球杆系统的内模PID控制

Internal Model PID Control of Ball and Beam System

本文针对开环不稳定球杆系统,提出了一种内模PID控制器设计方法。首先通过机理分析建立了系统的数学模型,并利用一阶环节逼近模型中的积分环节,然后在此基础上根据内模控制(inter-nal model control,IMC)原理设计了系统控制器,并推导出了相应的内模PID控制器,与常规PID控制器相比,该控制器仅有一个可调参数,且系统具有整定方便、鲁棒性强的优点。仿真和实验结果表明,内模PID控制器能使小球快速地稳定在目标位置,具有良好的稳定性和鲁棒性。

For open-loop unstable ball and beam system, a design approach of IMC-PID （internal model control PID） controller is proposed. Firstly, the mathematic model of the system is built through mechanism analysis, and the integrator in the model is replaced by a first-order lag, then, the system controller is designed based on internal model control principle, and the corresponding IMC-PID controller is deduced. Compared with conventional PID controller,the controller has only one adjustable parameter, and the system has such advantages as convenience tuning and strong robustness. The simulation and experimental results show that the IMC-PID controller can make the ball quickly stabilize to the target location , and has good stability and robustness.