Ball and beam is a popular benchmark problem in control engineering. Various control strategies have been proposed on ball & beam system in literature, In this paper, hybrid optimization algorithms have been implemented on PID controller to control ball position and beam angle. Hybrid algorithms combine exploration and exploitation ability of individual algorithm and find optimized value of performance index. In this paper, two hybrid algorithms namely PSO-GSA and PSO-GWO are used to tune controller parameters which in turn improve the system performance. Simulation results show effective and efficient improvement in system performance with these hybrid algorithms. To analyze the performance of these algorithms, time domain parameters and mean square error (MSE) has been taken as performance index. A comparative study of these algorithms with that of individual algorithms namely PSO, GWO, GSA has also been done.

中文翻译：

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基于混合优化的球梁系统PID控制

球和梁是控制工程中一个流行的基准问题。文献中已经提出了各种关于球和梁系统的控制策略，在本文中，已经在PID控制器上实现了混合优化算法来控制球的位置和束角。混合算法结合了单个算法的探索和开发能力，找到了性能指标的优化值。在本文中，使用两种混合算法（PSO-GSA和PSO-GWO）来调整控制器参数，从而提高系统性能。仿真结果表明，使用这些混合算法可以有效而有效地改善系统性能。为了分析这些算法的性能，已将时域参数和均方误差（MSE）用作性能指标。