Time-delayed Control Research Articles

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.

Short remarks on the paper: A novel methodology for a time-delayed controller to prevent nonlinear system oscillations

In this brief communication, we highlight several critical inaccuracies in the paper entitled “A novel methodology for a time-delayed controller to prevent nonlinear system oscillations,” identified by the DOI: 10.1177/14613484231195276. The core of the non-perturbative approach discussed in this paper is the introduction of a trial solution with an indeterminate nonlinear frequency. We elucidate the technical missteps and provide necessary corrections. The scrutinized article presents ample opportunities for enhancement, and we propose several amendments. Additionally, we reveal that the numerical outcomes showcased in the mentioned paper expose deficiencies in the proposed approximate solution. With the amendments implemented herein, a more precise numerical solution is achieved.

Analysis of vibration characteristics of face gear powering-split transmission system

A nonlinear dynamic model of the face gear powering-split transmission system was established, and the nonlinear dynamic characteristics of the face gear powering-split transmission system were studied by considering various factors such as support stiffness, time-varying meshing stiffness, lateral clearance of teeth, comprehensive transmission error and bearing stiffness. The Runge–Kutta integral method is used to solve the differential dynamics of the system. The nonlinear behavior of the system is described by the phase plane diagram, time history diagram, frequency domain diagram, and Poincare section diagram. The influence of external excitation frequency on the nonlinear behavior of the system is described by the bifurcation diagram. In addition, the multi-scale method is used to analyze the superharmonic resonance of the system and determine the stability conditions of the superharmonic resonance of the system. The influence of meshing damping, time-varying meshing stiffness, and time-delay control parameters on the amplitude-frequency characteristics of the system is studied by numerical analysis of the superharmonic resonance. The results show that the system will show periodic chaotic alternating motion characteristics under external excitation. Selecting meshing damping, meshing stiffness, and time delay control parameters in a reasonable range can effectively reduce the superharmonic co-amplitude and keep the system in a stable state.

A Class of Parameter Interpolation Iteration Algorithm based on Clem- Equations

The Newdon Iterative method and its deformation mostly require calculating the derivative of nonlinear equations. In practice, many functions are complex, and there are limitations in finding high-order derivatives. This paper fits an existing iterative format by establishing n times interpolated polynomials, n conditions are used to construct a system of linear equations with n equations and n + 1 unknowns, in which the previous n unknowns can be expressed by the n + 1 th unknown by Clem’s rule, to achieve the purpose of reducing the number of derivative calculations. Convergence analysis and numerical examples verify that the algorithm is better than Newdon iteration, and can be better used in path trajectory optimization and fractional time delay control.

Time-delayed Feedback Control of Chaotic Systems Based on Fractional Order Integration

Time-delayed Feedback Control of Chaotic Systems Based on Fractional Order Integration

Effects of global warming, time delay and chaos control on the dynamics of a chaotic atmospheric propagation model within the frame of Caputo fractional operator

The Lorenz-84 climate model is a simplified mathematical model that describes the chaotic behavior of atmospheric convection and its impact on global climate patterns. It captures the presence of chaotic behavior in the motion of westerly wind and helps understand the concept of sensitivity to initial conditions. But as observed over the years, the westerlies are gaining more strength due to the rise in atmospheric temperature. In this work, we have modified the old model to observe the changes in the behavior of the system due to global warming and time delay. The modified model has been generalized using Caputo fractional derivative to provide a more accurate representation of the system with memory effect and non-local behavior. The stability of the new model has been tested at all the equilibrium points. Using Picard’s operator and Banach’s Fixed Point theorem, it has been shown that there exists a unique and bounded solution for the new model. It has been observed that the sole effect of global warming makes the system gradually unstable from chaotic as the fractional order α is decreased from 0.80 to 0.50. Also, a shift in the bifurcation point has been noticed for the new model. All three Lyapunov exponents have been calculated for different fractional orders to confirm the presence of chaos in the modified model as well. A chaos control law has been constructed for the modified chaotic model using the sliding mode control theory. Interestingly, the chaos disappears completely when the effect of time-delay is considered in the modified model. Since our proposed time-delayed modified model shows an asymptotically stable nature for all fractional orders α less than 0.85, it is better suited to make more accurate predictions about the strength of the westerlies.

Manipulate mechanism design and synchronous motion application for driving simulator

The manipulate load system of a helicopter driving simulator is a complex mechatronic system. To simulate the load system of the joystick more effectively, this study provides a new manipulate mechanism with automatic position reset function that integrates a spring system within the joystick. The load simulation of this manipulate mechanism can be achieved by designing the nonlinear coefficient of the spring in a reasonable manner, thereby eliminating the need for complex control of motor simulation and system time delay. This greatly simplifies the complexity of the system and effectively meets the requirements of real-time and accuracy. Initially, the new manipulate mechanism is described in detail through kinematic analysis. Then, dynamic simulation is conducted in ADAMS software to simulate the motion of the operation mechanism. Considering the active–passive relationships between the manipulate mechanism and the driving simulator, a mapping is established to achieve synchronized motion. The synchronized motion is subsequently evaluated and verified in MATLAB/Simulink. The results reveal that this new manipulate mechanism has high reliability and can effectively achieve synchronized motion with the driving simulator. The new manipulate mechanism will be useful in advancing research into the design of manipulate mechanism processes.

A data-driven optimal time-delayed control approach and its application to aerial manipulators

In this paper, a data-driven optimal time-delayed control (TDC) approach is developed for Euler–Lagrange systems and applied to an aerial manipulator. The proposed approach is able to deal with the nonlinearity and handle unmodelled dynamics, model uncertainties and unknown disturbances in Euler–Lagrange systems. The time-delayed estimation employed in the proposed approach uses the measurement information at the last time instant to approximately estimate all the unknown factors at the current time instant. A constant gain matrix is the main design parameter and influences both the closed-loop stability and the tracking performance. Currently, this constant gain matrix is either calculated by using the system model based on a stability condition or obtained by trial and error, both of which are rather time-consuming in practice. The data-driven TDC approach developed in this paper can find the constant gain matrix directly from the input and output data without any knowledge of the inertia matrix. To achieve optimal control performance, an LQR term is integrated in the data-driven design. The input-to-state stability of the closed-loop system is proven. The proposed approach is characterized by easy implementation and low computational efforts. The application to the aerial manipulator and the experiment results with a hexacopter demonstrate the effectiveness of the proposed approach.

Nonlinear dynamics near a double Hopf bifurcation for a ship model with time-delay control

Nonlinear dynamics near a double Hopf bifurcation for a ship model with time-delay control

Optimization over the Pareto front of nonconvex multi-objective optimal control problems

Simultaneous optimization of multiple objective functions results in a set of trade-off, or Pareto, solutions. Choosing a, in some sense, best solution in this set is in general a challenging task: In the case of three or more objectives the Pareto front is usually difficult to view, if not impossible, and even in the case of just two objectives constructing the whole Pareto front so as to visually inspect it might be very costly. Therefore, optimization over the Pareto (or efficient) set has been an active area of research. Although there is a wealth of literature involving finite dimensional optimization problems in this area, there is a lack of problem formulation and numerical methods for optimal control problems, except for the convex case. In this paper, we formulate the problem of optimizing over the Pareto front of nonconvex constrained and time-delayed optimal control problems as a bi-level optimization problem. Motivated by existing solution differentiability results, we propose an algorithm incorporating (i) the Chebyshev scalarization, (ii) a concept of the essential interval of weights, and (iii) the simple but effective bisection method, for optimal control problems with two objectives. We illustrate the working of the algorithm on two example problems involving an electric circuit and treatment of tuberculosis and discuss future lines of research for new computational methods.

Two-dimensional phased array antenna beamforming system based on mode diversity.

In this paper, a two-dimensional phased array antenna beamforming system based on mode diversity is demonstrated for the first time. The system uses few-mode long-period fiber gratings to excite different modes, and utilizes few-mode fiber Bragg gratings and 2 × 2 optical switches to control the propagation paths of optical signals, so as to realize the true time delay control of optical signals of different mode channels and complete the two-dimensional scanning of the beam. In order to prove the feasibility of the two-dimensional phased array antenna beamforming system based on mode diversity, we conduct experimental verification and performance testing of the system using optical switches to select the loop structures composed of the optical circulators. The far-field radiation patterns of 2 × 3 phased array antenna system of different frequencies are tested at different beam pointing angles. The experimental results are compared with the simulation results to demonstrate that the beam pointing angles have no squint. The beamforming system based on mode diversity takes modes as independent channels for the transmission of signals, and excites and processes signals of different modes in a single few-mode fiber core, which effectively reduces the volume and complexity of the optically controlled phased array radar system.

Identification of Boolean control networks with time delay

This paper investigates the identification of time-delay Boolean networks (TBNs) and time-delay Boolean control networks (TBCNs) via Cheng product. According to all admissible (input-)output sequences, definition on identifiability of the (TBCN) TBN is given. Two algorithms are designed to select suitable delay parameters of the TBN and TBCN, respectively. Based on these, the original systems are divided into several subsystems. Then by virtue of observability, the criteria for identifiability of the TBN and TBCN are obtained. Moreover, the corresponding constructing processes are presented to establish the internal structures of the TBN and TBCN. Finally, two illustrative examples are given to show the feasibility of the proposed methods.

Novel Synchronization Criteria for Non-Dissipative Coupled Networks with Bounded Disturbances and Time-Varying Delays of Unidentified Bounds via Impulsive Sampling Control

The μ−synchronization issues of non-dissipative coupled networks with bounded disturbances and mixed delays are studied in this article. Different from existing works, three kinds of time delays, including internal delays, coupling delays, and impulsive sampling delays, have unidentified bounds and even evolve towards infinity over time, making the concerned network more practical. Considering μ−stability theory and impulse inequality techniques, a hybrid non-delayed and time-delayed impulsive controller including both current and historical state information is designed, and several novel sufficient conditions are derived to make nonlinear complex networks achieve μ−synchronization. Moreover, not only can the constriction of dissipative coupling conditions on network topology be relaxed, but also the restriction of various time delays on impulsive intervals can be weakened, which makes the theoretical achievements in this article more general than the previous achievements. Ultimately, numerical simulations confirm the effectiveness of our results.

An Improved Adaptive Sliding Mode Control Based on Time-Delay Control for Robot Manipulators

This paper proposes a new adaptive sliding mode control (ASMC) scheme for robot manipulators not only by designing a sliding variable and an adaptive law but also by compensating a time-delay estimation (TDE) error induced by time-delay control (TDC). Based on the operating cycle, because TDC utilizes the previous angular acceleration and input torque for the estimation of the dynamics of the manipulators, TDC produces an inevitable TDE error and this paper compensates the present TDE error by using the previous TDE error. For the ASMC, this paper constructs the sliding variable by additionally utilizing the previous error and its derivative. Also, this paper proposes an adaptive law, which guarantees the positive condition of the adaptive parameter, by using the current adaptive parameter value and the sampling period. For the stability analysis, this paper shows uniformly ultimately bounded (UUB) stability of the sliding variable for the manipulators controlled by the proposed ASMC scheme. The simulation and experimental results present the effectiveness of the proposed control schemes.

Response and Bifurcation of Fractional Duffing Oscillator under Combined Recycling Noise and Time-Delayed Feedback Control

Response and bifurcation of fractional Duffing oscillator under recycling noise and time-delayed feedback control are investigated. Firstly, based on the principle of the minimum mean square error and small time-delayed approximation and linearize the cubic stiffness term, the fractional derivative is equivalent to a linear combination of damping and restoring forces, and the original system is simplified into an equivalent integer order system. Secondly, the Itô differential equations and one-dimensional Markov process are obtained according to stochastic averaging method, and the stochastic stability and stochastic bifurcation of the system are analyzed. Lastly, through joint probability density function diagram and the stationary probability density function diagram, the stochastic bifurcation behavior of system under the different time-delay, fractional order and noise intensity are discussed respectively, the validity of the theory and the occurrence of bifurcation phenomenon are verified.

Time-Delay Active Disturbance Rejection Control of Wet Electrostatic Precipitator in Power Plants

Time-Delay Active Disturbance Rejection Control of Wet Electrostatic Precipitator in Power Plants