线性二次型最优控制在倒立摆系统中的实现

线性二次型最优控制是一类以线性系统为被控对象，以二次型泛函指标为性能指标的最优控制问题，由于特殊的指标形式和系统对象的线性性质，使所讨论的带有等式约束的动态优化问题可以获得基于Riccati方程表达的线性状态反馈，文中给出了一种利用线性二次最优控制理论实现小车倒立摆平面运动的控制方法，并在此基础上建立了相应的数学模型，同时，利用MATLAB工具进行了计算机仿真，仿真结果表明，该方案可以得到较为满意的结果。

Realization of Second-order Linear Optimal Control in the Inverted Pendulum System

The second order linear system is a type of problem that takes the linear system as the control object, with second order functional for the optimal control. Because of the linear quality of the special form and the system object, we can acquire the linear feedback based on the expression of Riccati according to the optimization problem of dynamic state of the equation constraint, This text gives a kind of control method that makes use of the small car inverted pendulum of the optimal control theory of the second--order linear to put the mo- tion of plane, and created the foundation of homologous mathematical model. Making use of the tool of MATLAB to carry on the computer simulation, the simulation result indicated that the program can get the more satisfied result.