Prediction and control of nonlinear instabilities in slewing boom lifting machines

Abstract Nonlinear instabilities are investigated in slewing boom lifting machines which are fundamental rotating multibody systems. The focus is on predicting and controlling the nonlinear bucket/load swing behaviour of draglines and large tower cranes under realistic operating conditions. Theoretically these machines are types of non-inverted Furuta pendulums (a two link mechanism) with a dragline being a very large, mainly inclined case, with a hoist and dragrope. These machines remove overburden for exposing minerals in mining. Tower cranes are another non-inclined case, where typically only a pair of hoist ropes is used to restrict in-plane swing. In contrast with previous research, we focus on instabilities occurring under real operation of the machine, whereby the changing rope lengths and loading/unloading are taken into account to perform typical lifting cycles. Validation of Lyapunov stability and chaotic analyses are first provided under normal oscillating boom slewing and constant rope length conditions. This is then extended for realistic cycles for a range of field measured operating parameters of representative slewing boom lifting machines using Melnikov’s analysis. Numerical simulations, conducted under field-measured conditions, demonstrate that the newly developed analytical criteria effectively predict the onset of chaotic instability in realistic loading/unloading cycles with changing rope lengths and mass. Results show the boom inclination under taut dragropes delays the onset, of a pitchfork bifurcation and chaotic instability, to larger slew torques. This is mainly due to centrifugal stiffening of the pendular swing. The importance of rope length and centre of mass dynamics are determined and show chaotic instability is realistically more likely, in deep digging/loading operations, under smaller cycle times. Finally, a Lyapunov controller is developed based on the underlying stability analysis and implemented to eliminate chaotic instability under typical dragline and tower crane operations. The global stability of the system under control is ensured via Lyapunov’s theorem and is shown to provide robust elimination of chaos over a wide range of sizes and applications for slewing boom lifting machines. The results provide insight into the occurrence and control of chaos in the dynamic operation of fast slewing boom lifting machines.