基于浸入与不变的静电驱动微机电系统有限时间滑模控制

The control problem in the presence of uncertainty is an important subject of modern control theory. The feature size on the system is shrunk to micrometer, the robust control research of Micro/Nano scale system has gradually been a hotspot and difficulty. Finite-time stability determines the transient performances of systems, based on the finite-time stability theory, this project will investigate the finite-time robust control schemes by utilizing geometric homogeneity and sliding mode control theory for nonlinear electrostatic actuated Micro Electro Mechanical system with uncertainties. The introduction of immersion and invariance to solve the problem that tradition adaptive law is not able to control the convergence performance of the estimation error.The basic criteria for the designing of the controllers will be proposed. Some unified criteria on the stability of the closed-loop system will be provided by using the Lyapunov based analysis and the LaSalle’s invariance theorem. The finite time convergence will be proved and the optimal estimation of the convergence time will be provided; The thresholds of the system at the happening of dynamical pull-in will be obtained by using the Melnikov method, the 4th Runge-Kutta and the point mapping methods will be employed to verify numerically the attraction basin of pull-in of the system．The developed control schemes will be used to optimize the electrostatic pull-in dynamic. The research of this project will provide effective finite-time robust control approaches for Micro/Nano scale system manipulation and pull-in instability problem, demonstrate a theoretical approach to understand the influences of feedback control on the pull-in dynamic of the electrostatic actuated Micro/Nano scale system more deeply.

不确定性条件下的控制问题是现代控制中的重要课题，当系统特征尺寸缩小到微米，微纳尺度系统的鲁棒控制逐渐成为研究热点和难点。有限时间稳定决定系统的暂态性能，本项目拟基于有限时间稳定理论，运用几何齐次理论和滑模控制，针对不确定非线性静电驱动微机电系统的有限时间鲁棒控制问题展开研究，引入浸入与不变方法解决传统自适应方法无法调节估计误差收敛速度问题，给出控制器设计基本准则。运用Lyapunov的分析方法和LaSalle不变性原理给出系统稳定的统一判据，并对算法的有限时间收敛性进行分析给出收敛时间最优估计；运用Melnikov函数法获得系统吸合失稳临界值，利用四阶Runge-Kutta方法和点映射方法数值验证系统的静电吸合区域，将算法成果用于吸合动态优化。本项研究将为微纳尺度系统操控和吸合失稳问题提供有效有限时间鲁棒控制策略，为更深入理解反馈控制对静电驱动微纳尺度系统吸合动态的影响提供理论分析方法。

微机电系统在光开关、高清晰显示、光学相干断层扫描等领域获得广泛应用，在这些基于MEMS扭转微镜的应用中，系统的应用效果取决于MEMS性能。因此，微纳尺度系统的鲁棒控制逐渐成为研究热点。.该课题基于滑模控制理论研究了静电驱动微机电系统的有限时间稳定性、鲁棒控制与扫描成像应用研究。主要包括以下三个方面：（1）针对微机电系统的有限时间控制问题，基于滑模控制理论和系统的动力学模型设计有限时间收敛滑模控制器，进行稳定性分析和有限时间收敛估计。（2）针对带不确定参数微机电系统的跟踪控制问题，基于输出反馈系统的输出调节框架，研究基于扩展内模的输出反馈控制器，实现系统不确定参数情况下的良好跟踪效果。（3）研究成果在静电驱动微机电系统控制与吸合失稳问题中的应用。将有限时间滑模控制控制策略应用于微机电系统的定点控制与扫描成像；将基于扩展内模的输出反馈控制器应用于微机电系统跟踪控制；考虑吸合失稳问题，针对微机电系统输入受限提出了最优复合非线性反馈二阶滑模控制策略。.本项目针对微机电系统基于滑模控制、输出调节、复合非线性反馈等理论设计了控制算法，实现有限时间稳定，改善系统暂态响应，避免吸合动态提供了有效控制策略。