弹性飞行器操纵机构最优位置的确定

 本文研究了弹性飞行器操纵机构最优位置的确定。在具有速率反馈的控制系统中,把控制作用看作等效阻尼,推导了由气动弹性效应所决定的舵面最优位置准则,给出了表征舵面位置与陀螺位置协调关系的公式。附有实例验证。

DETERMINATION OF OPTIMAL POSITION OF ACTUATORS FOR FLEXIBLE FLIGHT VEHICLES

Since the action of actuators on flexible flight vehicles is an important exciting source to elastic vibration, it is of practical significance to choose appropriate positions for actuators as well as for sensors. We shall in this paper study optimal positions of rate gyros and elevators that are modelled as lumped operating elements, Through the feedback control, a term （B1 GH1）q is introduced to the system to count for the damping force, where B1 is a control matrix, relying on the actuator locations, and H1 is a measurment matrix depending on the gyro locations. An effective damping matrix Da is defined in （ 5 ）,and then Rayleigh' s dissipation function can be obtained as F=1/2qrDcq.In order to make the system having most damping effect to vibration, the actuators and sensors are so positioned that the effective damping force （aF/eq） could be maximized.Because of its real symmetry, Dc can always be diagonalized. In accor-dance, suppose that , the elastic motion willbe decelerated by force bkqk, if bk< 0 , the motion will be decelerated by force bkqk, if bk< 0 , the motion will be accelerated. That is, the forcesderived from F may be either dissipating or accelerating. Whenit is thought that the dissipating force is leading to the accelerating one.Since the trace of a matrix will not be changed by a normal transfor-mation, we have . Then a new performance index is defined by （12）. The problem under consideration is to determine the positions of actuators and sensors so that index （12） is maximized.In general, the same results can be obtained from Lagrange's dynamic equations.A simple condition has been studied. Through analysis, we have derived a set of simple and practical formulae （7） and （8） that give the very positions at which the effective damping force is always dissipating. By applying formulae （ 7 ） and （ 8 ） to a given missile, it is shown that the present position of the elevator is suboptimal and is 0.06m away from the optimal position.