输入饱和及带宽限制下高超飞行器的闭环稳定边界研究

Stability boundary analysis of hypersonic vehicle with control saturation and bandwidth limitation

针对于吸气式高超声速飞行器开环不稳定的动力学特性,研究了控制信号存在饱和约束及带宽限制条件下的闭环稳定边界.首先,简要介绍了吸气式高超声速飞行器的建模方法与动力学特性的主要问题.考虑到飞行器控制信号的幅值限制及带宽约束,综合高超声速飞行器的开环不稳定特性,定量地分析了系统的闭环稳定边界:与系统不稳定极点的位置,其对应的左特征向量及控制信号的幅值约束有关;执行器的带宽限制在此基础上进一步缩小了反馈控制系统的稳定边界.根据高超声速飞行器短周期不稳定特性,解析地给出了闭环稳定边界的计算公式.采用蒙特卡洛分析方法对闭环系统的稳定边界及滑模变结构控制器作用下的稳定区域进行验证.仿真结果与理论分析具有一致性,验证了系统开环特性对于闭环稳定性的限制及控制信号带宽约束对稳定性的影响.

In order to declare the stability of open-loop unstable air-breathing vehicles system with control saturation and bandwidth limitation, the stability boundary along with null controllable region of such system is investigated. First, the modeling approach of a air-breathing hypersonic vehicle and the main issues of control system design are briefly introduced. Second, Considering the control input constraints, the stability boundary is quantitatively defined, which depends on the location of unstable pole, its left eigenvector, and control saturation. Besides, the bandwidth limitation of actuators will reduce the stability region. The analytical expressions of null controllable boundary for short mode of the hypersonic vehicle is proposed. With Monte-Carlo analysis, the simulation results indicate that, the null controllable region for unstable system with specific control law is within the stability boundary, and the impact of bandwidth limitation of actuators shows the same with theoretical analysis, regardless of the control law. The stability of open-loop unstable system is extremely restricted with control saturation and bandwidth limitation.