大结构系统的最优控制

Optimal Control of Large Structure Systems

此论文通过正则变换将受控结构系统状态方程解耦，把一个ｎ自由度系统的控制问题转化为其ｎ个振型的控制问题，在理论上证明了原系统的最优控制等价于它的全部振型的最优控制，并通过对振型的最优控制实现了对系统的最优控制．在讨论各振型的最优控制时，根据基本方程的物理意义和Ｒｉｃｃａｔｉ函数的性质方便地求出了Ｒｉｃｃａｔｉ函数，完全避免了在实际应用时解Ｒｉｃｃａｔｉ方程的繁琐计算，为实现大系统的最优控制带来了极大的方便。

The active control of an n-degree-of-freedom structure system is changed to the active control of its n modes as cononical transformation method is used in this paper to decouple the state equation of motion of the controlled system. It is proved in theory that the optimal control of a system is equivalent to the optimal control of all its modes. The closed-loop state feed-back control law for the system has been set up by the optimal control of all its modes. When optimal control theory is applied to the control problem of each mode, the Riccati function can be given out easily and directly based on the meaning shown in the basic equation and the characteristics of the Riccati function. Therefore, cumbrous calculation for solving the Riccati equation is avoided completely.The approach makes it very easy and convienient to synthesize the optimal control of large structure systems.