Wave control of crane rope-and-mass system

Abstract

This paper deals with the wave absorbing control of a suspended simple pendulum system by the lateral motion of the support. The control acceleration of the support was derived by the connecting condition of real pendulums to the wave-controlled multiple simple pendulums virtually existing above the support. The wave propagating solution of the homogeneous multiple simple pendulum system was theoretically derived and applied to the virtual pendulum system. The velocity and position feedback control of the support was added to the support acceleration for wave control because the wave control could not fix the support position. This control can place the support at other than the original position. The experiments of a three homogeneous rigid pendulum system and a rope-and-mass system were conducted. The rope-and-mass experimental system has the function of winding up and down of load mass. The effect of the virtual pendulum length on the wave control was also investigated. From the simulation and experiment, our presented control strategy was shown to be effective enough and practical for real crane systems.

Control of a crane rope-and-mass system by wave absorption with support feedback control

“…The uncontrollable non-dimensional natural frequency is approximately 1.5 (see Fig. 19 in Zheng and Saigo 2015). Figure 3 shows that the vibrations of the first and second natural frequencies are perfectly controlled.…”

“…Generally, lumped parameter systems have a wave propagation limit frequency (referred to hereinafter as the limit frequency). The limit frequency of an n -DOF homogeneous simple pendulum system of length c l is given by the following expression (Zheng and Saigo, 2015):…”

“…The above studies on crane control were based on vibration control, that is, natural-frequency-based control. Wavebased approaches that operate in terms of mechanical waves rather than vibration formulation have also been investigated, and these approaches may be easier to derive and implement compared to the time-optimal control (Saigo et al, 1998(Saigo et al, , 2003O'Connor, 2003;Zheng and Saigo, 2015). The previous approach by the authors (Zheng and Saigo, 2015) was to control the acceleration of the support of the real pendulum system using a multiple imaginary simple pendulum system that exists virtually above the support in combination with the velocity and position feedback control of the support.…”

“…Control strategy of the rope-and-mass system by wave control using imaginary pendulums and support feedback control Figure 1 shows the crane rope-and-mass system, length l and mass m , suspended by the imaginary homogeneous multiple simple pendulum system, length c l and mass m . The control below is applied by regarding the support position of the crane rope, r x , as the lateral displacement of the lowest pendulum of the imaginary system (Zheng and Saigo, 2015): (1) When the imaginary multiple pendulum system is wave controlled in the controller, Eq. (1) yields the wave control condition of the rope-and-mass system.…”

“…[DOI: 10.1299/mej. experimental apparatus used in the previous study (Zheng and Saigo, 2015). The sampling time was 10 ms for 1m c l  , 50 ms for 10 m c l  , and 100 ms for 100 m c l  , and the number of convolution integrals was 300.…”