Time-delayed Control Research Articles

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.

Nonlinear dynamic and time-delay vibration control of axially moving shape memory alloy plate immersed in fluid

Nonlinear dynamic and time-delay vibration control of axially moving shape memory alloy plate immersed in fluid

The Complexities in the R&D Competition Model with Spillover Effects in the Supply Chain

This study aims to investigate the research and development (R&D) competition within the supply chain, focusing on two aspects: R&D competition at the manufacturing level and competition in pricing strategies. This paper establishes a dynamic game model of R&D competition, comprising two manufacturers and two retailers, with both manufacturers exhibiting bounded rationality. The key findings are as follows: (1) an increase in the adjustment speed positively affects the chaotic nature of the R&D competition system, leading to a state of disorder. This chaotic state has adverse implications for manufacturing profitability. (2) The spillover effect exhibits a positive relationship with the level of chaos in the R&D competition system. A greater spillover effect contributes to a more turbulent environment, which subsequently impacts the profitability of manufacturers. (3) R&D cost parameters exert a positive influence on the stability of the R&D competition system. When the system reaches a state of equilibrium, an escalation in the R&D cost parameters poses a threat to manufacturer profitability. (4) Retailer costs play a detrimental role in the stability of the R&D competition system. As retailer costs increase, there is a decline in R&D levels, thereby diminishing manufacturer profitability. (5) To mitigate the chaotic state, we propose the implementation of the time-delayed feedback control (TDFC) method, which reflects a more stable state in the R&D competition system.

Time-delay feedback control of a suspended cable driven by subharmonic and superharmonic resonance

The longitudinal time-delay feedback control strategy is implemented to suppress the subharmonic and superharmonic responses of the suspended cable. Formulated based on the Hamilton variational principle and the longitudinal time-delay feedback strategy, the in-plane nonlinear differential equations for a suspended cable are formulated, and Galerkin method is utilized to transform the equations into delayed differential equations. By using the method of multiple scales, approximate solutions for the 1/2-subharmonic and second-order superharmonic resonance responses of the controlled suspended cable were derived. The effects of the time delay and control gain are obtained through numerical examples. The research results demonstrate that through the adjustment of control gain and time delay, resonance regions can be avoided, effectively suppressing large-amplitude vibrations in the suspended cable, thereby achieving favorable control performance.

Mobility, response and transport in non-equilibrium coarse-grained models

We investigate two different types of non-Markovian coarse-grained models extracted from a linear, non-equilibrium microscopic system, featuring a tagged particle coupled to underdamped oscillators. The first model is obtained by analytically ‘integrating out’ the oscillators and the second is based on a derivation using projection operator techniques. We observe that these two models behave very differently when the tagged particle is exposed to external harmonic potentials or pulling forces. Most importantly, we find that the analytic model has a well defined friction kernel and can be used to extract work, consistent with the microscopic system, while the projection model corresponds to an effective equilibrium model, which cannot be used to extract work. We apply the analysis to two popular non-equilibrium systems, time-delay feedback control and the active Ornstein–Uhlenbeck process. Finally, we highlight that our study could have important consequences for dynamic coarse-graining of non-equilibrium systems going far beyond the linear systems investigated in this manuscript.

Adaptive fuzzy event-triggered cooperative control for fractional-order delayed multi-agent systems with unknown control direction

In this paper, the cooperative control of fractional-order multi-agent systems with time delay and unknown control direction is studied by combining frequency distributed model and event-triggered mechanism. The Nussbaum function is employed to address the unmeasured control direction. Then, through the event-triggered mechanism, a corresponding controller is designed, which can guarantee that all signals are bounded while saving resources. The proposed theme is convenient for analyzing the stability of fractional-order systems based on a transformation of frequency distributed model. In particular, in order to enhance the universality of the proposed scheme in the fractional-order system stability analysis, a generalized fractional-order generalized lemma with respect to the Nussbaum function is given. Finally, the availability of the proposed method is confirmed by a simulation example.

Fractional order time-delayed feedback control of hysteresis dynamics in giant magnetostrictive actuators

Fractional order time-delayed feedback control of hysteresis dynamics in giant magnetostrictive actuators

Disturbance observer-based sliding mode control of active vertical suspension for high-speed rail vehicles

Disturbance observer-based sliding mode control (SMC) on the active vertical suspension (AVS) is developed to suppress the car body’s rigid and flexible vibration to improve ride comfort for a high-speed rail vehicle. A vertical-dynamics-intended vehicle model is foremost built with the bounce, pitch, and bending mode of the car body involved. Two sliding surfaces and disturbance observers are then designed for SMC, which only require the car body states, obviating the bogies’ states. The observer is successful in estimating the effect of unknown track irregularities perturbation as well as externally straightforwardly excitations on the car body with good accuracy. Control efficacy is verified through comparison with passive cases and sky-hook controls. With modal damping below 2% in passive cases, the mode shape function, especially with large displacement at the suspension support, would enlarge the car body acceleration. Moreover, the longitudinal traction rod can significantly multiply the flexible vibration at certain speeds. Comparative studies indicate that SMC provides satisfactory outcomes in the rigid and bending vibration suppression when all the car body’s three modes are considered in the sliding surface. However, it requires a high-frequency response actuator and allows a tighter tolerance of the control time delay than the sky-hook control.

Reachable Set Estimation and Controller Design for Linear Time-Delayed Control System with Disturbances

This paper investigates reachable set estimation and state-feedback controller design for linear time-delay control systems with bounded disturbances. By constructing an appropriate Lyapunov–Krasovskii functional, we obtain a delay-dependent condition, which determines the admissible bounding ellipsoid for the reachable set of the system we considered. Then, a sufficient condition in the form of liner matrix inequalities is given to solve the problem of controller design and reachable set estimation. Then, by minimizing the volume of the ellipsoid and solving the liner matrix inequality, we obtain the desired ellipsoid and controller gain. A comparative numerical example is given to show the effectiveness of our result.

Reinforcement Learning-Based Control of DC-DC Buck Converter Considering Controller Time Delay

Reinforcement Learning-Based Control of DC-DC Buck Converter Considering Controller Time Delay

Time-delayed feedback control for chaotic systems with coexisting attractors

<abstract><p>This study investigated the Hopf bifurcation of the equilibrium point of chaotic systems with coexisting attractors under the time-delayed feedback control. First, the equilibrium point and Hopf bifurcation of chaotic systems with coexisting attractors were analyzed. Second, the chaotic systems were controlled by time-delayed feedback, the transversality condition of Hopf bifurcation at the equilibrium point was discussed, and the time-delayed value of Hopf bifurcation at the equilibrium point was obtained. Lastly, the correctness of the theoretical analysis was verified by using the numerical results.</p></abstract>

Resonance analysis and time-delay feedback controllability for a fractional horizontal nonlinear roller system

<p>In this paper, we investigated the nonlinear vibration characteristics and time-delay feedback controllability of a fractional horizontal roll system, which is described by a fractional Duffing-van der Pol oscillator under an external harmonic excitation. We focused on the resonance of fractional roller systems and conducted corresponding vibration control. The amplitude-frequency equations of primary resonance and superharmonic resonance were obtained using the multiple scale method. The amplitude-frequency characteristic curves of the system with different parameters were presented, and the influence of system parameters on the curves was analyzed. In addition, the time-delay feedback controller was designed to control the parameter excitation vibration. The numerical simulation results have verified the effectiveness of the time-delay controller in eliminating the jumping and hysteresis phenomena of the rolling system. The comparisons of approximate analytical solution and numerical solution was fulfilled, and the result certifies the correctness and satisfactory precision of the approximately analytical solution. The analysis results provide certain theoretical guidance for the vibration reduction of the horizontal nonlinear roller system.</p>

Spectral Design and Experimental Validation of Noncollocated Vibration Suppression by a Delayed Resonator and Time-Delay Controller

Spectral Design and Experimental Validation of Noncollocated Vibration Suppression by a Delayed Resonator and Time-Delay Controller

Time-delay Feedback Control of Fractional Chaotic Rössler Oscillator

In this research, we explore the utilization of the time-delayed feedback method to stabilize unstable steady states and aperiodic orbits within the chaotic fractional-order Rössler Oscillator. Employing the time-delay feedback control algorithm, we identify specific parameter ranges enabling the successful stabilization of unstable equilibria, considering variations in both feedback gain and time delay. Unlike previous research works where Caputo and Riemann-Liouville characterization of fractional derivatives are used, we are using Grünwald-Letnikov (GL) characterization because of its simplicity and ease of implementation and demonstrating the stability using the analytical and numerical analysis and plots of eigenvalues. Additionally, our analysis highlight the effectiveness of a sinusoidally modulated time delay in the control law, significantly expanding the stability region of steady states beyond the capabilities of the traditional time-delayed feedback scheme with a constant delay. Furthermore, the analysis of eigenvalues before and after applying the control strategy offers tangible insights into the system's stability dynamics.

Absolute stability of time-delayed Lurie direct control systems with unbounded coefficients

Absolute stability of time-delayed Lurie direct control systems with unbounded coefficients

Time-delayed control of a nonlinear self-excited structure driven by simultaneous primary and 1:1 internal resonance: analytical and numerical investigation

<p>Main objective of this research to eliminate the resonant vibrations and stabilize the unstable motion of a self-excited structure through the implementation of an innovative active control strategy. The control strategy coupling the self-excited structure with a second-order filter, which feedback gain $ \lambda $ and control gain $ \beta $, as well as a first-order filter, which feedback gain $ \delta $ and control gain $ \gamma $. The coupling of the second-order filter to establish an energy bridge between the structure and the filter to pump out the structure's vibration energy to the filter. In contrast, the primary purpose of coupling the first-order filter to stabilize the closed loop by adjusting the damping of the system using the control keys $ \delta $ and $ \gamma $. Accordingly, the mathematical model of the proposed control system formulated, incorporating the closed-loop time delay $ \tau $. An analytical solution for the system model obtained, and a nonlinear algebraic system for the steady-state dynamics of the controlled structure extracted. The system's bifurcation characteristics analyzed in the form of stability charts and response curves. Additionally, the system's full response simulated numerically. Findings the high performance of the introduced controller in eliminating the structure's resonant vibrations and stabilizing non-resonant unstable motion. In addition, analytical and numerical investigations revealed that the frequency band within which the second-order filter can absorb the structure's resonant oscillation relies on the algebraic product of $ \beta $ and $ \lambda $. Furthermore, it was found that the equivalent damping of the system depends on the algebraic product of $ \gamma $ and $ \delta $, which can be employed to stabilize the negatively damped self-excited systems. Finally, it reported that although the loop delay can potentially degrade vibration control performance, the time-delay stability margin is nonlinearly proportional to the product of $ \gamma $ and $ \delta $. This finding that increasing the value of $ \gamma \times \delta $ can compensate for the adverse effects of loop delay on both system stability and vibration suppression efficiency.</p>

Handheld motorized injection system with fiber-optic distance sensors and adaptive time-delay controller

During the last decade, many ophthalmic therapeutic drugs have been clinically approved, and intraocular injection has been a common surgical intervention. Injecting drugs directly into the subretinal space is crucial to treat retinal complications effectively. Here, we report a handheld microinjector with two fiber-optic distance sensors and time-delay control (TDC) to mitigate nonlinear disturbances during the injection task. The conventional method exhibited a cosine error of approximately 77 μm at an angle of 45°, whereas our proposed needle reduced measurement errors to ∼6 μm. Also, TDC-based position regulation is designed to adaptively apply motor inputs by estimating disturbances during the handheld task and achieving fast system responses with minor control errors. Phantom studies show a maximum reduction of 26.5% in root-mean-square error (RMSE) compared to the existing approach. Moreover, ex-vivo experiments demonstrated superior and robust injection performance, resulting in an injection RMSE of 10.3 μm.

Active vibration hybrid control strategy based on multi-DOFs piezoelectric platform

With the increasing requirements for vibration isolation in multiple degrees of freedom (multi-DOFs), active control strategy is becoming more meaningful. However, the vibration isolation performance is limited by the time delay of feedback control, and cannot meet higher requirements. Therefore, this paper proposes a multi-DOFs active vibration hybrid control (AVHC) strategy based on a piezoelectric platform. The AVHC integrates the adaptive feedforward control based on the modified recursive least squares (MRLS) algorithm, and the feedback control based on the integral force feedback (IFF) algorithm. To achieve advanced response, the ground-based vibration signal is offset by the MRLS algorithm. To further reduce the coupling of multi-DOFs, the feedback and feedforward coordinates are fused through the matrix transformation, and the signals are linearly superimposed by the AVHC. The experimental results show that the AVHC can further reduce the resonance peaks of the three translational directions ( X/ Y/ Z) compared with the feedback (FB) control. The resonance peaks are reduced from 14.6 dB (FB) to 3.11 dB (AVHC), from 14.56 dB (FB) to 5.14 dB (AVHC), and from 12.44 dB (FB) to 3.78 dB (AVHC) in X/ Y/ Z directions, respectively. The attenuation rates are improved by 73.36%, 66.19%, and 63.10% in X/ Y/ Z directions, respectively.

Analysis of stability, energy consumption and [formula omitted] emissions in novel discrete-time car-following model with time delay under V2V environment

This article aims to explore the stability, energy consumption and CO2 emissions of a novel discrete car-following model with time delay. Under the assumption that the preceding two successive vehicles can realize the communication through V2V (Vehicle to Vehicle) communication environment. Moreover, the time-delayed average optimal velocity difference control scheme is also considered. Based on the proposed discrete car-following model, error dynamical system is formulated and asymptotic stability is developed. The sufficient condition for the time-delayed average optimal velocity difference control scheme of the discrete car-following model with time delay is obtained, the asymptotic stability is ensured. In addition, numerical simulations are constructed and further illustrated the cooperative driving by V2V communication can improve stability, reduce energy consumption and CO2 emissions of traffic system. Moreover, the time-delayed average optimal velocity control scheme is also conductive to improve stability, reduce energy consumption and CO2 emissions of traffic system.

Time-Delay Control Scheme with Adaptive Fixed-Time Convergent Super-Twisting Fractional-Order Nonsingular Terminal Sliding Mode for Piezoelectric Displacement Amplifier

Piezoelectric displacement amplifiers (PDAs) have been widely used in precision positioning fields. However, the inherent hysteresis and creep nonlinear effect of piezoelectric actuators (PEAs) and time-varying lumped disturbances bring extreme challenges to the precise motion control of PDAs. Although various control schemes based on PEAs have been developed and have shown significant results. However, due to the high sensitivity of precision positioning to environmental variations, the development and identification of accurate models and the control timeliness often become obstacles in engineering. To realize precise motion control of PDAs under complex lumped disturbances, a new time-delay control scheme (AFSTA-FONTSM) using an adaptive fixed-time convergent super-twisting algorithm (AFSTA) and a fractional-order nonsingular terminal sliding mode (FONTSM) is proposed. Specifically, the time-delay information obtained by time-delay estimation technology is used to estimate the lumped dynamic characteristic of the system, thus establishing a simple control framework without a system dynamic model. FONSTM is constructed as a sliding mode manifold, and satisfactory error dynamic characteristic is obtained. A new AFSTA is designed as the reaching law in the sliding mode phase. AFSTA has fixed-time convergence when the upper bound of lumped disturbances exists, which ensures the control timeliness. Benefiting from the newly designed adaptive algorithm, the upper bound value of lumped disturbances is no longer needed to determine the control gains, which effectively prevents overestimation of the control gains. Correspondingly, the convergence time of AFSTA is estimated, and the stability of the closed-loop system is analyzed by the Lyapunov theory. Three existing time-delay control schemes, namely MSTA-FONTSM, AMSTA-FONTSM, and ASTA-FONTSM are selected, and four scenes are designed for comparative experiments. The experimental results show that MSTA-FONTSM has the worst control performance among the four control schemes. For the step, and continuous cosine trajectories with periods of T=1s and T=2s, the root-mean-square error of the proposed AFSTA-FONTSM is reduced by 56.86%, 54.03%, and 50.24% compared with MSTA-FONTSM. For disturbance experiments under different loads, the control performance of the proposed AFSTA-FONTSM is still superior to the other three control schemes without load.