Autopilot Structured H_∞ Synthesis for Satisfying Gain and Phase Margin Constraints

满足增益相位裕度的自动驾驶仪结构化H_∞综合

School of Astronautics, Northwestern Polytechnical University, Xi’an 710072, China

Received: 17 April 2018

Abstract

Aiming at the static unstable Hypersonic vehicle, a method for designing H_∞ autopilot to satisfy gain margin and phase margin is proposed. Structured H_∞ synthesis is used to synthesize the autopilot under the fixed structure. The gain margin and phase margin were constrained by using H_∞ norm of the complementary of the scaled plant. The requirement for the gain margin and phase margin is represented by the distance between the open loop Nyquist curve and the circle that represents the gain margin and phase margin in the complex plane. The distance is adjusted by tuning the parameter of performance specifications automatically to reduce the conservatism of the controller. The present method is applicable to both static stable vehicle and static unstable vehicle, and a three loops acceleration tracking autopilot is design. The numerical simulations have demonstrated that the autopilot satisfys the performance specifications, gain margin and phase margin simultaneously.

摘要

针对具有静不稳定特性的高超声速飞行器，提出了一种同时满足增益裕度和相位裕度要求的飞行器自动驾驶仪设计方法。在预先设定自动驾驶仪结构的前提下，建立满足系统增益和相位裕度的H_∞范数性能指标，使用结构化H_∞综合方法求解使性能指标H_∞范数指标最优的自动驾驶仪参数。控制系统稳定裕度由标称系统增益放大补灵敏度传递函数的H_∞范数约束。这种约束方法把对系统的稳定裕度约束转化为复平面上开环系统Nyquist曲线到满足系统稳定裕度圆盘边界的距离约束。求解控制器参数时，在控制器设计指标中引入调节参数，通过调节参数的迭代变化，改变开环系统Nyquist曲线与稳定裕度圆盘边界的距离，减小控制器的保守性。这种自动驾驶仪的设计方法可同时适用于静稳定系统和静不稳定系统。将此方法应用在高超声速飞行器过载跟踪自动驾驶仪的设计中，仿真结果表明，自动驾驶仪具有良好的动态和稳态性能，并且控制器满足期望的稳定裕度。