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本文通过规范化带有分段非线性刚度的三自由度二元机翼的状态方程,研究机翼气动弹性控制律的饱和设计问题。基于参数变化引起的状态矩阵不稳定共轭特征根,分离出不稳定子系统。利用子系统时间可逆性寻找系统的零可控域和吸引域,结合高阶不变吸引域设计出针对不同可控区域的线性饱和反馈控制律。数值仿真结果表明:这种设计方法能快速镇定不稳定的气动弹性系统,在初始条件很苛刻的条件下亦能对模型进行有效控制。
In this paper, the problem of saturation design of aeroelastic control law of aeroengine is studied by normalizing the state equation of a two-wing with three degrees of freedom with piecewise nonlinear stiffness. Based on the instability of conjugate eigenvalues of the state matrix caused by the change of parameters, unstable subsystems are separated. Using the subsystem time reversibility, we search for the zero-controllable domain and the attracting domain of the system. Combined with the high order invariant attracting domain, a linear saturated feedback control law for different controllable domains is designed. Numerical simulation results show that this design method can quickly stabilize an unstable aeroelastic system, and can effectively control the model under very harsh initial conditions.