Abstract: As to solve the problem of multivariable controller design with modeling uncertainties of variable cycle engine，an augmented model reference adaptive tracking control compensation design method under the optimal law was given. Firstly，variable cycle engine modeling uncertainties analysis was clarified and lead to the dynamic tracking problem of LQR controller. Then under the based controller feedback structure，reference model with expected closed-loop dynamic performance was determined and the adaptive laws with modeling uncertainties were established under lyapunov function stability proof，which to achieve zero tracking error and eventually improve the dynamic tracing with uncertainties. The simulation results of variable cycle engine controller showed that augmented model reference adaptive control method improved the LQR controller performance with modeling uncertainties，effectively realized the tracking control，reached the expected response performance. The designed adaptive parameters had consistent gradual stability. Meanwhile，at the different state points，the steady control errors were less than 0.3%，overshoot values were less than 0.8%，the adjust times were less than 1s，which satisfies the requirements of the aero engine control system technology.

Key words: Variable cycle engine；Multi-variable control；Modeling uncertainties；MARC；Tracking compensation

摘要： 针对变循环航空发动机存在建模不确定情况下的多变量控制器设计问题，给出了一种最优律下的增广模型参考自适应跟踪补偿设计方法，阐明变循环发动机建模不确定性并引出LQR(Linear Quadratic Regulator)基准控制器动态跟踪不足的问题，进而在基准控制器反馈控制结构框架下，分别实现以下技术突破:确定期望闭环动态的参考模型、基于李亚普诺夫函数严格稳定证明下建立存在建模不确定性的自适应律等，最终以达到系统跟踪误差渐进为零的目标，改善系统不确定性的动态跟踪问题。对变循环航空发动机的控制器仿真结果表明:增广模型参考自适应控制方法改善了原LQR基准控制器对存在建模不确定性时的控制问题，有效地实现了控制指令跟踪，达到了所期望的动态响应，且自适应参数一致渐进稳定。同时，各标称点的稳态控制误差均小于0.3%，系统超调量小于0.8%，调节时间小于1s，符合航空发动机控制系统技术要求。

关键词: 变循环航空发动机；多变量控制；建模不确定性；模型参考自适应控制；跟踪补偿