球杆系统建模及其闭环控制器的设计

Modeling of ball-beam system and its closed-loop controller design

球杆系统是一个典型的非线性不稳定系统,其开环不稳定的特性对于控制理论及方法的研究大有裨益。针对传统的球杆系统,运用拉格朗日法建立系统动力学方程,并通过线性化处理,以状态空间表示法建立系统的数学模型。同时研究了基于线性二次型(LQR)的最优控制,设计系统状态反馈控制器。并提出了轨迹追踪器的设计方法,以达到闭环系统内部稳定、轨迹追踪的效果。在Matlab的Simulink环境下进行的建模仿真试验,验证了该设计方法的有效性。

Ball-beam system is a classic nonlinear and unstable system.The characteristics like the instability of the openloop system are beneficial to the studies on control theories and methods.Based on Lagrangian method,the dynamics equa-tions of the ball-beam system is established,then linearization is implemented in order to model the system by state-space representation.The state-feedback controller is designed by LQR(linear quadratic regulator)-based optimal control.A traj-ectory tracking approach is proposed in order the closed-loop system to realize the stability and trajectory tracking proposes.The design approach is verified by the modeling and simulation of the system under Matlab-Simulink environment.