基于混合区域极点配置的航空发动机全包线鲁棒变参数控制器设计

Robust Parameter-Varying Controller Synthesis with Mixed Regional Pole Assignment for Aeroengine in Full Envelope

关键词:  航空发动机  参数依赖Lyapunov函数  线性变参数模型  极点配置  鲁棒控制

Key words:  Aeroengine  Parameter-dependent Lyapunov functions  Linear parameter varying model  Pole assignment  Robust control

摘要:

针对航空发动机全包线多变量鲁棒变增益控制器设计问题，提出了一种基于混合区域极点配置的鲁棒变参数控制方法。利用Jacobian方法建立多调度参数下的发动机仿射线性变参数(Linear parameter varying，LPV)模型，用于描述发动机全包线内的非线性动态特性；针对上述LPV模型，采用仿射参数依赖Lyapunov函数设计具有 鲁棒性能的状态反馈控制器，给出了控制系统全局稳定性的证明；并利用混合区域极点配置方法，将闭环系统极点配置到左半平面指定位置，以保证控制系统的动态特性及稳定裕度；进而引入凸多胞技术，将参数依赖线性矩阵不等式(Linear matrix inequality，LMI)方程转化为有限维LMI进行控制器求解，并得到了全局解。针对涡扇发动机的仿真结果表明：存在复杂量测噪声干扰条件下，鲁棒变参数控制器可以实现发动机全包线内控制指令的精确跟踪，系统阶跃响应的调节时间不超过1.5s，系统无超调，对控制期望的稳态跟踪误差在0.02%以内，符合发动机控制系统技术要求。

Abstract:

In order to solve the problem of multivariable robust gain-scheduling controller design of aeroengine in full envelope, a robust parameter-varying control algorithm based on mixed regional pole assignment was presented. Firstly, the Jacobian linearization method was used to obtain aero-engine affine Linear Parameter Varying (LPV) model with multiple scheduling parameters, which can describe its nonlinear dynamic performance in full envelope. Aiming at the LPV model above, a state feedback controller was designed using affine parameter-dependent Lyapunov functions and the controller satisfied robust performance requirement. The proof of the global stability for control system was given. The poles of the closed-loop system were placed to the designated region of the left half plane based on mixed regional pole assignment method, to guarantee the dynamic characteristics and stability margin of the control system. By introducing convex polytope technology, the parameter-dependent Linear Matrix Inequality (LMI) were transformed into finite-dimensional LMIs to solving controller, and the global solution is obtained.The simulation results of a turbofan engine in full envelope showed that, under complex measurement noise disturbances, the robust parameter-varying controller can realize the accurate tracking of control commands with step response time less than 1.5s, no over shoot and steady-state tracking error less than 0.02%, which satisfies the technical requirements of aeroengine control system.