Overdamped System Research Articles

Sufficient condition for reliable logic operations in an over damped bistable system driven by Gaussian white noise.

In this paper, we investigate an overdamped bistable system subject to Gaussian white noise and logical inputs. By solving and estimating the steady distribution of the corresponding Fokker-Planck equation and considering the two essential features of the reliable logic operations (RLOs)-initial value independence and sign invariance-we establish the sufficient condition for RLO occurrence and identify parametric resonance phenomena in the system. Our numerical simulations confirm the reliability and accuracy of the theoretical results. This work offers insights into enhancing the accuracy of stochastic systems, particularly in the realm of logical stochastic resonance, thereby contributing to advancements in understanding and controlling stochastic dynamical systems.

Hybrid synchronization with continuous varying exponent in modernized power grid

Motivated by the modernized power grid, we consider a synchronization transition (ST) of the Kuramoto model (KM) with a mixture of first- and second-order type oscillators with fractions p and 1−p, respectively. Discontinuous ST with forward–backward hysteresis is found in the mean-field limit. A critical exponent β is noticed in the spinodal drop of the order parameter curve at the backward ST. We find critical damping inertia m∗(p) of the oscillator mixture, where the system undergoes a characteristic change from overdamped to underdamped. When underdamped, the hysteretic area also becomes multistable. This contrasts an overdamped system, which is bistable at hysteresis. We also notice that β(p) continuously varies with p along the critical damping line m∗(p). Further, we find a single-cluster to multi-cluster phase transition at m∗∗(p). We also discuss the effect of those features on the stability of the power grid, which is increasingly threatened as more electric power is produced from inertia-free generators.

Directed transport of two-coupled particles under the coordination of the coupling and an asymmetric potential

Directed transport of particles in asymmetric potential fields is an important topic in many scenarios. This article proposes a model to describe the transport of an overdamped system that is composed of two-coupled particles confined by a saw-tooth potential under the Gaussian white noise and driven by a rocking force. The transport of the two-coupled particles exhibits some interesting behaviors, such as the current varies non-monotonically/increase first and then decrease with the coupling strength, there are two inversion points of the transport direction as the free length between the two particles varies, etc. The effective potential defined by adding the asymmetric potential and the coupling between two particles can clearly interpret, based on its overall inclination, the generation of the directed transport in the model. And the direction of movement can be reversed by adjusting the strength of the rocking force and noise under certain ratchet potential. The findings and analysis method allow us to regulate the directed transport of coupled particles via adjusting the combination of the aforementioned factors.

Unified framework for over-damped string stable adaptive cruise control systems

Many recent experiments have shown that the current commercially available adaptive cruise control (ACC) systems demonstrate string instability phenomena. The lower-level time-lag, the sensor time-delay, and the input disturbance primarily contribute to such instability. This paper presents a unified strategy to design ACC systems compensating the lower-level time-lag, the sensor time-delay, and the input disturbance, by fulfilling the over-damped string stability criterion for homogeneous platoons. The over-damped feature associated with string stability explicitly addresses the safety of a platoon in a stricter sense, considering the transient convergence effects, such as over-shoot, under-shoot, and oscillations, and satisfying all the Lp stability norms, where p∈1,∞. In this article, the derived over-damped string-stable strategy compensating lag, delay, and disturbance (OSSCLDD) is presented in a general unified form that applies to any linear or convex velocity-dependent spacing functions. The derived strategy is demonstrated and validated via simulation using a linear constant time gap spacing function and two nonlinear spacing functions, namely, the variable time gap and the quadratic range spacing function.

Classical and quantum dynamics of over-damped non linear systems

Overdamping is a regime in which friction is sufficiently large that the motion either decays to its equilibrium position or it crosses the equilibrium position exactly once before returning monotonically towards the equilibrium position. The phenomena of overdamping has been studied classically and quantum mechanically only for the case of the linear damped harmonic oscillator. Here we study the classical and quantum dynamics of a family of over-damped non linear systems. The main objective of this paper is to find a Lagrangian and Hamiltonian framework to study over-damped non linear systems and to show that a quantum mechanical description can be developed in the momentum representation. Our results reduce to the well known solution of the linear damped harmonic oscillator when the non linear part is set to zero.

Approximation Technique for Solving High-Order Non-Oscillatory Vibration Systems with Slowly Changing Coefficients Represented by Strong Non-Linearity and Multiple Integrated Roots

A formula for the asymptotic solution of an over-damped strongly nonlinear vibration system combining the extended KBM method and the harmonic balance (HB) method with slowly varying coefficients is proposed. This article aims to establish a slowly time-varying solution of an over-damped nonlinear vibration system where one eigenvalue is an integer multiple (greater than two hundred times) of the other eigenvalues. The integrated multiple eigenvalues can provide a better result than other eigenvalues for strong linearity (even if). We found solutions by considering initial conditions and comparing the percentage error of present solutions with unified solutions by using this procedure in examples. Finally, the findings are addressed, especially to improve the physical prospects and shown graphically by using Excel, Dev C++, MATHEMATICA, and MATLAB software.

Proxy-based torque control of motor-driven exoskeletons for safe and compliant human-exoskeleton interaction

Exoskeletons are considered as promising devices for motion assistance of mobility impaired patients and motor ability augmentation of healthy people. Considering the interactive action between exoskeletons and human body, a safe and comfortable human-exoskeleton interaction is essential to achieve effective exoskeleton operation for human motion assistance. In this paper, a proxy-based torque controller (PTC) is designed for safe and performant interaction torque control of motor-driven exoskeletons under different scenarios. Firstly, the dynamics of commonly applied motor-based conventional stiff actuator (CSA) and series elastic actuator (SEA) for exoskeletons are modelled and analyzed. Then, the PTC with specified compensation is designed based on proxy-based sliding mode control (PSMC) strategy and the stability is theoretically proved for the closed-loop system of the two types of actuators. Meanwhile, an adaptive law is designed for online adjustment of the PTC parameter to produce an overdamped system response for the two actuators under unexpected interruptions. Following the adaptive law, the PTC robustly realizes a compliant torque control while keeping accurate torque tracking under normal operation. Experiments are conducted for two back-support exoskeletons with CSA and SEA, verifying the effectiveness of the proposed controller for safe human-exoskeleton interaction assurance under different scenarios.

Bistable chaotic family and its chaotic mechanism

The emergence of many chaotic families shows that chaos can be generated by deterministic approaches. From the perspective of the mechanism of chaos, we add the opposite time-delayed effects to an overdamped bistable system to obtain chaos. The effect of time delay is determined by the change of the optimal window which origin from logical stochastic resonance. A variety of chaotic systems with different chaotic attractors are obtained by different combinations of opposite effects. Furthermore, we propose the mechanism of chaos in time-delayed bistable systems, that is, the opposite time-delayed effects lead to repeated increasing and decreasing in depth of potential wells. This mechanism is verified by constructing a force-free Duffing equation with an oscillatory double-well potential. Results show that the bistable systems can form bistable chaotic family based on the same chaos generation mechanism.

Strongly enhanced dynamics of a charged Rouse dimer by an external magnetic field.

While the dynamics of dimers and polymer chains in a viscous solvent is well understood within the celebrated Rouse model, the effect of an external magnetic field on the dynamics of a charged chain is much less understood. Here, we generalize the Rouse model for a charged dimer to include the effect of an external magnetic field. Our analytically solvable model allows a fundamental insight into the magneto-generated dynamics of the dimer in the overdamped limit as induced by the Lorentz force. Surprisingly, for a dimer of oppositely charged particles, we find an enormous enhancement of the dynamics of the dimer center, which exhibits even a transient superballistic behavior. This is highly unusual in an overdamped system for there is neither inertia nor any internal or external driving. We attribute this to a significant translation and rotation coupling due to the Lorentz force. We also find that magnetic field reduces the mobility of a dimer along its orientation and its effective rotational diffusion coefficient. In principle, our predictions can be tested by experiments with colloidal particles and complex plasmas.

Design Methodology to Derive Over-Damped String Stable Adaptive Cruise Control Systems

In this paper, we formulate a common design methodology to derive an adaptive cruise control algorithm in order to compensate the effect of the lower level time-lag on the stability. Here the dynamics of the vehicle is approximated by a first order system. The lower level time-lag is referred to the lag associated with the vehicle dynamics to attain the desired condition computed by the adaptive cruise controller. Inclusion of such dynamics reduces the performance of an adaptive cruise control system, both locally and collectively. The solutions presented here can be applied to design a new adaptive cruise control model or to extend any model with velocity dependent spacing function. The derived design method fulfills the over-damped string stability condition in presence of a time-lag in the plant, irrespective of the choice of the equilibrium operating point of linearization. The over-damped characteristic improves both safety and performance. To demonstrate the application of the presented method, two existing models are extended using the derived strategy, viz. the variable time gap and the quadratic range policy. Later the extended models are simulated with rigorous driving conditions, in order to illustrate the improvements in comparison with the respective original models as well as with the extended models using an existing compensation strategy.

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.

Taming the Time Evolution in Overdamped Systems: Shortcuts Elaborated from Fast-Forward and Time-Reversed Protocols.

Using a reverse-engineering approach on the time-distorted solution in a reference potential, we work out the external driving potential to be applied to a Brownian system in order to slow or accelerate the dynamics, or even to invert the arrow of time. By welding a direct and time-reversed evolution toward a well chosen common intermediate state, we analytically derive a smooth protocol to connect two arbitrary states in an arbitrarily short amount of time. Not only does the reverse-engineering approach proposed in this Letter contain the current-rather limited-catalog of explicit protocols, but it also provides a systematic strategy to build the connection between arbitrary states with a physically admissible driving. Optimization and further generalizations are also discussed.

Energy harvesting from anisotropic fluctuations.

We consider a rudimentary model for a heat engine, known as the Brownian gyrator, that consists of an overdamped system with two degrees of freedom in an anisotropic temperature field. Whereas the hallmark of the gyrator is a nonequilibrium steady-state curl-carrying probability current that can generate torque, we explore the coupling of this natural gyrating motion with a periodic actuation potential for the purpose of extracting work. We show that path lengths traversed in the manifold of thermodynamic states, measured in a suitable Riemannian metric, represent dissipative losses, while area integrals of a work density quantify work being extracted. Thus, the maximal amount of work that can be extracted relates to an isoperimetric problem, trading off area against length of an encircling path. We derive an isoperimetric inequality that provides a universal bound on the efficiency of all cyclic operating protocols, and a bound on how fast a closed path can be traversed before it becomes impossible to extract positive work. The analysis presented provides guiding principles for building autonomous engines that extract work from anisotropic fluctuations.

Study the Effects of Mass in a Simple Damped Harmonic Motion of a Mass-spring System Using Simulation

The effect of mass on the behavior of oscillatory systems in a damped spring-mass system was studied using simulation. It was found that the mass affects the amplitude and displacement in the case of an undamped oscillatory system. In critically damped systems, the mass affects the displacement exponentially, and the system doesn’t oscillate. In the case of an overdamped system, there is also no oscillatory motion, and an increase in the mass was not affected, since the system gets to rest very quickly. The study shows that simulation can be a very helpful tool to study the behavior of oscillatory physical systems. Keywords: Simple harmonic motion damped mass-Spring system, simulation

An Explicit Analytical Solution for Transient Two-Phase Flow in Inclined Fluid Transmission Lines

Due to the complex nonlinearity characteristics, analytical modeling of compressible flow in inclined transmission lines remains a challenge. This paper proposes an analytical model for one-dimensional flow of a two-phase gas-liquid fluid in inclined transmission lines. The proposed model is comprised of a steady-state two-phase flow mechanistic model in-series with a dynamic single-phase flow model. The two-phase mechanistic model captures the steady-state pressure drop and liquid holdup properties of the gas-liquid fluid. The developed dynamic single-phase flow model is an analytical model comprised of rational polynomial transfer functions that are explicitly functions of fluid properties, line geometry, and inclination angle. The accuracy of the fluid resonant frequencies predicted by the transient flow model is precise and not a function of transmission line spatial discretization. Therefore, model complexity is solely a function of the number of desired modes. The dynamic single-phase model is applicable for under-damped and over-damped systems, laminar, and turbulent flow conditions. The accuracy of the overall two-phase flow model is investigated using the commercial multiphase flow dynamic code OLGA. The mean absolute error between the two models in step response overshoot and settling time is less than 8% and 2 s, respectively.

Pull-In Dynamics of Two MEMS Parallel-Plate Structures for Acceleration Measurement

This paper investigates the pull-in dynamics of single-sided and double-sided parallel-plate (SSPP and DSPP) structures employed in MEMS devices for acceleration measurement. A lumped electromechanical model considering a variable damping coefficient and external acceleration is developed for studying their pull-in dynamical behavior. The critical pull-in displacement and pull-in voltage for both parallel-plate structures operated with external acceleration are derived based on the static and dynamical analysis of the proposed model, which are in good agreement with the experimental results. The derived closed-form solutions are shown to be capable of predicting the pull-in behavior of both parallel-plate structures in an overdamped system. Two MEMS parallel-plate structures exhibit distinct pull-in characteristics due to their distinct configurations. The commonly used SSPP structure for MEMS devices is shown to have a relatively linear response to the external acceleration in terms of the critical pull-in displacement and pull-in voltage. However, the DSPP structure exhibits much larger yet nonlinear sensitivity of both the critical pull-in displacement and the critical pull-in voltage to a small range of external acceleration, which has the potential of developing high-sensitivity accelerometers whenever the sensitivity nonlinearity is compensated. Moreover, the effects of pressure are characterized for both DSPP and SSPP devices, which affects the difference between the critical static and dynamic pull-in voltages. The SSPP structure is shown to have the critical pull-in voltage proportional to the logarithmic magnitude of the pressure, while that of the DSPP structure do not vary linearly with respect to the logarithmic magnitude of the pressure.

Theoretical and experimental investigation on novel 2D maglev servo proportional valve

This paper presents a novel two-dimensional maglev servo proportional cartridge valve (2D maglev valve), where a contactless maglev coupling is introduced between electro-mechanical converter and valve body to realize functions of force transmission, spool position feedback and linear-rotary motion conversion. Such configuration can effectively reduce cost of both valve manufacturing and electro-mechanical converter, while still maintain features of 2D valve such as null pilot leakage, high power-to- weight ratio and excellent anti-pollution capacity. Firstly, the characteristic equation of the valve is derived using linear theory, and the stability criterion is established for parameter determination. The influences of crucial structural parameters such as initial height of overlapping area, width of high-pressure and low-pressure holes, acting radius of magnetic force, pitch angle of maglev coupling, length of sensitive chamber and system pressure on the dynamic response are investigated based on AMESim numerical simulation. The prototype valve is then designed and manufactured and a special test rig is built. The no-load flow characteristic, load flow characteristic, leakage characteristic, amplitude and phase frequency characteristics and step response under different system pressures are measured. The experimental results are in a good agreement with the simulated analysis. As an over-damped system, the prototype valve has excellent working stability, which can reach a no-load flow rate of 105.9 L/min with hysteresis of 3.51%, amplitude bandwidth of 28.7 Hz and phase bandwidth of 42.8 Hz under 21 MPa. The research indicates that the 2D maglev valve can be a potential solution of flow rate control valve for flight control surface system of civil aircraft with high pressure and large flow rate application.

Stabilization Domains for Second Order Delay Systems

In this paper, an analytic condition is given for determining delayed positive feedback controller for stabilizing an oscillatory system. The $\tau $ -decomposition and $D$ -decomposition methods are employed in deriving this condition. The obtained results are then used to stabilize second order delay systems by a proportional controller. Under-damped and over-damped systems are treated separately, where the Smith-predictor structure is used in the over-damped case to obtain the stability conditions. Illustrative examples are given to show the effectiveness of the proposed approach.

Proposal of a simplified Coulomb friction numerical model for the preliminary design of electrohydraulic servomechanisms

Electrohydraulic servomechanisms (EHAs) are particularly interesting for aviation application, in fact tanks to the high power to weight ration are widely diffused in medium to large cargo and passengers planes or fighters. This work is focused on the proposal of a new dry friction numerical algorithm, based upon Coulomb’s approach, which can be integrated into simulation algorithms obtained by degrading the systems dynamic models (e.g. an over-damped second-order system reducible to a simpler first-order one). This approach, if correctly applied, significantly reduces the computational burden, without significant losses in simulation accuracy. The authors evaluated the approach proposed by a numerical test bench simulating the behaviour of an electrohydraulic linear actuator commonly used in primary flight controls.

Closed-loop flow control of an ultra-compact serpentine inlet based on nondimensional model

Ultra-compact serpentine inlet faces serve inlet-engine compatibility issues due to flow distortion. To ensure inlet-engine compatibility over a wide range of Mach number, novel active flow control techniques with the ability of being opened or adjusted as needed draw many attentions in recent years. In this paper, a feedback control system was developed based on the method of microjet blowing. The proposed system includes a pressure adjusting valve to adjust the control effort, a dynamic pressure sensor to sense the inlet distortion intensity, a signal processing instrument to calculate the Root-Mean-Squared (RMS) pressure, and a controller to implement feedback control. To achieve high quality closed-loop controls at dynamic conditions, a novel nondimensional feedback method was developed. The advantage of this nondimensional method was validated at both off-design and arbitrarily changing Mach number conditions. With a sectional PI control law, the RMS control error reduced more than 56% at arbitrary changing conditions. Works in this paper also showed that the dynamics of this nondimensional system can be simplified as a stable second-order overdamped system.