. 基于李雅普诺夫方法证明了闭环系统的稳定性和固定时间收敛特性, 并给出了收敛时间上界. 最后将该方法应用到含有极限环的非线性系统跟踪控制中, 仿真结果验证了该方法的有效性.Abstract: Based on model reference method, a nonsingular terminal sliding-mode control method with fixed time convergence is proposed for a class of time-varying nonlinear systems with model uncertainties and external disturbances. Firstly, a model reference controller structure considering input saturation and compensation signal filtering is proposed. Then a sliding mode controller based on a novel nonlinear terminal sliding mode manifold is constructed for generalized errors, which balances the convergence speed near and away from the equilibrium point. The fixed time convergence and stability of closed-loop system are proved with the Lyapunov method, and the upper bound of convergence time is obtained. Finally, the method proposed is applied to tracking control of nonlinear systems with limit cycle.The simulation results verify its effectiveness.
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表 1 标量系统参数和收敛时间 (s)
Table 1 Coefficients and convergence time (s) of the scalar system
参数 $\beta $ $q $ $\alpha $ $p $ $T $ 1 1 5/9 0 5/9 1.08 2 1 5/9 1 5/9 0.80 3 3 5/9 1 5/9 0.34 4 1 3/9 1 5/9 0.68 5 1 5/9 3 5/9 0.56 6 1 5/9 1 3/9 0.75 表 2 模型A的气动数据
Table 2 Aerodynamic coefficients for Model A
$\alpha\;{\rm{(rad)}}$ $\hat a_0$ $ \hat a_1 $ $ \hat a_2 $ $ \hat a_3 $ $ \hat a_4 $ 0.4363 0.00543 −0.01426 0.41336 −0.00465 0.00263 0.4800 0.00594 −0.01765 0.38793 −0.00487 0.01689 0.5236 0.00657 −0.02040 0.38008 −0.00537 0.02596 0.5672 0.00732 −0.03104 0.53884 −0.00623 0.04189 0.6109 0.00794 −0.03137 0.53455 −0.00751 0.05144 0.6545 0.00914 −0.00246 0.00105 −0.01059 0.03736 0.6981 0.00902 −0.01881 0.62351 −0.01187 0.06119 0.7418 0.00999 −0.03219 1.51180 −0.02862 0.06867 0.7854 0.01135 −0.03712 2.42520 −0.08113 0.02935 表 3 模型C的气动数据
Table 3 Aerodynamic coefficients for Model C
$\alpha\;{\rm{(rad)}}$ $\hat a_0$ $ \hat a_1 $ $ \hat a_2 $ $ \hat a_3 $ $ \hat a_4 $ 0.4363 0.00615 −0.02644 0.82603 −0.00940 0.04934 0.4800 0.00310 −0.00057 1.00250 −0.01157 −1.19080 0.5236 0.00523 −0.00406 0.09998 −0.00167 −0.00183 0.5672 0.00729 −0.01260 0.33063 −0.00506 −0.00378 0.6109 0.00591 −0.03024 1.07030 −0.00285 −0.03726 0.6545 −0.00406 −0.00588 1.0840 0.03646 −0.15374 0.6981 0.00574 −0.00771 −0.03172 −0.01095 0.16302 0.7418 −0.0040 −0.03261 2.3447 0.13848 0.90542 0.7854 −0.00089 −0.02071 0.8361 0.13752 2.8685 -
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