关键词: 驾驶员诱发振荡, 速率限制, 人机闭环系统, 稳定域, 凸优化, 线性矩阵不等式, 椭球体, 极限环

Abstract:

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.

Key words: pilot induced oscillation, rate limiting, closed-loop pilot-vehicle system, stability region, convex optimization, linear matrix inequality, ellipsoidal, limit cycle