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SUMMARYThis paper addresses the energy-based swing-up control problem for the Acrobot, a two-link underactuated robot with a single actuator at the joint of the two links. In line with the energy-based control approach, this paper presents a necessary and sufficient condition for non-existence of any singular point in the derived control law, and provides a complete analysis of the convergence of the energy and the motion of the Acrobot. Specifically, for any initial state of the Acrobot, this paper shows clearly how to choose control parameters such that the Acrobot will eventually either be swung up to any arbitrarily small neighbourhood of the upright equilibrium point, or remain in a set containing a finite number of equilibrium points. Moreover, this paper shows that these equilibrium points are unstable. Furthermore, imposing a stronger condition on a control parameter yields that the equilibrium set contains only the downward equilibrium point, which is shown to be hyperbolic and unstable. This proves that the Acrobot will eventually enter the basin of attraction of any stabilizing controller for all initial conditions with the exception of a set of Lebesgue measure zero.

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This paper systematically evaluated the effect of oxide, wire source and heat treatment on the mechanical properties of wire + arc additively manufactured (WAAM) INCONEL 718. Comparison of the as deposited grain structure was made with laser-powder based AM and wrought INCONEL 718. Results showed that oxides formed during deposition had no effect on the mechanical properties since a 0.5μm thick passivation layer consisting of Cr2O3 and Al2O3 formed upon deposition and prevented further oxides from forming inside the bulk. Wires from different suppliers resulted in around 50 MPa difference in UTS possibly due to the slight compositional variation and uncertainties in TiN inclusion. Standard heat treatment improved the strength from 824 MPa to 1110 MPa in the horizontal direction, but the average strength was 105 MPa lower than the wrought alloy. The as deposited WAAM INCONEL718 featured large columnar grains and numerous Laves phase, as compared to the fine grains of laser powder bed fusion and wrought INCONEL 718. This starting microstructure led to less favourable and less numerous precipitates forming during heat treatment, which is the main reason for the strength mismatch. A different heat treatment would not help due to the starting microstructure.