导弹高度控制变结构设计中Lyapunov方法应用

Application of Lyapunov Method in VSC for Missile Height Control

基于Lyapunov方法的变结构系统中运动分为正常运动及滑模运动。正常运动不具有对参数摄动及外界干扰的鲁棒性,故期望其运动稳定且快速地趋近滑模面,而这主要受Lyapunov矩阵Q及变结构控制参数k的影响;滑模运动具有鲁棒性,而滑模面的大小及滑动性能受制于Q。为了达到期望的性能指标,需要选择适当的Q和k。通过理论推导,分析了Q和k对运动性能的影响,得出了参数间的具体耦合作用,建立了相应的优化模型。通过某巡航导弹高度控制仿真,证明了按照理论分析所采取的优化能满足各项设计指标,且抖振得到较好削弱;通过弹体参数扰动仿真分析证明了变结构控制的鲁棒性优势。

As for the Lyapunov based variable structure control system, the state movement is divided into two phases： normal phase and sliding mode. The normal phase has no robustness to missile parameter perturbation and outer disturbance, so the requirement for normal phase is to move steadily and quickly. Fortunately, by adjusting the Lyapunov matrix Q and parameter k, this goal can be achieved. The sliding phase has robustness, and the size of sliding mode surface and the sliding performance can only be affected by Q. In conclusion, the Q and k must be adjusted to achieve the expected performance. By theoretical analysis, the affection of Q and k ro performance was got, the coupling action of parameters was analyzed and the optimization model was built. The simulation of cruise missile height control proves that the optimization method can satisfy each design requirement, and the vibration is preferably weakened. The simulation of missile parameter disturbance proves the robustness of variable structure control.