Time-delayed Feedback Control Research Articles

A New Vibration-Absorbing Wheel Structure with Time-Delay Feedback Control for Reducing Vehicle Vibration

To address the contradiction between ride comfort and handling stability, a new vibration-absorbing wheel structure with time-delay feedback control was proposed by applying a time-delay feedback-controlled dynamic vibration absorber to the wheel structure. Using H2 optimization and the particle swarm optimization algorithm (PSO), the design parameters of the time-delay vibration-absorbing wheel structure were obtained with sprung mass acceleration (SMA), suspension deflection (SD) and dynamic tire deflection (DTD) as the optimization objective functions. The stability interval of the system was analyzed using the Routh–Hurwitz criterion and the Sturm criterion. The vehicle vibration reduction performance of the new vibration-absorbing wheel structure was simulated and verified in the time domain under harmonic excitation and random excitation. The simulation results show this new structure can effectively solve the contradiction between the ride comfort and handling stability. It provides a new technical idea for reducing vehicle vibration.

Non-Markovian systems out of equilibrium: exact results for two routes of coarse graining

Generalized Langevin equations (GLEs) can be systematically derived via dimensional reduction from high-dimensional microscopic systems. For linear models the derivation can either be based on projection operator techniques such as the Mori–Zwanzig (MZ) formalism or by ‘integrating out’ the bath degrees of freedom. Based on exact analytical results we show that both routes can lead to fundamentally different GLEs and that the origin of these differences is based inherently on the non-equilibrium nature of the microscopic stochastic model. The most important conceptional difference between the two routes is that the MZ result intrinsically fulfills the generalized second fluctuation–dissipation theorem while the integration result can lead to its violation. We supplement our theoretical findings with numerical and simulation results for two popular non-equilibrium systems: time-delayed feedback control and the active Ornstein–Uhlenbeck process.

Effect of time-delay feedback control on vehicle seat vibration reduction and suspension performance

To reduce seat vibration caused by uneven road surfaces, the time-delay feedback control into the seat suspension system was introduced and an active seat suspension control method based on time-delay feedback was proposed in this paper. A three-degree-of-freedom (3-DOF) suspension model with time-delay feedback control was established. The time-delay independent stability region and critical stability curve of the system were derived using the method of characteristic root and stability switching. The effect of feedback control parameters on system vibration was investigated in the stability region. The seat acceleration (SA), body acceleration (BA), suspension dynamic deflection (SDD), and tire dynamic displacement (TDD) were used as multi-objective optimization functions and the optimal values of feedback control parameters were obtained based on the particle swarm algorithm (PSO) with above optimization functions. The numerical simulation was conducted to validate the proposed model. The simulated results show that the time-delay feedback control can significantly suppress the vibration response of the seat and effectively improve the suspension performance under different road excitation compared with the passive suspension. It can be seen that the active seat suspension with time-delay control significantly improve ride comfort and handling stability of the vehicle, which can be used as a reference for the active control technology of vehicle suspension.

Dynamic performance and stability analysis of an active inerter-based suspension with time-delayed acceleration feedback control

Dynamic performance and stability analysis of an active inerter-based suspension with time-delayed acceleration feedback control

Precise Motion Control of a Power Line Inspection Robot Using Hybrid Time Delay and State Feedback Control.

Intelligent robotic inspection of power transmission lines has proved to be an excellent alternative to the traditional manual inspection methods, which are often tedious, expensive, and dangerous. However, to achieve effective automation of the robots under different working environments, the dynamic analysis and control of the robots need to be investigated for an efficient inspection process. Nonetheless, the application of control techniques for the position, speed and vibration control of these robots has not been explored in detail by the existing literature. Thus, an approach for precise motion control of the sliding inspection robot is presented in this paper. The main contribution of the study is that the chattering problem associated with the traditional command shaping time delay control (TDC) was minimized by smoothing the chattered input signal. Then, the improved control (iTDC) which is effective for oscillation control is hybridized with a pole placement based feedback control (PPC) to achieve both position and the sway angle control of the robot. The nonlinear and the linearized models of the sliding robot were established for the control design and analysis. Three parameters of the robot, namely, the length of the suspended arm, the mass of the payload, and the friction coefficient of different surfaces, were used to assess the robustness of the controller to model uncertainties. The iTDC + PPC has improved the velocity of TDC by 201% and minimizes the angular oscillation of PPC by 209%. Thus, the results demonstrate that the hybridized iTDC + PPC approach could be effectively applied for precise motion control of the sliding inspection robot.

Time-delayed feedback control of nonlinear dynamics in a giant magnetostrictive actuator

Time-delayed feedback control of nonlinear dynamics in a giant magnetostrictive actuator

Research on Vibration Reduction of Half-Vehicle Active Suspension Sys-tem Based on Time-delayed Feedback Control with Wheel Displacement

This paper proposes parameter controlling optimization of the time-delay feedback that is based on "equivalent harmonic excitation" in effective frequency band towards optimization of delay feedback control parameters for vehicle semi active suspension system. In this way, the optimal values of delay feedback control parameters based on different types of delay feedback control (displacement, velocity and acceleration) of wheels in the effective frequency band are obtained. Finally, through the stability analysis of vehicle semi-active suspension system based on different types of wheel delay feedback control and the numerical simulation analysis of time-domain response of suspension system performance evaluation index, the superiority of the time-delay feedback control strategy based on wheel displacement and the effectiveness and feasibility of the equivalent harmonic excitation optimization strategy are verified. Therefore, it provides a theoretical reference for the selection of time-delay feedback control strategy and the optimal design of time-delay feedback control parameters of vehicle active and semi-active suspension system.

Investigating the dynamics of a buck converter with time-delay feedback control

The paper deals with the dynamics features of a closed automatic control system based on a buck converter with a function to control nonlinear dynamic processes. A comprehensive analysis of the system under study is carried out using both small-signal average dynamic models and nonlinear dynamic models. For the first time, a small-signal average model of a system with a control function for nonlinear dynamic processes based on a time-delay feedback control has been obtained. The influence of this control method on Bode plots of an open system is shown. It is noted that the use of the time-delay feedback control ensures the stability of both the equilibrium point of the small-signal average model and the fixed point of the periodic mode of the nonlinear dynamic model of the system under consideration. This enables to achieve high quality output voltage. The application of the time-delay feedback control does not require to correct the system parameters, which ensures a given speed and low losses in the power switch of the converter. In addition, the quality of the transition process in the system is improved, namely, oscillation is eliminated and overshoot is reduced. Using the time-delay feedback control, it is possible to provide the desired dynamic mode in the areas of instability of the initial system without controlling nonlinear dynamic processes, which makes it possible to increase the speed due to the small time constant of the regulator. These results were obtained for the first time and can be used in the design of pulse power supply systems of a wide variety.

Research on Time Delay Feedback Control of Lateral Vibration Axially Moving Viscoelastic Beam

The nonlinear dynamic behavior of a viscoelastic beam in axially variable motion under time delay is studied. Considering that the axial velocity pulsation and radial tension change periodically with time under the action of time delay, the viscous damping and finite support stiffness are taken into account, and the viscoelastic constitutive relationship adopts Kelvin model. A mathematical model of lateral vibration of an axially moving viscoelastic beam with changes in axial velocity and tension under time delay is established, and a partial differential-integral control equation describing the lateral nonlinear vibration of an axially moving beam is given. Based on the Galerkin truncation method, the control equations established based on the mechanical model are discretized, so that the direct multi-scale method obtains the numerical solution of the lateral nonlinear vibration of the axially moving beam under the action of time delay, and determines the nonlinear dynamic behavior of the system under the action of time delay. By analyzing the numerical solution of the vibration displacement and velocity at the midpoint of the beam, the whole process of the average velocity of the axially moving structure along the axis, the amplitude of the disturbance tension and the change of the viscoelastic coefficient is simulated. It provides a numerical theoretical basis for the study of the nonlinear dynamic behavior of axially moving beams under time delay.Through the research in this article, the introduction of time delay is studied, and the time delay is used to analyze the axial force that changes along the radial direction of the beam caused by the speed pulsation, and the theoretical framework for nonlinear vibration analysis of the axially moving viscoelastic beam is constructed to expand the time delay. The application scope of the nonlinear vibration theory and nonlinear dynamics theory, the development and improvement of the approximate analysis and numerical solution of the nonlinear continuum (especially the gyro body) under the action of time delay, to provide a theoretical basis for the analysis and design of the corresponding engineering system and technical reserves.

Stabilization of exact coherent structures in two-dimensional turbulence using time-delayed feedback

Time-delayed feedback control, attributed to Pyragas (1992 Physics Letters 170(6) 421-428), is a method known to stabilise periodic orbits in low dimensional chaotic dynamical systems. A system of the form $\dot{\mathbf{x}}(t)=f(\mathbf{x})$ has an additional term $G(\mathbf{x}(t)-\mathbf{x}(t-T))$ introduced where $G$ is some `gain matrix' and $T$ a time delay. The form of the delay term is such that it will vanish for any orbit of period $T,$ therefore making it also an orbit of the uncontrolled system. This non-invasive feature makes the method attractive for stabilising exact coherent structures in fluid turbulence. Here we begin by validating the method for the basic flow in Kolmogorov flow; a two-dimensional incompressible Navier-Stokes flow with a sinusoidal body force. The linear predictions for stabilisation are well captured by direct numerical simulation. By applying an adaptive method to adjust the streamwise translation of the delay, a known travelling wave solution is able to be stabilised up to relatively high Reynolds number. We discover that the famous `odd-number' limitation of this time-delayed feedback method can be overcome in the fluid problem by using the symmetries of the system. This leads to the discovery of 8 additional exact coherent structures which can be stabilised with this approach. This means that certain unstable exact coherent structures can be obtained by simply time-stepping a modified set of equations, thus circumventing the usual convergence algorithms.

The effect of fractional damping and time-delayed feedback on the stochastic resonance of asymmetric SD oscillator

This paper proposes the stiffness nonlinearities and asymmetric SD (smooth and discontinuous) oscillator under time-delayed feedback control with the fractional derivative damping. With the effect of displacement and velocity feedback, the oscillator can be adjusted to the desired vibration state, and then the stochastic resonance (SR) is achieved. This article discusses the contribution of various system parameters and time-delayed feedback to SR, especially which induced by fractional order. It should be noted that this paper provides effective guidance for fault diagnosis and weak signal detection, energy harvesting, vibration isolation and vibration reduction.

On stability and feedback control of discrete fractional order singular systems with multiple time-varying delays

In this paper, we study discrete fractional order singular systems with multiple time-varying delays. By use of new techniques, some useful fractional order difference inequalities are given. Then, conditions based on matrix inequalities and discrete fractional Lyapunov direct method have been obtained for the asymptotic stability of such systems. Further, the stability theories are applied to the stabilization problem of such systems via state feedback control (SFC) and time-delayed feedback control (DFC). Finally, an example is presented to illustrate one of the results.

Resonances of a fractional-order biomedical model with time delay state feedback

In the present paper, the primary resonance of a fractional-order Willis aneurysm system with time-delay state feedback control is studied. Using the multiple scale method, the amplitude and phase equations are obtained. The first order approximate solution is derived and the influence of time delay on resonance is studied. The concept of equivalent damping related to time-delay feedback is proposed, and the reasonable selection of feedback gain and time delay is discussed from the point of view of vibration control. The frequency response and external excitation response curves of the system are given. In order to test the stability of the system, bifurcation analysis is carried out. The obtained results are very useful in the clinical diagnosis and treatment of cerebral aneurysms.

Bifurcation control strategy for a fractional-order delayed financial crises contagions model

<abstract><p>In this paper, we propose a novel fractional-order delayed financial crises contagions model. The stability, Hopf bifurcation and its control of the established fractional-order delayed financial crises contagions model are studied. A delay-independent sufficient condition ensuring the stability and the occurrence of Hopf bifurcation for the fractional-order delayed financial crises contagions model is obtained. By applying time delay feedback controller, a novel delay-independent sufficient criterion guaranteeing the the stability and the occurrence of Hopf bifurcation for the fractional-order controlled financial crises contagions model with delays is set up.</p></abstract>

Time-Delay Feedback Control of an Axially Moving Nanoscale Beam with Time-Dependent Velocity

Time-Delay Feedback Control of an Axially Moving Nanoscale Beam with Time-Dependent Velocity

An optimal control method for time-delay feedback control of 1/4 vehicle active suspension under random excitation

Time-delay feedback control can effectively broaden the damping frequency band and improve the damping efficiency. However, the existing time-delay feedback control strategy has no obvious effect on multi-frequency random excitation vibration reduction control. That is, when the frequency of external excitation is more complicated, there is no better way to obtain the best time-delay feedback control parameters. To overcome this issue, this paper is the first work of proposing an optimal calculation method that introduces stochastic excitation into the process of solving the delay feedback control parameters. It is a time-delay control parameter with a better damping effect for random excitation. In this paper, a 2 DOF one-quarter vehicle suspension model with time-delay is studied. First, the stability interval of time-delay feedback control parameters is solved by using the Lyapunov stability theory. Second, the optimal control parameters of the time-delay feedback control under random excitation are solved by particle swarm optimization (PSO). Finally, the simulation models of a one-quarter vehicle suspension simulation model are established. Random excitation and harmonic excitation are used as inputs. The response of the vehicle body under the frequency domain damping control method and the proposed control method is compared and simulated. To make the control precision higher and the solution speed faster, this paper simulates the model by using the precise integration method of transient history. The simulation results show that the acceleration of the vehicle body in the proposed control method is 13.05% less than the passive vibration absorber under random excitation. Compared with the time-delay feedback control optimized by frequency response function, the damping effect is 12.99%. The results show that the vibration displacement, vibration velocity, and vibration acceleration of the vehicle body are better than the frequency domain function optimization method, whether it is harmonic excitation or random excitation. The ride comfort of the vehicle is improved obviously. It provides a valuable tool for time-delay vibration reduction control under random excitation.

Chaos Control for a Fractional-Order Jerk System via Time Delay Feedback Controller and Mixed Controller

In this study, we propose a novel fractional-order Jerk system. Experiments show that, under some suitable parameters, the fractional-order Jerk system displays a chaotic phenomenon. In order to suppress the chaotic behavior of the fractional-order Jerk system, we design two control strategies. Firstly, we design an appropriate time delay feedback controller to suppress the chaos of the fractional-order Jerk system. The delay-independent stability and bifurcation conditions are established. Secondly, we design a suitable mixed controller, which includes a time delay feedback controller and a fractional-order PDσ controller, to eliminate the chaos of the fractional-order Jerk system. The sufficient condition ensuring the stability and the creation of Hopf bifurcation for the fractional-order controlled Jerk system is derived. Finally, computer simulations are executed to verify the feasibility of the designed controllers. The derived results of this study are absolutely new and possess potential application value in controlling chaos in physics. Moreover, the research approach also enriches the chaos control theory of fractional-order dynamical system.

Research on vibration reduction of semi-active suspension system of quarter vehicle based on time-delayed feedback control with body acceleration

In this paper, the mechanical model of two-degree-of-freedom vehicle semi-active suspension system based on time-delayed feedback control with vertical acceleration of the vehicle body was studied. With frequency-domain analysis method, the optimization of time-delayed feedback control parameters of vehicle suspension system in effective frequency band was studied, and a set of optimization method of time-delayed feedback control parameters based on “equivalent harmonic excitation” was proposed. The time-domain simulation results of vehicle suspension system show that compared with the passive control, the time-delayed feedback control based on the vertical acceleration of the vehicle body under the optimal time-delayed feedback control effectively broadens the vibration absorption bandwidth of the vehicle suspension system. The ride comfort and stability of the vehicle under random road excitation are significantly improved, which provides a theoretical basis for the selection of time-delayed feedback control strategy and the optimal design of time-delayed feedback control parameters of vehicle suspension system.

Amplitude resonance response and feedback control of cantilever beams with tip-mass under aerodynamic load

The dynamic of a cantilever beam with tip mass is studied under an aerodynamic loading. The effects of coupling is investigated by tacking into account the fluid flow. Using the multiple time scale method, the approximative solutions are found and the study of their stability is made by the Routh-Hurwitz stability criterion. The influence of parameters on the system is studied at the harmonic and subharmonic resonances. The results show that, the effects of tip mass can be neglected in harmonic resonance case, while they are more important in subharmonic resonance cases. The results equally demonstrate that an increase of the stable state fluid velocity reduces the amplitude of vibrations. In addition, the hysteresis phenomenon studies show that it is principally induced by nonlinearity coefficients. Finally, time-delay feedback control is applied and the effects of controlling are observed on amplitude response curve at the harmonic resonance, from where we note that optimized choice of control parameters can be useful in controlling vibrations.

Mitigation of rare events in multistable systems driven by correlated noise.

We consider rare transitions induced by colored noise excitation in multistable systems. We show that undesirable transitions can be mitigated by a simple time-delay feedback control if the control parameters are judiciously chosen. We devise a parsimonious method for selecting the optimal control parameters, without requiring any Monte Carlo simulations of the system. This method relies on a new nonlinear Fokker-Planck equation whose stationary response distribution is approximated by a rapidly convergent iterative algorithm. In addition, our framework allows us to accurately predict, and subsequently suppress, the modal drift and tail inflation in the controlled stationary distribution. We demonstrate the efficacy of our method on two examples, including an optical laser model perturbed by multiplicative colored noise.