Theory of Decentralized Control for Large Space Structures

本文主要研究具有不确定性的大型空间结构的姿态控制和振动抑制问题。目标是制定与各子系统兼容的分散控制策略。主要贡献如下：1.传感器和执行器配置的空间结构的传递函数是对称的。结果表明，对于这类系统，对称控制器比非对称控制器具有更好的镇定效果。提出了对称控制器的设计方法。针对由多个子系统组成的大系统，提出了一种分散H~*控制方案。局部控制器是各个子系统的H~*输出反馈控制器。提出了二次镇定方法。提出了考虑控制性能的结构优化设计方法。采用H*控制器抑制时变扰动。待最小化的目标函数表示给定初始载荷的影响。针对带有柔性太阳桨的卫星，研究了其建模和振动抑制方法。为了将降阶模型用于控制器设计，提出了溢出抑制方法。对频率相关LQ控制器和H*控制器进行了比较。具有可变运行条件的线性对象通过对应于多个典型运行条件的标称模型的内插来描述。提出了一种标称模型镇定控制器的插值法，以镇定这类被插补对象。得到了系统稳定的条件。将参数稳定性的概念推广到具有不确定参数和恒定参考输入的Lur‘e型非线性控制系统。给出了参数绝对稳定的条件，该条件保证了系统在参数变化和参考输入变化引起平衡漂移的情况下仍保持稳定。

This research is concerned with attitude control and vibration suppression of large space structures with uncertainties. The objective is to develop decentralized control strategies compatible with subsystems. The main contributions are as follows :1. The transfer functions of space structures with collocated sensors and actuators are symmetric. It is shown that for such systems, symmetric controllers are more effective than non-symmetric ones in robust stabilization. Design methods for symmetric controllers are developed.2. A decentralized H* control scheme is proposed for large-scale systems composed of a number of subsystems. The local controllers are H* output feedback controllers for individual subsystems. Quadratic stabilization methods are also developed.3. Optimum design of structures is proposed considering control performances. An H* controller is employed to suppress time-varying disturbances. The objective function to be minimized represents the effect of given initial loads.4. Modeling and vibration suppression methods are developed for a satellite with flexible solar paddles. To use reduced-order models for design of controllers, spillover suppression methods are proposed. Comparisons between frequency-dependent LQ controllers and H* controllers are presented.5. A linear plant with variable operating conditions is described by an interpolation of nominal models corresponding to a number of representative operating conditions. An interpolation of stabilizing controllers for nominal models is proposed to stabilize such an interpolated plant. Stabilizability conditions are obtained.6. The concept of parametric stability is extended to include Lur'e-type nonlinear control systems with uncertain parameters and constant reference inputs. Conditions for parametric absolute stability are derived, which guarantee that the system remains stable despite equilibrium shifts caused by parameter variations and changes in the reference input.