基于线性矩阵不等式的电传飞机人机闭环系统稳定域

 针对静不稳定电传飞机作动器速率限制环节引起的Ⅱ型驾驶员诱发振荡(PIO)严重威胁飞机飞行安全的问题,研究了考虑作动器速率限制因素的人机闭环系统稳定域。引入增广状态变量分离速率限制环节,建立了人机闭环系统饱和非线性模型。为得到尽可能大的人机闭环系统稳定域估计,首先将稳定域求解问题转化为凸优化问题,再通过Schur补引理将其转化为线性矩阵不等式的求解问题,最终得到了人机闭环系统椭球体稳定域估计的一般算法。时域仿真研究表明:所估计的稳定域略微保守但不冒进,静不稳定电传飞机的Ⅱ型PIO是一种发散很快的振荡而非极限环振荡,驾驶员操纵增益以及作动器速率限制值是影响稳定域的重要因素。稳定域法物理意义清晰、结果直观,可用于非线性人机闭环系统稳定性的评估。

Stability Region of Closed-loop Pilot-vehicle System for Fly-by-wire Aircraft Based on Linear Matrix Inequalities

To improve the flight safety of static-unstability fly-by-wire airplanes caused by category Ⅱ pilot induced oscillations (PIO), the stability regions of a closed-loop pilot-vehicle system with actuator rate limiting are studied. Augmented state variables are introduced to segregate the rate limiting element. Thus, a saturation nonlinear model of the closed-loop pilot-vehicle system is built. In order to obtain the maximal estimator of the stability region, the estimation of the stability region of the closed-loop pilot-vehicle system is transformed into a convex optimization problem first. Secondly the Schur complement lemma is applied to transform the convex optimization problem into linear matrix inequalities formulations. Finally an ellipsoidal stability region estimating algorithm is obtained. The time-domain simulation results show that the estimated stability regions are slightly conservative and within the real stability region of the closed-loop pilot-vehicle system. The category Ⅱ PIO of static-unstability fly-by-wire airplanes are rapidly divergent oscillations rather than limit cycle oscillations. The pilot control gain and rate limiting value are distinct influence factors on the stability region. Therefore, the stability region method with specific physical concepts and illustrative results can be applied to evaluate the stability of a nonlinear closed-loop pilot-vehicle system.