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针对自不稳定球-车系统的结构特点,基于拉格朗日方程对球-车系统建立完整数学模型,并对其进行了简化。观察根据经典控制理论设计的球-车系统双闭环PID控制仿真实验结果,发现双闭环PID控制的快速性与鲁棒性并不理想。为提高控制的快速性与鲁棒性,采用滑模变结构控制对球-车系统的控制进行优化,取得了更优的控制效果。仿真实验验证了球-车系统滑模变结构控制具有更好的快速性与鲁棒性,实现了对自不稳定球-车系统的稳定控制,验证了滑模变结构控制对自不稳定系统具有较好的控制效果。
Aiming at the structural characteristics of self-unstable ball-and-car system, a complete mathematical model of ball-and-car system is established based on Lagrange equation and simplified. Observe the simulation results of the double closed-loop PID control based on the classical control theory, and find that the fastness and robustness of the double closed-loop PID control are not ideal. In order to improve the controllability and robustness, the sliding-mode variable structure control is used to optimize the control of the ball-car system and achieve better control results. The simulation results show that the sliding-mode variable structure control of ball-vehicle system is more rapid and robust, and the stable control of self-unstable ball-vehicle system is achieved. It is verified that the sliding mode variable structure control Has a good control effect.