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The paper indicates a correct thermodynamically consistent way to take into account higher order inertia effects within continuum mechanics.
Coal flotation is a nonlinear process with extreme static characteristics and dynamics described by the first order inertia with time delays.
The paper indicates the correct way to describe the inertia forces in the presence of higher order inertia; it extends and improves previous findings by the author [Polizzotto, C., 2012. A gradient elasticity theory for second-grade materials and higher order inertia. Int. J. Solids Struct. 49, 2121 2137].
The classical linear and angular momentum theorems are suitably extended for higher order inertia, from which the local motion equations and the moment equilibrium equations (stress symmetry) can be derived.
Previous findings by the author [Polizzotto, C., 2012. A gradient elasticity theory for second-grade materials and higher order inertia. Int. J. Solids Struct. 49, 2121 2137] are improved and extended.
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Gsh(s) is the first-order inertia element used to simulate the UPFC shunt side, as shown in Fig. 5.
The nonlocality is shown to be equivalent to higher-order inertia modelling for the dynamics analysis.
From (16) and (17), we find that θadd can be influenced by the angle of the first-order inertia element Gsh(s) with an independent shunt side.
Gsh(s) and Gse(s) are first-order inertia elements that simulate the function of the shunt side and the serial side, respectively.
With the proposed internal control, the model of STATCOM can be simplified to be a first-order inertia block, which can significantly simplify the design of system control.
A first-order inertia element Gse(s) with a gain of Kse and time constant Tse, as shown in Fig. 5, is used to simulate the UPFC transmission line impedance control on the UPFC serial side.
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