受控旋转弹飞行动力学建模和稳定性分析

MODELING AND STABILITY ANALYSIS OF SPINNING MISSILE WITH CONTROL SYSTERM

选取带有控制系统的旋转弹为研究对象,考虑到控制环节不可避免的时滞及气动非线性效应,从理论上进一步完善了旋转弹动力学模型.从模型的特征方程出发,以时滞、控制增益为分岔参数,对系统的零平衡点稳定性进行了分析,得到平衡点失稳后发生Hopf分岔的临界参数值,并在理论预测的情况下数值模拟了攻角和侧滑角在不同情况下的失稳情况以及Hopf分岔周期解振幅随分岔参数的变化情况.数值结果表明了理论预测的正确性,时滞虽未改变旋转弹锥形运动方式,但是却大幅度的减小了稳定飞行控制增益的取值范围,因此在旋转弹姿态稳定性系统设计过程中时滞的影响不可忽略.

A spinning missile with control system was chosen as the research object in this paper. The dynamic model of the spinning missile was improved in theory by considering nonlinear aerodynamics and time delay in control segment. Setting time delay and control gains as the bifurcation parameters,stability analysis of one equilibrium point was made based on the characteristic equation of this model. Critical Hopf bifurcation values were obtained when the equilibrium point lost its stability. Then,the instable states of the attack angle and sideslip angle were numerically simulated under theoretical prediction. Meanwhile,the amplitude of periodic solutions changing with congtrol gains and tiem delay were achieved. The numerical results indicate that the theoretical prediction is relatively reasonable. Time delay made little change on the coning motion of the spinning missile,but it dramatically decreases the selectable ranges of control gains in keeping the system stable. In consequence,time delay can not be ignored for designing stability system of the spinning missile.