This paper presents a new approach to estimating a flight envelope for a helicopter flying under clean and icing conditions based on a zonotopic reachability analysis. The helicopter is stabilized with a state-feedback linear controller to maintain its attitude around a trim point. Given the sets of possible initial conditions and disturbance inputs, and control effectiveness indices, this analysis results in reachable sets of state variables of the helicopter for a finite time interval. The reachability analysis is thus useful for predicting whether or not the helicopter evolves into an unsafe flight condition when it undergoes degraded control effectiveness ensued from the icing condition. The merit of this approach is shown through a case study about the Raptor-90 unmanned helicopter stabilized with either the linear quadratic regulator (LQR) or the $H_{\infty }$ controller in a hover-flight mode. This helicopter is considered to be affected by both symmetric and asymmetric icing conditions. The case study shows that the $H_{\infty }$ controller outperforms the LQR controller as the former is able to cope with greater loss of control effectiveness caused by the icing conditions. Moreover, as compared to the longitudinal control input, the lateral and directional control inputs are more susceptible to adverse effects of the icing conditions. These results verify not only the effects of ice contamination upon the helicopter dynamics and control, but also the capability of the proposed approach for flight envelope estimation.

本文提出了一种新的方法，用于基于区域性可达性分析来估计在洁净和结冰条件下飞行的直升机的飞行包线。直升飞机通过状态反馈线性控制器进行稳定，以保持其在调整点附近的姿态。给定可能的初始条件和扰动输入的集合以及控制有效性指标，此分析会在有限的时间间隔内得出直升飞机状态变量的可到达集合。因此，可达性分析对于预测直升机在由于结冰状况而导致的控制效果下降时是否演变为不安全的飞行状况很有用。$H_{\infty }$控制器处于悬停飞行模式。该直升机被认为受对称和不对称结冰条件的影响。案例研究表明$H_{\infty }$该控制器的性能优于LQR控制器，因为前者能够应对由于结冰条件而导致的更大的控制有效性损失。此外，与纵向控制输入相比，横向和方向控制输入更容易受到结冰条件的不利影响。这些结果不仅验证了冰污染对直升机动力学和控制的影响，还验证了所提出的方法用于飞行包线估计的能力。