MFC驱动主动反射器形面的有限时间动态变形控制

Finite-time dynamic shape control of an active reflector surface actuated by MFC

利用智能压电作动器可实现反射面天线的形面主动调整,提升形面精度和信号传输性能。常规的静态形面控制策略仅能估计作动器的末端电压值,实际电压加载过程易引发柔性反射面结构的瞬态动力学响应和残余振动,难以实现高精度动态形面控制效果,且影响系统稳定性。为此,该研究以宏纤维复合材料(macro fiber composites, MFC)驱动的抛物面形反射器为对象,研究有限时间的动态形面控制算法。首先,基于有限元模型推导控制方程,并将控制问题转化为有限时间的时变LQ终端控制和跟踪控制问题,进而通过求解微分Riccati方程组(differential Riccati equations, DREs)得到反馈–前馈时变控制律。结果表明,利用所提有限时间动态变形控制算法,可实现连续、平滑的反射器动态形面调整效果,避免了电压加载过程激发的结构附加振动,可有效提升这类主动反射器的静态、动态控制性能。

The shape of a reflector antenna can be actively adjusted to improve shape accuracy and signal transmissibility by a smart piezoelectric actuator. Conventional static shape control strategy can only evaluate the value of terminal voltage, but transient dynamic response and residual vibration are easily excited during voltage loading process. It is difficult to achieve high accurate dynamic shape control effect by the static control strategy, even it would affect the stability of the system. To this end, the parabolic reflector actuated by macro fiber composites(MFC) was used as the object for investigating the finite-time dynamic shape control algorithm. First, the dynamic equations were derived based on the finite element method, and the control problem was transformed into the finite time time-varying LQ terminal control and a tracking control problem, and then the feedforward and feedback time-varying control law was obtained by solving the differential Riccati equations(DREs). Results show that the proposed finite time dynamic shape control algorithm can realize continuous and smooth dynamic surface adjustment effect of the active reflector with the avoidance of the excitation of incidental vibrations during voltage loading process, and effectively improve the static and dynamic control performance of the active reflector.