Design of a Fractional-order Finite-time Controller for High-speed Train With Uncertain Model and Actuator Failures
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摘要:
针对具有输入非线性, 不确定的气动阻力, 未知的车间力, 外部扰动以及未知的执行器故障等特征的高速列车非线性系统, 结合分数阶稳定性原理以及有限时间控制理论, 本文设计了一种分数阶有限时间控制器以实现高速列车更快速且更高精度的跟踪控制. 该控制器能够直接补偿高速列车的不确定性和非线性以及执行器故障而不需任何“试错”过程, 且稳定时间可由控制参数的不同选择来调整. 仿真研究验证了所设计控制器的有效性和优越性.
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关键词:
- 分数阶有限时间控制器 /
- 高速列车 /
- 不确定性 /
- 执行器故障 /
- 非线性
Abstract:This paper focuses on the position/velocity tracking control problem of high speed train (HST) with considering some uncertain and nonlinear characteristics such as input nonlinearity, aerodynamic resistance, in-train force, external disturbance and unknown actuator failures. Aiming at the system characteristics of HST, a fractional-order finite-time controller is designed on the basis of the principle of fractional stability and finite-time control theory to achieve higher tracking accuracy in finite time. It should be pointed out that the designed controller is able to deal with uncertainties and nonlinearities as well as actuator failures without any “trail and error” process, and the settling time can be adjustable by different selection of control parameters. The feasibility and effectiveness of the designed controller is verified by Lyapunov theoretical analysis and numerical simulation studies. Furthermore, compared with traditional PID controller, the designed fractional-order finite-time controller is superior.
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图 1 基于分数阶与传统PID控制器的跟踪过程和误差
Fig. 1 The tracking process and errors of the fractional-order or PID controller
图 2 分数阶控制器在
$ t\in(0,200) $ 的跟踪过程和误差Fig. 2 The tracking process and errors of the designed controller in
$ t\in(0,200) $ 表 1 列车相关参数
Table 1 Parameters of the vehicles
变量 参数含义 仿真值 $\varrho_i$ 第$i$节车厢的旋转质量系数 $\varrho_i\in[0.08,0.11]$ $m_i$ 第$i$节车厢的总体质量 $m_i = (50+\Delta m_i)\quad\Delta m_i\in[-6,13]$ $a_{0i},a_{1i},a_{2i}$ 第$i$节车厢的阻力系数 $a_{0i}\in[50,85],\quad a_{1i}\in[30,100],\quad a_{2i} = [0.1,6.5]$ $\Lambda$ 牵引/制动分配矩阵 $\Lambda ={\rm{ diag} }\{0.5, 0.3, 0.5, 0.3, 0.6, 0.4, 0.6, 0.4\}$ $r$ 分数阶阶次 $0<r = r_1/r_2<1$且$r_2$为奇数 $h$ 执行器健康参数 $h2$, $h5$, $h6$ 
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