Novel resonance stability criterion for the 2D magnetically levitated servo-proportional valve

The leakage of the pilot stage of the 2D valve mainly depends on the size of its initial opening. According to the Routh criterion, the pilot stage of the two-dimensional magnetically levitated servo-proportional valve (2D-MSP valve) needs to be designed to have certain positive values to increase the damping ratio to improve valve stability, which leads to the leakage flow representing a non-negligible power loss. In order to reduce leakage flow and achieve goal of energy saving, this paper presents a novel resonance stability criterion by considering nonlinear characteristics of the fluid dynamic system. First, the 2D-MSP valve is regarded as a three-way valve-controlled differential cylinder system. Based on the frequency response of the resonance state, the energy conservation method is used to solve the flow “backfilling” area, the motion equation of the cylinder piston (valve spool displacement) and the pressure waveform of the sensing chamber under different opening and pressure amplitude ratio. Then, the analytical expression of the resonance peak amplitude is obtained and the resonance stability criterion is deduced. The result is compared with the Routh stability criterion, which illustrates that the positive openings of the pilot stage can be reduced to one-third of the original value. The prototype valve is then designed and manufactured based on the resonance stability criterion. The dynamic and static characteristics under different system pressures are measured. Experimental results show that the prototype valve is an over-damped system without any overshoot, which has excellent working stability, and its static and dynamic performance can meet the demands of the industry servo-proportional control system. The research work validates the effectiveness of the proposed resonance stability criterion.

Relativistic Dynamical Stability Criterion of Multiplanet Systems with a Distant Companion

Multiplanetary systems are prevalent in our Galaxy. The long-term stability of such systems may be disrupted if a distant inclined companion excites the eccentricity and inclination of the inner planets via the eccentric Kozai–Lidov mechanism. However, the star–planet and the planet–planet interactions can help stabilize the system. In this work, we extend the previous stability criterion that only considered the companion–planet and planet–planet interactions by also accounting for short-range forces or effects, specifically, relativistic precession induced by the host star. A general analytical stability criterion is developed for planetary systems with N inner planets and a relatively distant inclined perturber by comparing precession rates of relevant dynamical effects. Furthermore, we demonstrate as examples that in systems with two and three inner planets, the analytical criterion is consistent with numerical simulations using a combination of Gauss’s averaging method and direct N-body integration. Finally, the criterion is applied to observed systems, constraining the orbital parameter space of a possible undiscovered companion. This new stability criterion extends the parameter space in which an inclined companion of multiplanet systems can inhabit.

Periodicity on Neutral-Type Inertial Neural Networks Incorporating Multiple Delays

The classical Hopefield neural networks have obvious symmetry, thus the study related to its dynamic behaviors has been widely concerned. This research article is involved with the neutral-type inertial neural networks incorporating multiple delays. By making an appropriate Lyapunov functional, one novel sufficient stability criterion for the existence and global exponential stability of T-periodic solutions on the proposed system is obtained. In addition, an instructive numerical example is arranged to support the present approach. The obtained results broaden the application range of neutral-types inertial neural networks.

Stability Analysis of Drilling Inclination System with Time-Varying Delay via Free-Matrix-Based Lyapunov–Krasovskii Functional

This study provides an insight into the asymptotic stability of a drilling inclination system with a time-varying delay. An appropriate Lyapunov–Krasovskii functional (LKF) is essential for the stability analysis of the abovementioned system. In general, an LKF is constructed with each coefficient matrix being positive definite, which results in considerable conservatism. Herein, to relax the conditions of the derived criteria, a novel LKF is proposed by avoiding the positive-definite restriction of some coefficient matrices and introducing additional free matrices simultaneously. Subsequently, this relaxed LKF is applied to derive a less conservative stability criterion for the abovementioned system. Finally, the effect of reducing the conservatism of the proposed LKF is verified based on two examples.