陀螺寻北仪限幅系统鲁棒近时间最优控制器

摘要

针对陀螺寻北仪的限幅系统设计了一种鲁棒近时间最优控制器。首先将陀螺寻北仪的快速限幅问题转化为时间最优控制问题，然后提出设计一种鲁棒近时间最优控制器来克服理论时间最优控制器的缺陷。该控制器结合了传统的 bang-bang 控制，滑模控制以及一种备份控制。滑模控制器的设计运用时间最优控制的思想并通过 Lyapunov 稳定性理论推导出控制器参数的选择标准。为了解决控制器在原点处不稳定问题，提出了另一类具有线性滑模面的滑模控制器作为备份控制。数值仿真结果证明了提出的控制器的可行性，在明显降低抖振的同时在时间指标上与理论控制器相近。这种控制器的设计方法同样适用于小阻尼项的二阶系统。%A robust,time-suboptimal controller is proposed for damping systems of gyroscopes.The tech-nique involves the combination of traditional “bang-bang”control with sliding-mode control and an alternating control.It incorporates the time optimal control idea into the sliding mode control design and the sliding mode control is established by Lyapunov function approach.A special situation about the instability problem near the origin is analyzed.To solve this problem,another sliding mode control with linear sliding surface,is proposed as an alternating control.Numerical simulation results demonstrate the effectiveness of the proposed controller, reducing chattering significantly while performing nearly as well as the theoretical controller.This technique can be also applied to other similar second-order systems,which can neglect the damping term practically.