起重机大摆角PD防摇控制方程Runge-Kutta求解

Runge-Kutta Solution of PD Anti-sway Control Non-linear Equation for Crane with Large Sway Angle

针对桥式起重机大摆角防摇控制问题,建立非零初始条件“小车-吊重”大摆角非线性PD(比例微分)控制动力学方程。给出非线性微分方程的Runge-Kutta数值求解方法并进行了实例计算。计算结果表明:PD控制本质上是对有经验司机“跟车操作”的模拟;比例系数Kp的引入相当于添加了系统等效阻尼,微分系数Kd的引入相当于增加了系统等效质量。这为后续的PLC控制编程提供了动力学参考。

A nonlinear PD(proportional differential)controlling equation for a large swing angle of the"trolley-crane"was presented.The influence of non-zero initial conditions were fully considered.The solution steps of Runge-Kutta method were used and a numerical example was given.The results show that the essence of PD control is to simulate the"following operation"of experienced drivers;the introduction of proportional coefficient Kp equals the addition of equivalent damping of the system,and the introduction of differential coefficient Kd equals the addition of equivalent mass of the system.Which provides a dynamic reference for subsequent PLC control programming.