不确定多变量线性系统的快速收敛滑模控制

Fast convergent sliding mode control of uncertain multivariable linear systems

讨论了一类不确定多变量线性系统滑模变结构控制的快速收敛问题,提出一种指数型快速终端滑模变结构控制方案。通过非奇异线性变换将不确定系统化为简约标准型,而后设计了非线性指数型快速终端滑模超曲面,给出了滑模面参数矩阵的选择方法。在此基础上设计了变结构控制律,使系统状态在有限时间内到达滑模面上,随后保持在滑模面上并按指数型终端滑模的规律运动,在有限时间内收敛到平衡点。与普通的快速终端滑模相比,系统状态能以更短的时间到达平衡点。该方法具有全局稳定性和鲁棒性,仿真结果证明其有效性。

An exponential fast terminal sliding mode control methodology for a class of uncertain multivariable linear systems is proposed.The nonlinear exponential fast terminal sliding mode hypersurface and variable structure control law are designed.The uncertain system is transformed into a certain canonical form by using nonsingular linear transformation,then the corresponding nonlinear terminal sliding mode hypersurface is designed and the selection of parameter matrices in the sliding mode hypersurface is given.Based on it,the variable structure control law is derived.The system state variables can be driven to reach the sliding hypersurface in finite time,then retain on the sliding hypersurface and converge to the equilibrium point in finite time according to the motion law of exponential fast terminal sliding mode.Compared with the ordinary fast terminal sliding mode control,the system state variables can reach the equilibrium point in shorter time.This method can get global stability and robustness.Simulation results prove the validity of the proposed method.