Time-delayed Control Research Articles

Combined Impact of Multidelay Feedback Number and Interval: A Novel Mechanism for Controlling the Stability of Stochastic Duffing Systems

In this paper, we study a class of nonlinear stochastic Duffing oscillators with multidelay feedback. We propose an effective reduction approach with the help of center manifold theory and stochastic averaging method. Taking the initial time-delay [Formula: see text] as the parameter, we reduce the original system to a one-dimensional averaged Itô equation. Our analysis reveals that the original system exhibits stochastic bifurcations, including stochastic D and P bifurcations. Once we have a clear understanding of the bifurcation structure, we can use this knowledge to choose appropriate system parameters and place the system in the desired state. For instance, by adjusting the initial time-delay [Formula: see text] of the control system, we can stabilize the system and achieve the desired outcome. Numerical simulations also verify the theoretical results. With appropriate parameter choices, multiple time delays can destabilize the equilibrium and promote chaotic behaviors, and can also lead to more stable dynamical behavior. Remarkably, we discovered that increasing the interval of time delays and feedback numbers can enhance system stability. It may potentially serve as a novel mechanism for stabilizing stochastic systems. The study provides a solid theoretical foundation for exploring stochastic systems subject to complex time-delay feedback control, and offers a valuable framework for related fields.

Delay-independent stability of a tri-stable energy harvesting system with time-delayed feedback control

This paper analyzes the delay-independent stability and harvesting performance of a tri-stable vibrational energy harvester (TVEH) with time-delayed feedback control. The dynamical model of the controlled electromechanical TVEH is established, and the method of multiple scales is employed to derive the steady-state response near the primary resonance. The delay-independent stability conditions of the TVEH are obtained using Routh Hurwitz criterion and classical Sturm criterion. The influences of time-delayed feedback control on the TVEH's output and jump phenomena are discussed through the steady-state response. Furthermore, appropriate choices of feedback gains and time delays can ensure the system stability and enhance the output power. The theoretical results are validated through numerical simulations, demonstrating the effectiveness of the proposed control strategy.

Secondary resonance of a cantilever beam with concentrated mass under time delay feedback control

The present work discusses the strongly nonlinear dynamical characteristics of the secondary resonance in a cantilever beam system with concentrated mass regulated through displacement and velocity time delay. Through the homotopy analysis method, the potential superharmonic and subharmonic resonance issues are resolved. A detailed analysis is conducted to investigate the influences of the time delay, feedback gain coefficient, excitation amplitude, and damping coefficient on the nonlinear response. The results show that the system exhibits hardening behavior for superharmonic resonance with one or two peaks and softening behavior for subharmonic resonance. In time delay control systems, increasing the damping coefficient occasionally causes an increase in amplitude. Due to the complexity of the system, it is challenging to definitively determine whether displacement or velocity time delay control is more suitable. Only when specific working conditions are given can it be compared which way is better. Prudently choosing the velocity and displacement time delay factors can restrain the amplitude of the system, adjust the response region, jump frequency and the number of solutions. The findings of this paper are thought to be useful in the design of time delay feedback controllers.

Path-following control of an underactuated stratospheric airship with unknown dynamics and external disturbances using time-delay control

In this paper, the path-following problem for an underactuated stratospheric airship with unknown dynamics and external disturbances has been studied. Vector field guidance is employed to fix the underactuated issue and generate desired heading. Time-delay control (TDC) is utilised to track desired states and estimate the model uncertain and disturbances using simple delayed states. To compensate time-delay estimation (TDE) errors, terminal sliding-mode is utilised and combined with TDC. The stability of the proposed controller is provided by using Lyapunov function. A numerical simulation is demonstrated to prove the performance of the proposed control algorithm.

Bifurcation Analysis and Chaos Control of Carrier Phase-Shifted Cascaded H-Bridge Inverter

Cascaded H-bridge inverters, which belong to strongly nonlinear time-varying system with complex dynamics, have been widely used in high-voltage and high-power engineering fields. In this paper, a carrier phase-shifted sinusoidal pulse-width modulation cascaded H-bridge inverter is taken as an example with piecewise analysis to establish the discrete iterative mathematical model. Furthermore, the nonlinear dynamic behavior of this inverter system is investigated using folding diagrams, spectrum diagrams, bifurcation diagrams, Lyapunov exponents, etc. We find that this inverter can exhibit multiperiod bifurcation, tangential bifurcation and paroxysmal chaos within certain ranges of control coefficients and other circuit parameters, which will influence the system’s stability seriously. On the basis of this discovery, the sinusoidal time-delay feedback control method is proposed. The difference between the load current of the controlled object and its own delay is used to form a feedback term, which is then fed into the sine function and proportional link to obtain the control term. Moreover, the Jacobian matrix of this feedback inverter system is derived, and the constraints on the feedback control coefficient are obtained based on the Jury criterion. Simulation results have verified the effectiveness of such a sinusoidal time-delay feedback control method, which can improve the stability and anti-interference of the system. The research can be used to provide some reference and guidance for the circuit design, debugging and control of cascaded H-bridge inverters.

Impact of Intermediate Species in Simulating Oblique Detonation with Pre-Vaporized N-Decane/air Mixtures Substituting for Kerosene/Air Mixtures

ABSTRACT A renewed two-step n-decane mechanism is presented to improve reliable and robust simulation results, substituting for kerosene. This mechanism demonstrates that effective control of ignition delay time and heat release, based on the Chapman – Jouguet condition, enables successful simulation of oblique detonation waves. Chain reactions influence the overall reaction heat and explosion temperature, especially in simplified mechanisms with few steps. Therefore, carbon monoxide (CO) generation is crucial for balancing the overall reaction heat and reducing species sensitivity to pressure, a factor previously not discussed in simplified models. The computational time for solving detailed chemical kinetics increases exponentially with species count, driving the pursuit for further reduction in kinetic mechanism size. The sensitive interaction between density and temperature during the fuel/air mixture explosion process affects initiation zone formation and cellular structure. Analyzing the distribution of CO can provide insights into structural details. The study considers applying the Rankine – Hugoniot curve to confirm detonation speeds, temperatures, and kinetic energy changes induced by chemical reactions.

Stochastic response and stability analysis of nonlinear vehicle energy-regenerative suspension system with time delay

With the rapid development of new energy vehicles, a novel vehicle energy-regenerative suspension for simultaneous vibration suppression and energy harvesting has become one of the key development directions of the next generation of vehicle design. In order to improve the performance of suspension system, the time-delayed feedback control is applied to the novel suspension system subjected to different external excitation. At the same time, there are few studies related to the stochastic dynamics of nonlinear vehicle energy-regenerative suspension system with time delay. This paper studies stochastic response and stability of nonlinear vehicle energy-regenerative suspension with time-delayed feedback control under the excitation of Gaussian white noise. First of all, a stochastic dynamic model of the nonlinear vehicle energy-regenerative suspension with time delay system is established. Secondly, using the stochastic averaging method based on generalized harmonic function, the steady-state probability density function (PDF) of amplitude is obtained. The accuracy of the presented approach is verified through the comparison of analytical and numerical solutions. In addition, through combining the stochastic averaging method with the Khasminskii method, the top Lyapunov exponent (TLE) of the system is obtained, and then the influence of time delay and system parameters on the asymptotic Lyapunov stability is discussed. Finally, the effects of time delay and system parameters on system performance are also studied.

[formula omitted] sampled-data load frequency control with time-varying delays considering delay compensation

Time delays in load frequency control (LFC) systems may deteriorate the control performance or cause instability. How to mitigate such adverse effects of delays in a simple but effective way is worth investigating and motivates this work. For sampled-data LFC systems with time-varying delays, this paper introduces two delay compensation techniques, namely linear and division-based methods, aimed at enhancing the robustness of LFC. A stability criterion based on H∞ is derived to ensure LFC system stability under delay compensation. Building upon this criterion, we propose an H∞ controller optimization method to tune delay compensation controller gains offline by searching for a minimum H∞ disturbance attenuation level and effectively segmenting the geometric region formed by the delays. The effectiveness of the proposed delay compensation techniques and the controller design method is verified via numerical examples on an LFC system with both generation unit and energy storage participation.

Enhancing energy recovery in automotive suspension systems by utilizing time-delay

This study introduces time-delay active control technology to with the aim of enhancing the system's energy harvesting potential and ride smoothness. The time-delay active suspension represents a nonlinear, multivariable system, and stability analysis in this context is intricate. The mainly challenge lies in effectively leveraging time delay to augment the system's energy collection potential while harmonizing the vehicle's ride comfort and energy efficiency. Addressing this issue, our study proposes enhancing the suspension's energy recovery capability through time-delay control. Initially, the impact of time-delay control parameters on energy collection ability under various operational conditions was analyzed, establishing that appropriate time-delay parameters can enhance energy harvesting capacity. Subsequently, to balance the relationship between vehicle comfort and energy efficiency, the research introduces a method for constructing an optimized objective function based on linear equivalent excitation, thereby quantifying the relationship between system time-domain vibrational response, time-delay control parameters, and external excitations. This approach enables the comprehensive optimization of the suspension system's comfort, safety, and energy efficiency. The control system's stability was analyzed using cluster treatment of characteristic roots method. Finally, simulations and experiments were conducted to evaluate the effectiveness of time-delay active across different scenarios, confirming the efficacy of the proposed control methodology.

Dynamical analysis of a stay cable with a nonlinear energy sink and time-delayed feedback control

Stay cables exist commonly in engineering and can exhibit sustainable and large vibrations under external excitations. The unexpected oscillations always lead to the fatigue and damage of structures, resulting in the economical loss. This paper studies the vibration control of a stay cable system with a nonlinear vibration absorber and time delay control. The governing equations of motion of the stay cable system under harmonic excitations are given. The stability and different bifurcations of the trivial equilibrium point of the system are analyzed. The bifurcation diagrams with respect to the control parameters are illustrated. The frequency responses of the forced system are obtained by using the harmonic balance method. Numerical simulations are performed to validate the obtained results and various dynamical phenomena are shown, such as the multi-period oscillations, quasi-periodic responses and chaotic motions. The effects of the time-delayed feedback control on the nonlinear dynamics and vibration reduction of the system are extracted. It is shown that the proper values of the time delay and feedback gain can improve the vibration reduction performance of the system, such as the suppression of the resonance peaks and elimination of the complex responses.

Adaptive Time-Delay Attitude Control of Jumping Robots Based on Voltage Control Model

Adaptive Time-Delay Attitude Control of Jumping Robots Based on Voltage Control Model

New expectation-based conditions for almost sure exponential stability of discrete-time semi-Markovian linear systems with time-delayed control

This paper studies almost sure exponential stability of discrete-time semi-Markovian linear systems with time-delayed control. New expectation-based sufficient conditions for almost sure exponential stability of the system are derived by employing the coupled Lyapunov function related to the sojourn time and the ergodic property of semi-Markov chains. Compared with known results on almost sure exponential stability of discrete-time semi-Markovian linear systems, the results in this paper are shown to be less conservative. At last, three numerical examples are given to illustrate the results.

Robust predictive regulation of uncertain time-delay control systems with non-zero references and disturbances

Robust regulation is predictively investigated in time-delay models including uncertainties, non-zero reference, and disturbance. Hence, to handle the complexities induced because of the time-delays, disturbances, and uncertainties, enhancing the transient performance would be a main control goal. To this purpose, the required transient and steady-state specifications are achieved through an integral control structure with adjustable gains. The constraints on the signals and aims of the control algorithm are also described by some linear matrix inequalities. Guaranteeing the stability, a minimisation procedure is found to specify the predictive controller. Several simulations are performed to establish the effectiveness of the introduced plan in comparison with the similar strategy.

Adaptive Backstepping Time Delay Control for Precision Positioning Stage with Unknown Hysteresis

Piezoelectric-actuated precision positioning stages are widely used in high-precision instruments and high-end equipment due to their advantages of high resolution, fast response, and compact size. However, due to the strong nonlinearity of hysteresis, the presence of hysteresis in piezoelectric actuators seriously affects the positioning accuracy of the system. In addition, it is challenging to identify the model parameters for hysteresis. In this paper, an adaptive backstepping time delay control method is proposed for piezoelectric devices system with unknown hysteresis. Firstly, the Bouc–Wen model is used to describe the hysteresis characteristics, and the model is interpreted as a linear term and a bounded uncertain hysteresis term. Then, the time delay estimation technique is used to estimate the hysteresis term of the Bouc–Wen model online, and the unknown parameters of the system and hysteresis model are obtained through adaptive updating laws. Furthermore, the stability of the control scheme is proved based on Lyapunov stability theory. Finally, the effectiveness and superiority of the proposed control scheme are demonstrated by comparing it with two typical hysteresis compensation control algorithms through three different sets of input signals.

Dynamic stability and control of vortex induced oscillations of tension leg platform tethers

Dynamic stability and control of sway oscillations of Tension Leg Platform (TLP) tether under regular vortex shedding are investigated. The TLP is modelled as a single degree of freedom simply supported uniform beam under pretension, assuming transverse oscillation to take place only in its fundamental natural mode. The tether is subjected to parametric excitation due to the heave motion of the TLP. The incremental harmonic balance (IHB) method is employed to investigate the period-1 and period-2 responses of the TLP as a function of the detuning parameter. The same system is then investigated under time-delayed state feedback control. Suitable control parameters are selected from the analysis of the local stability of the system equilibrium. The stability of solutions is analyzed by the semidiscretization method with the modified Floquet theory. The stable and periodic responses obtained by the IHB method are verified by directly integrating the equation of motion using the fifth-order Runge-Kutta algorithm at discrete points. Finally, the efficacy of the control scheme has been investigated in the plane of response amplitude versus excitation amplitude. The results show that appropriate selections of control parameters can effectively reduce the response amplitude to a great extent with the improved measure of stability.

Augmented Kalman Estimator and Equivalent Replacement Based Taylor Series-LQG Control for a Magnetorheological Semi-Active Suspension

This research presents an augmented Kalman estimator and an equivalent replacement-based Taylor series (ERBTS)-linear quadratic Gaussian (LQG) control strategy to cope with the control accuracy and response delay of magnetorheological (MR) dampers for vehicle semi-active suspensions. The parameters in the MR model are identified from experimental measurements. Then, two main sources of control error, namely, modelling error and real-time variety of the MR damper output force, are defined as an integrated compound real-time variety. Subsequently, they are written into a differential equation with characteristics of the minimum system to augment the state equation of the semi-active suspension system. The augmented Kalman estimator is constructed to estimate the abovementioned compound real-time variety. To calculate an acceptable time-delay compensation predictive control force, an equivalent operation is implemented beforehand in the suspension comprehensive performance index by replacing a part of the squared time-delay control force with the corresponding predictive control force. Simulation results verify the effectiveness of the proposed augmented Kalman estimator, and the newly developed ERBTS-LQG controller almost achieves control effectiveness of the ideal time delay free semi-active suspension.

Design of Optimal FOPI Controller for Two-Area Time-Delayed Load Frequency Control System with Demand Response

Design of Optimal FOPI Controller for Two-Area Time-Delayed Load Frequency Control System with Demand Response

Fuzzy-based adaptive control method for automatic mooring systems

An automatic mooring system is not only safer and more economical than a traditional mooring system with ropes but also significantly reduces the mooring time. In this paper, we propose an automatic mooring system designed to securely berth vessels entering a port, along with an efficient control method aimed at constraining vessel movement within a specific range. To assess the operational range and control performance of the proposed system in a marine environment, a dynamic analysis program was employed to create a simulator. The simulator incorporated a parallel structured Stewart platform to replicate the 6-DOF motion of a marine vessel. The proposed automatic mooring system controller regulates the position using a time-delay controller (TDC). TDC has proven to be excellent for effectively predicting system uncertainty and handling changes in system dynamics. However, given the unpredictable nature of extreme disturbances in marine environments, it is essential to adaptively modify the control parameters to ensure optimal performance. The method presented in this paper employs a fuzzy logic controller (FLC) to dynamically adjust the control parameters of the TDC, enabling effective adaptation to rapidly changing marine conditions, including waves and wind.

Small-Signal Stability of Hybrid Inverters with Grid-Following and Grid-Forming Controls

In the modern power grid, characterized by the increased penetration of power electronics and extensive utilization of renewable energy, inverter-based power plants play a pivotal role as the principal interface of renewable energy sources (RESs) and the grid. Considering the stability characteristics of grid-following (GFL) inverters when the grid is relatively weak, the application of grid-forming (GFM) controls becomes imperative in enhancing the stability of the entire power plant. Thus, there is an urgent need for suitable and effective models to study the interaction and stability of the paralleled inverters employing GFL and GFM controls. Thus, the small-signal modeling with full-order state-space model and eigenvalues analysis are presented in this paper. First, the small-signal state-space model of the individual GFL and GFM inverters is obtained, considering the control loop, interaction, reference frame, transmissions, and time delays. Then, the models of the individual inverter are extended to the hybrid inverters to study the effects of the GFM inverters on the small-signal stability of the entire system. And the impacts of the inertia and damping are analyzed by the eigenvalues of the state-transition matrix. A case comprising three parallel GFL inverters and two GFL inverters with one GFM inverter, respectively, are studied to examine the effectiveness and accuracy of the model. Finally, the stability margin obtained from the eigenvalue analysis of the entire system is verified by time-domain simulations.

Sequential time scaling transformation technique for time-delay optimal control problem

The time-scaling transformation technique used within the computational framework of control parameterization serves as an effective method for the optimization of control switching time as well as the control value for time-delay optimal control problems. However, the conventional time-scaling transformation stipulates that the switching times for all control components must be identical, which may not be feasible in real-world scenarios. To address this limitation, we introduce the sequential time-scaling transformation technique for solving time-delay optimal control problems. By sequentially applying control parameterization and time-scaling transformation to each of the control variable, the new technique enables the configuration of a varying number of segments for the control, and the switching time for each control component can be adaptively selected. Numerical results demonstrate that our approach not only achieves superior cost performance but also offers enhanced flexibility in control strategy.