Strong Stabilization of a Non-uniform SCOLE Model
Strong Stabilization of a Non-uniform SCOLE Model
复制标题
非均匀SCOLE模型的强稳定性
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
G. Weiss
中科院分区：
文献类型：
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作者：
Xiaowei Zhao;G. Weiss
SCOLE（NASA Spacecraft Control Laboratory Experiment）模型被认为是一端固支、另一端与刚体连接的柔性梁耦合系统的最佳模型。该模型已被广泛研究，大多数论文假设柔性梁是均匀的。在我们的研究中，我们允许梁方程的系数随位置而变化，就像郭[2002]中考虑了梁的非均匀结构一样。已经证明，均匀SCOLE模型的指数镇定是不可能通过来自自然输出信号（刚体的速度和角速度）的边界反馈来实现的（参见Rao [1995]）。因此，通过使用这些信号，非均匀SCOLE模型通常不是指数稳定的。虽然SCOLE模型的指数镇定可以通过高阶输出反馈获得（参见Guo [2002]和Rao [1995]），但相应的闭环系统不是适定的。此外，这种反馈在实践中难以实现。因此，我们不得不妥协，以实现强有力的稳定。根据最近Curtain和韦斯[2007]中关于无源系统的强镇定定理，我们证明了非均匀SCOLE模型通过来自刚体速度或角速度的静态输出反馈是强可镇定的。
Abstract The SCOLE (NASA Spacecraft Control Laboratory Experiment) model is considered the best model for the coupled system consisting of a flexible beam with one end clamped and the other end linked to a rigid body. This model has been studied extensively, with most papers assuming that the flexible beam is uniform. In our study we allow the coefficients of the beam equation to vary with position, like in Guo [2002] which has considered the non-homogeneous structure of the beam. It has been proved that the exponential stabilization of the uniform SCOLE model is impossible to achieve by boundary feedback from the natural output signals (the speed and the angular velocity of the rigid body) (see Rao [1995]). Thus the non-uniform SCOLE model is not exponentially stabilizable in general, by using these signals. Although the exponential stabilization of the SCOLE model can be obtained by high order output feedback (see Guo [2002] and Rao [1995]), the corresponding closed-loop system is not well-posed. In addition, such a feedback is difficult to realize in practice. Thus we have to compromise for strong stabilization. Following a recent strong stabilization theorem for passive systems in Curtain and Weiss [2007], we have shown that the non-uniform SCOLE model is strongly stabilizable by static output feedback from either the speed or the angular velocity of the rigid body.