板球系统的最优组合趋近律滑模控制

Sliding mode control of optimal combinatorial reachinglaw of ball and plate system

针对板球系统轨迹跟踪精度低、震荡大以及实时性差的问题,提出了一种基于遗传算法优化的组合趋近律滑模控制方案。首先运用Ackermann公式设计的滑模面来表达不连续的超平面;其次,在滑模前期采用指数趋近律来减小抖振幅度,后期运用变速趋近律使抖振收敛;最后,运用遗传算法来进行参数选定。实验结果表明,组合趋近律相对变速趋近律起始输出振幅降低了2.2,遗传算法优化后收敛时间较优化前减少了0.4 s。采用Lyapunov理论证明了控制器的稳定性,仿真验证了控制策略具有良好的动态品质和稳态性能,满足板球系统轨迹跟踪要求。

In order to solve the problems of low tracking accuracy, large oscillation and poor real-time performance of ball and plate system, a sliding mode control scheme of combinatorial reaching law based on genetic algorithm is proposed. Firstly, the sliding mode surface designed by Ackermann formula is used to express the discontinuous hyperplane;secondly, the exponential reaching law is used to reduce the buffeting amplitude in the early stage of the sliding mode, and the variable speed reaching law is used to converge the buffeting in the later stage. Finally, the genetic algorithm is used to select the parameters. the experimental results show that the initial output amplitude of the combined reaching law is reduced by 2.2 compared with the variable speed reaching law, and the convergence time after genetic algorithm optimization is reduced by 0.4 s. The stability of the controller is proved by Lyapunov theory, and the simulation results show that the control strategy has good dynamic quality and steady-state performance, and meets the trajectory tracking requirements of the ball and plate system.