Swing-up control of a single pendulum from the pendant to the upright position is firstly surveyed. The control laws are comparatively studied based on swing-up time from a given initial state to the upright position. The State Dependent Riccati Equation is found effective for designing the swing-up control law under saturating control input. The control law is extended to a linear combination of sine function of the angle and the angular velocity, and a variable structure control with a sliding mode given by the linear combination. Making the swing-up time correspond to a colour, which is similar to the Fractal analysis, colour maps of the swing-up time for given control parameters and initial conditions yield interesting Fractal-like figures.

The present study modelled the effects of operational parameters on the performance of the Falcon concentrator. For this purpose, the Falcon L40 concentrator was tested in narrow particle-size fractions (−600 + 425 μm, −425 + 300 μm, −300 + 212 μm, −212 + 150 μm, −150 + 106 μm, and −106 + 75 μm) at different washing water pressures and artificial gravity forces generated by a spinning bowl. The test samples were prepared artificially, comprising 2% magnetite (Fe3O4) and 98% calcite (CaCO3) by weight. The recovery and grade values of the 60 experimental conditions were investigated and compared for different operational parameters, including particle-size distributions, water pressures, and artificial gravity forces. Two empirical models were developed using non-linear regression analysis to indicate the effects of the operating parameter of the Falcon concentrator on its recovery and grade values. The operational parameters were found to impact the separation performance considerably. Therefore, the Falcon concentrator should operate under optimum conditions, which can be easily predicted using these models, to achieve improved recovery and grade values.