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

Xiaochuan Ma,Jie Yan,Wenxing Fu,Kang Chen

doi:10.1051/jnwpu/20193720211

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.

Highlights

数可以表示为控制器 C(s) 的线性分式变换: Tzω = Fl( P,C) = P11 + P21( I + CP22 ) P12 (2) 标准的 H∞ 控制问题是求解使系统(1) 内稳定且保证 Tzω( s) 的 H∞ 范数最小的控制器 C( s) 。与标准 H∞ 控制不同的是结构化 H∞ 综合需要预先设计好控制器 C( s) 的结构,例如 PID 控制器、校正网络、
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

Summary

Introduction

数可以表示为控制器 C(s) 的线性分式变换: Tzω = Fl( P,C) = P11 + P21( I + CP22 ) P12 (2) 标准的 H∞ 控制问题是求解使系统(1) 内稳定且保证 Tzω( s) 的 H∞ 范数最小的控制器 C( s) 。与标准 H∞ 控制不同的是结构化 H∞ 综合需要预先设计好控制器 C( s) 的结构,例如 PID 控制器、校正网络、器参数的部分。在结构化 H∞ 综合中,控制问题就转换成求解使系统(1) 内稳定且 ‖Tzω( s) ‖∞ 最小的一组控制器参数。结构化 H∞ 控制把经典 H∞ 控制器求解问题转变为控制器参数优化问题[15⁃17] 。轴夹角为 29°。系统开环 Nyquist 曲线与圆 O 没有交表 1 中给出了选取不同 η 时使用结构化 H∞ 综合的结果。图 4 给出了相应 η 值时系统的 Nyquist 曲线。系统的断开点选取在控制器输出端,即图 3

Results

Conclusion