Abstract The aim of the paper is to analyze the impact of the PID controller settings on the crane positioning accuracy. The PID controller is applied to minimize the load swingings during realization and after the ending of the working motion. In the proposed control system the tangent component of the load oscillations is compared with the assumed (leading) setpoint signal. The obtained controlling error is used to compensate for driving torque applied to the rotary column of crane. The controlled object in the considered control system is a truck-mounted crane. The paper presents a mathematical model of this crane. Dynamics equations are derived using the joint coordinates, homogeneous transformation matrices and the Lagrange equations of the second kind. The flexibility of the boom, supports, rope and drives as well as friction in joints are taken into account in the dynamics model. The Rigid Finite Element Method is applied to model the boom’s flexibility. The friction phenomenon in joints is modeled in the sense of the LuGre friction model. The numerical results obtained for the proposed control system at various controller settings are presented in the paper and discussed.

中文翻译：

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PID控制器设置对动臂柔性和关节摩擦随车起重机运动的影响

摘要 本文的目的是分析PID控制器设置对起重机定位精度的影响。PID 控制器用于在实现过程中和工作运动结束后最小化负载摆动。在建议的控制系统中，负载振荡的切线分量与假定的（超前）设定点信号进行比较。得到的控制误差用于补偿施加在起重机回转柱上的驱动力矩。所考虑的控制系统中的受控对象是车载起重机。本文介绍了这种起重机的数学模型。动力学方程是使用关节坐标、齐次变换矩阵和第二类拉格朗日方程推导出来的。臂架的灵活性，支撑，在动力学模型中考虑了绳索和驱动器以及关节中的摩擦。刚性有限元方法用于模拟吊臂的柔韧性。关节中的摩擦现象是在 LuGre 摩擦模型的意义上建模的。本文介绍并讨论了在各种控制器设置下为所提出的控制系统获得的数值结果。