大型索网天线机电耦合动力学建模与主动变形控制

索网天线因其折叠收纳比高、质量轻以及口径大等优点,成为众多空间任务的首选天线形式,但反射面精度较低限制了大型索网天线的在轨性能指标。在索网天线竖向张力索中加入压电陶瓷堆(PZT)作动器,通过主动控制提高反射面的形面精度。首先,将张紧的索网天线分为含有作动器的主动索单元和不含作动器的被动索单元,通过压电本构方程、几何方程和哈密顿原理推导出主动索单元的动力学模型,并与被动索单元一起组装得到索网天线的机电耦合动力学模型。然后,根据天线反射面的初始形面误差和所建立的天线机电耦合动力学模型,基于模型预测控制(MPC)方法计算出各作动器的控制输入电压曲线。最后,以一个10m口径的索网天线为算例,验证本文所建立的模型和控制方法的有效性。

Electromechanical coupling dynamic model and active shape control of large cable-network antenna

Due to the advantages of high stowing ability,lightweight mass and large aperture,cable-network antenna has become the first choice for many space missions.While its in-orbit performance is impacted by low shape accuracy of the reflector.In this paper,the PZT actuators are added in vertical tension cables of the cable-network antenna,and the shape accuracy is therefore improved via active shape control.Firstly,the elements of tensioning cable-network antenna was divided into two types,including active cable elements with actuators and passive cable elements without actuators.The dynamic model of active cable element was obtained through the piezoelectric constitutive equations,geometric equations and Hamilton''s principle,and the electromechanical coupling dynamic model of cable-network antenna equipped with passive and active cable elements was then formulated.According to the initial shape error and the dynamic model of cable-network antenna,the control voltage profiles for actuators were then computed by a model predictive control (MPC) method.Finally,a numerical example of a 10 m-diameter cable-network antenna has been provided to verify the availability of the proposed dynamic model and the active shape control method.