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针对平面二级倒立摆系统具有的多变量、非线性、强耦合、稳定控制实时性和快速性要求高的特点,设计了利用协调因子优化控制效果的改进型LQR控制器。运用分析动力学方法对倒立摆建立数学模型,以LQR理论设计了平面倒立摆的最优控制器,在此基础上加入性能协调因子,它能根据状态变量的变化实时调整控制作用的大小,进而对LQR输出的预控制作用进行精细处理,优化控制作用,进一步改善控制效果,经系统仿真与实验室实时控制验证,其结果表明这种控制器设计简单,实时性好,并能同时保证在不同的运行条件下具有较高的控制精度,较快的响应速度,良好的稳定性和鲁棒性。
Aiming at the characteristics of planar two-stage inverted pendulum system with multivariable, nonlinear, strong coupling, real-time stability control and high requirements of rapidity, an improved LQR controller was designed with the coordination factor to optimize the control effect. The mathematical model of the inverted pendulum is established by using the analytic dynamics method. The optimal controller of the inverted pendulum is designed based on LQR theory. Based on this, the performance coordination factor is added, which can adjust the control effect in real time according to the change of the state variables. The precontrol effect of LQR output is finely processed to optimize the control effect and further improve the control effect. The system simulation and laboratory real-time control verification show that the controller has the advantages of simple design, good real-time performance, The operating conditions of a higher control accuracy, faster response speed, good stability and robustness.