中心刚体-柔性梁系统的最优跟踪控制

OPTIMAL TRACKING CONTROL OF A FLEXIBLE HUB-BEAM SYSTEM

对考虑阻尼影响的中心刚体-柔性梁系统的动力特性和主动控制进行研究．研究中考虑了3种动力学模型:一次近似耦合模型、一次近似简化模型和线性化模型．一次近似模型中同时考虑了柔性梁的轴向变形和横向变形．若在一次近似耦合模型中忽略轴向变形的影响,则可得出一次近似简化模型．线性化模型是对一次近似简化模型的线性化处理．另外研究中考虑了3种阻尼因素:结构阻尼、风阻、中心刚体轴承处的阻尼．控制设计采用最优跟踪控制方法．给出了从物理测量中提取模态坐标的滤波器方法．研究结果显示,一次近似简化模型能够有效地对系统的动力学行为进行描述;阻尼对系统的动力学特性有着重要影响;当系统大范围运动为低速时,模态滤波器能够较好地提取出控制律所需的模态坐标,最优跟踪控制方法能够使得系统跟踪所期望的运动轨迹,并且柔性梁的弹性振动可得到抑制．

In this paper, dynamics and control of a flexible hub-beam system are investigated with considering the effect of damping. Three dynamic models are employed： a first-order approximation coupling （FOAC） model, a simplified first-order approximation coupling （SFOAC） model and a linearization model. In the FOAC model, axial and transverse deformations of flexible beam are both taken into consideration. If the effect of axial deformation is neglected in the FOAC model, the resulting model obtained is the SFOAC model. The linearization model is the linearization treatment for the SFOAC model. Three kinds of damping are considered in this study： structural damping of beam material, wind damping, and damping at the bearing of hub. Active controller is designed using optimal tracking control theory. Since the controller designed is a function of modal coordinate of the beam, a modal filter used to extract the modal coordinate from actual physical measurements is presented. Simulation results indicate that the SFOAC model is valid for dynamic description of flexible hub-beam system and may be used for control study. Damping has important effect on dynamic characteristics of the system. In the case that angular velocity of large motion of the system is low, modal filter is effective in extracting the modal coordinate for the controller. By the optimal tracking controller, the desired motion trajectory may be obtained and the vibration of flexible beam may be suppressed.