摘要
针对直线三级倒立摆仅给小车一个驱动力,控制目标为3个摆杆均可以在不稳定平衡点保持稳定且具有较好的抗外界干扰能力的难题,采用基于辅助反馈的光滑超螺旋滑模控制策略,设计了一个鲁棒控制器。首先,结合线性矩阵不等式技术利用构造辅助反馈的方法求解出基于辅助反馈的滑模控制律中的对称正定阵,进而完成滑模面的设计。其次,针对滑模控制算法本身存在的抖振问题进行削弱,并为了进一步保证控制率是平滑的,将光滑超螺旋滑模算法引入控制器设计框架。最后,经李雅普诺夫函数证明了闭环系统稳定性。仿真结果表明,该控制策略对于复杂高阶次不稳定系统具有很好的控制效果,达到了控制目标且有较强的鲁棒性。
Aiming at the problem that the triple inverted pendulum only provides one driving force to the trolley,and the control objective is that all three pendulum rods can remain stable at the unstable equilibrium point and have a good ability to resist external interference,a robust controller was designed by adopting the smooth super-twisting sliding mode control strategy based on auxiliary feedback.Firstly,by combining the linear matrix inequality technique and using the method of constructing auxiliary feedback,the symmetric positive definite matrix in the sliding mode control law based on auxiliary feedback was solved,and then the design of the sliding mode surface was completed.Secondly,the buffeting problem existing in the sliding mode control algorithm itself was weakened,and in order to further ensure that the control rate is smooth,the smooth super-twisting sliding mode algorithm was introduced into the controller design framework.Finally,the stability of the closed-loop system was proved by the Lyapunov function.The simulation results show that this control strategy has a very good control effect on complex high-order unstable systems,achieving the control objective and having strong robustness.
作者
张保葵
韩光信
ZHANG Baokui;HAN Guangxin*(School of Information and Control Engineering,Jilin University of Chemical Technology,Jilin City 132022,China)
出处
《吉林化工学院学报》
2025年第7期46-52,共7页
Journal of Jilin Institute of Chemical Technology
关键词
直线三级倒立摆
光滑超螺旋滑模控制
线性矩阵不等式
辅助反馈
triple inverted pendulum
smooth super-twisting sliding mode control
linear matrix inequality
auxiliary feedback
