The influence of the PID controller settings on the motion of a truck-mounted crane with a flexible boom and friction in joints

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.