The ongoing energy transition challenges the stability of the electrical power system. Stable operation of the electrical power grid requires both the voltage (amplitude) and the frequency to stay within operational bounds. While much research has focused on frequency dynamics and stability, the voltage dynamics has been neglected. Here, we study frequency and voltage stability in the case of simple networks via linear stability and bulk analysis. In particular, our linear stability analysis of the network shows that the frequency secondary control guarantees the stability of a particular electric network. Even more interesting, while we only consider secondary frequency control, we observe a stabilising effect on the voltage dynamics, especially in our numerical bulk analysis.

In this paper, the k-valued logic control network is introduced to study the cooperative pursuit control problem of multiple underactuated underwater vehicles (UUVs) with time delay in three-dimensional space. The semi-tensor product of matrices is used to solve the complex calculation problem of the large dimension matrix. The influence of communication delay on multiple UUVs’ optimization and cooperative pursuit control is expressed in a matrix. Under the leadership of evader UUV, the control algorithm can ensure that all the pursuit UUVs reach the desired position. The stability of the closed loop system is proved.

Ramp load/unload (L/UL) mechanisms are widely used to rest sliders in hard disk drives (HDDs). Loading/unloading a slider swiftly and smoothly is crucial in a HDD design. A novel, efficient simulation scheme is proposed to investigate the behaviors of a head disk interface (HDI) in ramp unloading processes. A dual scale model is enabled by decoupling the nano-meter scale change of an air bearing and the micro- or milli-meter scale deformation of a suspension. A modified Reynolds equation governing the air bearing was solved numerically. The slider design was characterized with performance functions. Three stages in an unloading process were analyzed with a lumped parameter suspension model. Key parameters for the model were estimated with a comprehensive finite element suspension model. Finally, simulation results are presented for a commercial HDI design.

In this paper we look at the performance of trigonometric integrators applied to highly oscillatory differential equations. It is widely known that some of the trigonometric integrators suffer from low-order resonances for particular step sizes. We show here that, in general, trigonometric integrators also suffer from higher-order resonances which can lead to loss of nonlinear stability. We illustrate this with the Fermi–Pasta–Ulam problem, a highly oscillatory Hamiltonian system. We also show that in some cases trigonometric integrators preserve invariant or adiabatic quantities but at the wrong values. We use statistical properties such as time averages to further evaluate the performance of the trigonometric methods and compare the performance with that of the mid-point rule.