涡扇发动机变参数鲁棒H∞滤波器设计

Parameter-Varying Robust Filter Design for a Turbofan Engine

关键词:  涡扇发动机  参数依赖Lyapunov函数  线性变参数  线性矩阵不等式  鲁棒滤波器

Key words:  Turbofan engine  Parameter-dependent Lyapunov functions  Linear parameter varying  Linear matrix inequality  Robust filter

摘要:

针对存在建模误差及测量噪声干扰条件下的涡扇发动机性能参数估计问题，标准卡尔曼滤波及其改进算法滤波估计误差收敛速度慢，滤波估计精度低，对不确定测量噪声及建模误差较为敏感，为此本文提出了一种变参数鲁棒滤波器设计方法。该方法采用仿射参数依赖Lyapunov函数设计满足性能指标要求的鲁棒滤波器，通过引入凸多胞技术，将参数依赖线性矩阵不等式(Linear Matrix Inequality,LMI)中变参数Lyapunov矩阵与系统系数矩阵之间耦合乘积导致的非凸优化问题，转化为常规LMI约束下的凸优化问题进行求解，降低了线性变参数(Linear Parameter Varying,LPV)鲁棒滤波器设计的保守性，得到了全局解。针对涡扇发动机的仿真结果表明：与扩展卡尔曼滤波器对比，采用该方法设计的滤波器具有较快的动态跟踪速度和较高的滤波精度，的稳态估计误差不大于0.1%，的相对估计误差不大于2.5%，同时对建模误差和测量噪声干扰具有较强的抑制能力。

Abstract:

As to solve the problem of performance parameters estimation of turbofan engine, under modeling error and measurement noise disturbances, there are some flaws including the low filter estimation accuracy, the slow filter convergence rate, and sensitive to uncertain measurement noise and modeling errors in Kalman filter algorithm and its extension. An approach based on the parameter-varying robust filter technique is investigated. A robust filter, which satisfied robust performance requirement, is developed by using affine parameter-dependent Lyapunov functions. The couping product term, between parameter-varying Lyapunov functions matrix and system coefficient matrix in parameter-dependent Linear Matrix Inequalities (LMIs), will lead to non-convex optimization problem. By introducing convex polytope technology, the problem above can be transformed into conventional LMIs constraint convex optimization problem to solve. The conservatism of Linear Parameter Varying (LPV) robust filter design is reduced, and the global solution is obtained. The simulation results of a turbofan engine showed that, compared with the extended Kalman filter, the designed filter has fast dynamic tracking speed and high filtering accuracy, with steady-state estimation error of less than 0.1% and relative estimation error of less than 2.5%. Beyond that, it can restrain modeling error and measurement noise disturbance strongly.