Time-delayed Control Research Articles

A novel TDE error compensation method based on manipulator time-delay control

A novel TDE error compensation method based on manipulator time-delay control

Vibration suppression of suspended cables with three-to-one internal resonances via time-delay feedback

Based on the time-delay feedback control, the vibration suppression of suspended cables with three-to-one internal resonances are investigated. Initially, the nonlinear differential equation of motion for a suspended cable under time-delay feedback control is considered, and a discrete model is derived using the Galerkin method. Subsequently, the method of multiple scales is employed to perturbatively solve the discrete time-delay differential equation, determining the modulation equations around the first primary resonance. Steady-state and periodic solutions of the modulation equations are detected numerically. Numerical results indicate that the internal resonance enhances the nonlinear dynamical complexity of the controlled suspended cable. It is observed that the time delay and control gain affect the controlled system: in particular, an increase in control gain leads to a reduction in response amplitude. By adjusting the time delay and control gain, the critical excitation can be altered, an aspect that could be very useful from a pratical point of view. This research sheds light on the intricate dynamics of suspended cable and provides a theoretical foundation for designing more effective control strategies in engineering applications.

Chaotic band-gap modulation mechanism for nonlinear vibration isolation systems based on time-delay feedback control

Abstract Systems designed for nonlinear vibration isolation that incorporate chaotic states demonstrate superior capabilities in vibration attenuation, adeptly modulating the spectral constituents of vibrational noise. Yet, the challenge of eliciting low-amplitude chaotic dynamics and perpetuating these states across a diverse array of parameters remains formidable. This study proposes a pioneering strategy and technique for modulating the chaos band by incorporating a time-delayed feedback control mechanism within the framework of nonlinear vibration isolation systems.The investigation commences with an exhaustive analysis of the nonlinear dynamics, shedding light on the principles dictating the evolution of chaos. The study then advances to scrutinize the dynamics of systems with delays to elucidate the chaos-inducing processes engendered by feedback with temporal lags. Building upon the system’s responses, the chaotic performance and the effectiveness of the vibration isolation are crafted. Consequently, the time-delayed feedback control parameters are identified as pivotal design variables, which are then employed to dissect the control mechanisms influenced by the time-delayed feedback on the chaos band. Utilizing the delineated control mechanism, the nonlinear vibration isolation system is precipitously transitioned from a state of stable periodicity to one of chaos, fostering low-amplitude chaotic dynamics across an expansive parameter space, and in turn, resolving the previously stated challenge. Perhaps most significantly, the mechanism for attaining low-amplitude chaos introduced here paves the way for innovative methodologies in the active vibration isolation design of similar systems. Furthermore, it is anticipated to yield theoretical guidance for the manipulation of chaos bands and the formulation of active vibration isolation strategies within the domain of nonlinear vibration isolation systems.

An Adaptive Sliding Mode Control Using a Novel Adaptive Law Based on Quasi-Convex Functions and Average Sliding Variables for Robot Manipulators

This paper proposes a novel adaptive law that uses a quasi-convex function and a novel sliding variable in an adaptive sliding mode control (ASMC) scheme for robot manipulators. Since the dynamic equations of robot manipulators inevitably include model uncertainties and disturbances, time-delay estimation (TDE) errors occur when using the time-delay control (TDC) approach. Further, the ASMC method used to compensate for TDE errors naturally causes a chattering phenomenon. To improve tracking performance while reducing or maintaining chattering, this paper proposes an adaptive law based on a quasi-convex function that is convex at the origin and concave at the gain switching point, respectively. We also adopt a novel sliding variable that uses previously sampled tracking errors and their time derivatives. Further, this paper proves that the sliding variable of the robot manipulator controlled by the proposed ASMC satisfies uniformly ultimately bounded stability. The simulation and experimental results illustrate the effectiveness of the proposed methods in terms of tracking performance.

Time-delay feedback control on vertical vibration of maglev train under unsteady aerodynamic force

The stability and safety of maglev trains are significantly affected by unsteady aerodynamic forces during high-speed operation. In this paper, we employ a time-delay feedback control strategy to suppress the nonlinear vertical vibrations of maglev train under periodic unsteady aerodynamic force. Firstly, the amplitude-frequency response equation of the maglev vehicle is derived using the multiple scales method, and the stability of the steady-state solutions is determined. Then, the influences of velocity feedback gain coefficient and velocity time delay on the nonlinear vibrations of the maglev vehicle are investigated. The optimal value range of the time delay is identified. The results demonstrate that the time delay feedback control can effectively suppress the nonlinear vibration of maglev vehicles and enhance their operational stability under the premise of reasonable selection of time delay parameters. The theoretical research presented in this paper can serve as a theoretical reference for the design, improvement, and optimization of control systems for high-speed maglev trains.

Vibration control of nonlinear viscoelastic systems with displacement delay feedback

In this study, the nonlinear vibration characteristics of a nonlinear Zener model under harmonic excitation, equipped with linear and nonlinear displacement delay feedback control, were investigated. The amplitude–frequency curve of the system’s main resonance was computed using the multi-scale method. Stability conditions for the system were then established based on the Lyapunov stability theory. The influence of several parameters on the system’s dynamic behavior was also analyzed, including time delay, displacement feedback gain coefficient, nonlinear term coefficient, damping coefficient, and external excitation. The findings revealed that the nonlinear displacement feedback gain coefficient was observed to exert a more substantial effect on the system’s amplitude than other factors. Further, the nonlinear displacement delay feedback gain coefficient and time-delay value diminish the amplitude of the vibration, leading all solutions to achieve a stable state. In instances with time-delay control, the impact of the main system parameters on system vibration was significantly diminished. The aim of this study is to provide a theoretical basis for the implementation of displacement delay controllers in nonlinear viscoelastic systems.

A comprehensive control paradigm for prescribed performance attainment in complex nonlinear systems

This paper presents a comprehensive control framework tailored for achieving Prescribed Performance Control (PPC) in the context of complex nonlinear systems, addressing multifaceted challenges prevalent in control design. The focus is on a control scenario characterized by the simultaneous presence of nonlinearity, external disturbances, time delay, and unknown control direction—issues that pose considerable obstacles for existing solutions. To surmount these challenges, our proposed approach integrates well-established techniques, including neural networks, Nussbaum-type gains, and adaptive control strategies within a unified control design framework. The specific technical challenge addressed in this work involves the effective management of these intricate complexities in Single-Input Single-Output (SISO) systems. Our contributions extend the theoretical foundations, presenting an ideal PPC control design and introducing two adaptive neural network-based control methods capable of accommodating both known and unknown control directions. Utilizing Lyapunov–Krasovskii functionals, we showcase a unique integration that surpasses a mere combination of individual techniques. This work advances the theoretical underpinnings of control engineering tailored for real-world scenarios. The proposed controller’s efficacy is validated through rigorous simulations and compared with recent results and benchmark PPC controllers, establishing its superiority in addressing the intricacies of complex control scenarios.

Time-Delay Sliding Mode Control for Trajectory Tracking of Robot Manipulators

Time-Delay Sliding Mode Control for Trajectory Tracking of Robot Manipulators

Cartesian Time-delayed Control to Improve Hybrid Force Control Performance of Robot Manipulators Under Uncertain Environment and Unknown Dynamics

Cartesian Time-delayed Control to Improve Hybrid Force Control Performance of Robot Manipulators Under Uncertain Environment and Unknown Dynamics

A new model reduction method based PBC control for grid-connected inverter with LCL-filter

Passivity-based control (PBC) exhibits robustness against parameters shift, providing a substantial level of stability. However, for the LCL-filtered grid-connected inverter (GCI), the conventional PBC (called C-PBC) controller has a narrow control bandwidth due to the control time delay, resulting in poor dynamic performance, especially in the weak grid state. This paper proposes a new PBC (called P-PBC) method to increase the closed-loop bandwidth of the system by setting an appropriate feedback proportional coefficient between the grid-side current and the inverter-side current. By extending the closed-loop bandwidth of the system, the proposed P-PBC method offers improved dynamic performance, particularly in challenging grid conditions. In addition, a state observer is also employed to reduce sensors, which saves costs and enhances the system's reliability. A 110 V/50 Hz/3 kW/3-phase experimental setup has been developed using the dSPACE DS1202 platform to validate the effectiveness of the proposed control method.

Wave attenuation in a metamaterial beam with time delay control

Wave attenuation in a metamaterial beam with time delay control

Time-delay feedback control of nonlinear forced vibration of graphene/piezoelectric sandwich nanoplates under a mechanical shock

In this study, the nonlinear forced vibration of graphene/piezoelectric sandwich nanosheets under mechanical impact was investigated. For the first time, linear (displacement and velocity) and nonlinear (displacement) time-delay proportional derivative (PD) controllers were applied to graphene/piezoelectric sandwich nanosheets, and the primary/secondary resonance under different time-delay parameters were analyzed. An approximate analytical solution for the nonlinear forced vibration control equation was obtained using the multiple scale perturbation method, and the stability of graphene/piezoelectric sandwich nanosheets under primary/secondary resonance conditions was discussed using the Ross Herwitz theorem. Finally, the results of this study were compared with those of other studies. The feasibility of the research methodology was demonstrated. On this basis, the research results indicate that linear displacement delay, nonlinear displacement delay, and velocity delay parameters can suppress the unsteady vibration characteristics of the main system. And comparing the linear and nonlinear displacement time-delay, it is found that the nonlinear displacement time-delay has a greater effect on the system. Specifically, the presence of nonlinear displacement time-delay changes the vibration characteristics of the curve from hard spring characteristics to soft spring characteristics. Comparison of displacement time-delay and velocity time-delay reveals that velocity time-delay gives better control over the system. In addition, the results show that the excitation amplitude, nonlocal parameters, and external voltage enhance the nonlinear characteristics of the system under the main and superharmonic resonance conditions before the time-delay control. Subharmonic resonance conditions, the system parameters make the vibration range wider. After the time-delay control, the influence of these three factors on the system vibration is significantly reduced for the three resonance conditions, especially for the non-local parameters. The results of the study can provide guidance for active control of time delay in different types of nanodevices for engineering applications.

Dynamic impact analysis of the time-delay levitation control system on maglev vehicle system after adding smith predictor

The time delay (TD) in the levitation control system significantly affects the dynamic performance of the closed-loop system in electromagnetic suspension (EMS) maglev vehicles. Excessive TD can cause levitation instability, making it essential to explore effective mitigation methods. To address this issue, a Smith Predictor (SP) is integrated into the traditional PID levitation control system. The combination of theoretical analysis and numerical simulation is employed to assess the stability of the time-delay levitation control system after the integration of the Smith Predictor. Theoretical analysis reveals that when TD exceeds a critical threshold, the levitation system becomes unstable. The addition of SP alters the root trajectory of the system characteristic equation from positive to negative, and recovers the levitation system to stable status. Assuming complete knowledge of the dynamic system, the TD compensation value in the SP becomes a key parameter that determines its performance. A minimum effective value (MEV) for TD compensation is identified, correlating with the system's stability region. Under the influence of TD, more complex systems and higher running speeds of the maglev vehicle lead to a narrower stable region and a larger MEV for TD compensation. Given the simulation parameters in this paper, with a system TD of 15 ms and a maximum vehicle speed of 160 km/h, the MEV for TD compensation in the SP should be set at 12 ms.

A class of nonlinear ship stability analysis: Stochastic dynamics with time-delayed control in crosswind and wave conditions

The impact of ocean waves and crosswinds on ships has long been a focal point of research for many scholars. This paper proposes a stochastic ship rolling model influenced by crosswinds, ocean waves, and time delays. The safe operating region for ship navigation is presented through the phase space of the system. A quantitative discussion of the system is conducted using the stochastic Melnikov function, and the stochastic P-D bifurcation of the system is discussed using topological data analysis techniques. The research indicates that incorporating time delay feedback can effectively enhance the system’s stability.

Research on time-delayed vibration reduction control of 1/4 vehicle semi-active suspension system with three degrees of freedom

Research on time-delayed vibration reduction control of 1/4 vehicle semi-active suspension system with three degrees of freedom

Calculation method of renewable maximum penetration considering frequency response of renewable energy

The calculation of maximum penetration is crucial for planning renewable energy integration and ensuring the safe operation of power systems. This paper proposes a method for calculating maximum penetration under kinetic energy constraints. In scenarios where renewable energy lacks additional frequency control, we construct a frequency response model to reveal the energy change mechanism during active disturbances. By converting the frequency constraint into a kinetic energy constraint, we derive an analytical expression for maximum penetration under these constraints. Key influencing factors were quantitatively analyzed, revealing nonlinear relationships between system capacity, frequency constraints, and maximum penetration, while also calculating the minimum operational generator capacity. When renewable energy participates in frequency control, its frequency regulation can significantly enhance maximum penetration. However, frequency oscillations caused by time delays in current source frequency control become the primary constraint. The proposed method and conclusions are validated using actual sending-end and receiving-end grid data, providing valuable guidance for grid operation planning.

Analytical design of modified Smith predictor for second-order stable time delay plants incorporating a zero

Simplified control tuning not only enhances engineers' proficiency in control theory and its application but also contributes to their skill development. This study focuses on the control of stable second-order plus time delay (SOPTD) plants incorporating a zero, by employing a modified Smith predictor structure. A forward path PID controller and a PID controller with a lead/lag filter in the feedback path contribute to the proposed control system. The PID controller determines the set-point tracking. The load disturbance rejection is influenced by both the PID and lead/lag filter. Each controller is simply designed using pole placement, while considering a tuning parameter to make a balance between performance and robustness. Filtering of the set-point signal is implemented to enhance its response. To assess the effectiveness of the proposed technique, the study involves examining a SOPTD plant and either a negative or a positive zero. Simulation and comparison analysis show that the proposed controller is appropriate for industrial usage since it quickly tracks the set-point and efficiently rejects disturbances, resulting in a smooth control signal. Furthermore, robustness tests reveal its satisfactory degree of robustness against model parameter uncertainties. In summary, the proposed approach is straightforward and outperforms recently published design methodologies in terms of both performance and robustness.

Disturbance rejection analysis of singular time-delay systems based on state decomposition method

The state decomposition technique (SDT) based on memory state-feedback control (MSFC) is used in this article to provide a new disturbance-rejection (DR) method for singular time-delay systems (STSs). First, under MSFC, a singular time-delay control system with disturbance estimator is constructed. Then, a DR control law, which contains disturbance information and MSFC, is designed. Second, the STS is split into algebraic and differential subsystems based on the SDT. Next, a brand-new enhanced Lyapunov–Krasovskii function (LKF) with fewer state vectors is designed. Additionally, a new delay-dependent admissible criterion with fewer decision variables is obtained based on the LKF by combining a Jensen inequality and two zero equations. Third, the controller is designed according to the decomposition component of the controller gain. Finally, the usefulness and efficiency of the strategy are demonstrated by comparing it to a sliding mode control and a traditional control technique.

Dynamic response and stability analysis of vehicle systems with double time-delay feedback control

In this paper, the vehicle suspension dynamic response of time delay feedback control is analyzed considering the suspension of the seat. An active suspension vibration reduction control method based on double time-delay feedback control is proposed to further improve the ride comfort. Firstly, the double time-delay dynamic response equation of the system with three degrees of freedom is established. Then, the root mean square values of seat acceleration and body acceleration are used as the objective functions. Meanwhile, the RMS values of suspension dynamic deflection and tire dynamic displacement are used as constraints, and the optimal feedback parameters are obtained using particle swarm optimisation. The Routh-Hurwitz criterion and frequency domain scanning methods are used to verify the stability of the double time-delay system. Finally, simulation in the time domain and frequency domain is accomplished. It is verified that this feedback control method has strong robustness and anti-interference ability.

Adaptive control for a class of stochastic nonlinear time-delay systems with unknown control coefficients

This paper mainly investigates the adaptive state feedback control problem for a class of stochastic nonlinear systems with time-delay and unknown control coefficients. The proposed control scheme leverages the dynamic gain technology and Nussbaum function to develop a state feedback controller, aiming to simplify its implementation and eliminate the influence of unidentified time-varying control coefficients. Through the utilization of suitable Lyapunov–Krasovskii (L–K) functionals and stochastic stability theories, it is demonstrated that the designed control mechanism guarantees the boundedness in probability for all closed-loop signals, ultimately regulating the state of the plant to zero. The availability and superiority of the developed adaptive management strategy are further certified through simulation results.