Input Time Delay Research Articles

Closed Loop Identification and Control for Input Time Delay Systems

In this research, the identification results for open-loop time delay systems are extended to closed-loop systems. It is shown that a subspace identification method used in open-loop systems can be applied to closed-loop systems. When the subspace identification method was used directly, problems such as increasing poles and unstable zeros caused by numerical errors were encountered; however, these problems can be prevented by a shift operation. Finally, the simulated identification results for the time delay system and the improved control performance using the estimated time delay are shown.

Smart-Leader-Based Distributed Charging Control of Battery Energy Storage Systems Considering SoC Balance

Battery energy storage systems are widely used in energy storage microgrids. As the index of stored energy level of a battery, balancing the State-of-Charge (SoC) can effectively restrain the circulating current between battery cells. Compared with passive balance, active balance, as the most popular SoC balance method, maximizes the capacity of the battery cells and reduces heat generation. However, there is no good solution in the battery management system (BMS) to ensure active balance during distributed charging. In view of this, this paper designs two novel distributed charging strategies based on a kind of smart leader, in which a constant static leader is modified by a dynamic leader. The modified leader is in charge of guiding SoC to converge to the target value and repress SoC imbalance. The maximum and weighed error between the state of the leader and its neighbor cells are used in the two methods, respectively, both in an event triggered manner. When the relevant index exceeds the threshold, the two methods are used to regulate the leader’s state. Under this modification, the eigenvalue of the followers’ error dynamic system is reduced, and SoCs follow the dynamic leader faster, thus repressing SoC imbalance. Compared with a constant leader, the smart leader pays more attention to improving SoC imbalance. Additionally, to facilitate analysis, a reduced method is applied to transform the system with an unified input time delay into a nondelay system. Several cases are designed to verify the effectiveness of the designed strategies and test it under different parameters and different time delays.

Robust optimal attitude control for hexarotors with disturbances, uncertainties, and delays

AbstractA robust optimal attitude controller for hexarotor helicopters is proposed. Compared to the previous research studies on hexarotors, the current study takes account of the influences of non‐linear and coupling dynamics, structured and unstructured uncertainties, external time‐varying disturbances, and input time delays. A linear time‐invariant system is derived for each Euler angle by considering the actual rotational dynamic model as a nominal non‐linear system plus an equivalent perturbation, including non‐linear and coupling dynamics, uncertainties, disturbances, and time delays. Using this approach, a Linear Quadratic Regulation controller is first designed for the nominal linear system of each angle to accomplish the desired tracking performances. Then, a robust compensator based on the robust compensation method is proposed to counteract the effects of the equivalent perturbation on the system. Moreover, the robust attitude tracking property and uniform asymptotical stability of the closed‐loop hexarotor system are proved using Lyapunov stability theory. Several simulations have been performed to demonstrate the effectiveness and robustness of the proposed controller. Finally, experimental results are provided to confirm the robust performance of the proposed controller.

Prediction-Based Preview Control of Motion Platform With Time Delay

This paper presents a new control strategy for a spherical motion platform capable of three DOFs translational and three DOFs unlimited rotational motion undergoing time delay problems. The control is based on a state prediction and preview method to make a state correctly track a time-varying desired trajectory despite input time delay and disturbance. The spherical motion platform can suffer from a delay effect since it needs a wireless data link to control a cockpit sphere without any mechanical linkage. The delay decreases operation efficiency and further causes control instability. The proposed prediction-based preview control (PPC) offers that a state vector under input time delay is predicted using a disturbance predictor attenuating the disturbance effect. In addition, a predictor-based previewed reference with the state prediction is applied to the controller to achieve desired tracking control. In numerical simulations, it is shown that the proposed controller stabilizes the state to the desired trajectory under delay and disturbance, whereas most existing controllers only show delayed tracking. Finally, the proposed controller is applied to the motion platform, and the result shows excellent performance minimizing the effect of time delay and disturbance.

Practical fixed-time observer-based generalized cascade predictor design for synchronization of integrator systems with delays and complex unknowns

This paper studies output feedback leaderless synchronization problem for high-order integrator chains subject to nonlinear dynamics, measurement noises, matched disturbances, and time delays in both input and output. First, we consider the varying normal-scale input delay case and propose a novel extended state observer (ESO)-based predictor device for each agent using relative output of neighbors. Then, in combination with integral sliding mode, leaderless fully distributed synchronization protocols are designed which can highly compensate for delays and unknowns. In particular, the ESO combines the transient performance of fixed-time algorithms with the continuous/smooth, anti-noise and low-cost strengths of linear algorithm via linear structure and time base gains. Also, any disturbances considered in this protocol are not generated by known exosystem and hence the proposed anti-disturbance time delay compensation scheme is more general. Second, aiming to cope with a larger class of input delays, the above device is extended to a ESO-based cascade predictor device. Synchronization analysis is placed in the Lyapunov–Krasovskii functional frame and sufficient conditions are deduced to ensure that the synchronization errors converge to a residual set in fixed time. Detailed numerical simulation studies and thorough comparisons are provided to verify the effectiveness and superiority of the designed ESO and devices.

Design of compensatory backstepping controller for nonlinear magnetorheological dampers

• A novel magnetorheological fluid damper inverse model is constructed based on the radial basis function neural network. • The filter performance function is employed in the semi-active suspension system as the reference state. • A unified frame is developed to study the semi-active suspension system with various disturbances. The magnetorheological fluid semi-active suspension system has been widely employed in vehicles. In general, the output force of the magnetorheological fluid damper varies with service time and temperature, which will cause the controller performance to degrade or even fail. To conquer this problem, this study proposes a compensatory backstepping strategy for the magnetorheological fluid suspension system. First, the normalized phenomenological model is introduced to simulate the nonlinear characteristics of the magnetorheological fluid damper. Second, the adaptive radial-basis function neural network is employed to construct the inverse model of the magnetorheological fluid damper. Next, the reference state is calculated by the filter performance function to trade off the vehicle handling stability and ride comfort. Finally, the voltage-force compensator is constructed to improve the robustness of the controller under input time delay, external noise disturbance, and actuator failures. Furthermore, the performances of the magnetorheological fluid damper, inverse magnetorheological fluid model, and compensatory backstepping controller are simulated under bump and random excitations. It is found that the proposed compensatory backstepping controller shows good improvement in the semi-active suspension system with time delay, noise disturbance, and actuator failure.

Synchronization of Chaotic Neural Networks: Average-Delay Impulsive Control.

In the brief, delayed impulsive control is investigated for the synchronization of chaotic neural networks. In order to overcome the difficulty that the delays in impulsive control input can be flexible, we utilize the concept of average impulsive delay (AID). To be specific, we relax the restriction on the upper/lower bound of such delays, which is not well addressed in most existing results. Then, by using the methods of average impulsive interval (AII) and AID, we establish a Lyapunov-based relaxed condition for the synchronization of chaotic neural networks. It is shown that the time delay in impulsive control input may bring a synchronizing effect to the chaos synchronization. Furthermore, we use the method of linear matrix inequality (LMI) for designing average-delay impulsive control, in which the delays satisfy the AID condition. Finally, an illustrative example is given to show the validity of the derived results.

Stability of Sliding Mode ILC Design for a Class of Nonlinear Systems With Unknown Control Input Delay.

This article studied the stability and convergence of a robust iterative learning control (ILC) design for a class of nonlinear systems with unknown control input delay. First, the iterative integral sliding mode (IISM) design was proposed, which comprised iterative actions. The iterative action made the convergence of the tracking error under the ideal sliding mode. Then, a suitable iterative update law was provided for the IISM-based robust ILC controller. The controller had the capability of both minimizing the steady tracking error and suppressing the unrepeatable disturbance. Using the controller, the closed-loop system stability was analyzed, and the stability conditions were given. Consequently, the sliding mode convergence in the iteration domain was proved by a composite energy function (CEF). In addition, by analyzing the influence of affection on the tracking error, several measures were taken to solve the chattering problem of the sliding mode control. Finally, a one-link robotic manipulator and a vertical three-tank system were used to verify the control design. The application simulations validated the performance of the proposed sliding mode iterative learning control (SMILC) design, which achieved the stability of the nonlinear system and overcame the control input time delay.

Distributed event-triggered secondary frequency control of islanded AC microgrids under cyber attacks with input time delay

This article proposes a distributed event-triggered secondary frequency control considering cyber attacks and disturbances subject to input delay for islanded AC microgrids (MGs). The reliance on communication networks exposes MGs to cyber attacks. Therefore, detection and prevention of cyber attacks is one of the most important issues for islanded MGs. The purpose of this article is the analysis of the impacts of cyber attacks, such as false data injection (FDI) and denial-of-service (DoS) on communication links and local controllers (LCs), in the presence of time delay in communication links. Our method conserves communication resources by reducing the number of transmissions of sampled data. Also, each distributed generation (DG) can quickly detect and isolate corrupted links and controllers. Moreover, we have analyzed the stability of our proposed strategy by the Lyapunov theory. The superior features of our proposed method, including cyber security, number of transmissions of sampled data, and communication time delay, have been investigated in MATLAB/SimPowersystems Toolbox.

Lithium-Ion Batteries Long Horizon Health Prognostic Using Machine Learning

Long horizon state of health (SOH) monitoring and remaining useful life (RUL) prediction are of industrial value in prognostic and health management (PHM) of lithium-ion batteries (LIBs) to ensure their reliable functionality by early detection. Machine Learning, as a data-driven health diagnostic technique, has been widely utilized in solitary and hybrid structures. However, an accurate SOH estimation and RUL prediction method with less computational burden are highly desirable for the online state prediction in an electric vehicle application. This paper evaluates nonlinear autoregressive with external input (NARX) recurrent neural network (RNN) and time delay neural network (TDNN) in their prediction precision using the NASA dataset. The superior method, NARXRNN, is employed for two different datasets to estimate the battery's SOH and predict its RUL on a broad horizon. The results reveal the outstanding performance by presenting the root mean square error within 3% and mean absolute error within 2% for unseen data. Therefore, this method is capable to accurately predict the SOH of LIBS from historical data at low computational complexity. It is a promising model for long horizon SOH and RUL prediction and practical for online applications.

A fully probabilistic control framework for stochastic systems with input and state delay

This paper proposes a unified probabilistic control framework for a class of stochastic systems with both control input and state time delays. Both of the stochastic nature and time delays in the system dynamics are considered simultaneously, thus providing a comprehensive and rigorous control methodology. The problem is formulated in a fully probabilistic framework, where the system dynamics and its controller are fully characterised by arbitrary probabilistic models. In this framework, the Kullback–Leibler Divergence between the actual joint probability density function of the system dynamics and controller and a predefined ideal joint probability density function is used to characterise the discrepancy between the two distributions and derive the randomised controller. Time delays in the control input and system state are taken into consideration in the optimisation process for the derivation of the optimal randomised controller. Besides, the analytic control solution of the time delay fully probabilistic control problem for a class of linear Gaussian stochastic systems is derived while the successive approximation approach is implemented to deal with the time-advanced components in the control law that result from the existence of time delays. The effectiveness of the proposed control framework is then illustrated on a numerical example and a real-world example.

Bounded controls for discrete-time linear systems subject to input time delay

This paper investigates the global stabilization of discrete-time linear systems with input time delay by bounded controls. Based on some special canonical forms containing time delays both in its input and state, two special discrete-time linear systems---multiple integrators and oscillators are first considered. The global stabilizing controllers are respectively established, and moreover, explicit conditions are established to guarantee the stability of the closed-loop systems. Subsequently, a concise design method is proposed for globally stabilizing general discrete-time linear system by combining the design methods for multiple integrators and oscillators. The designed controller is in the explicit form with explicit stability conditions being given, and thus is easier to use than the existing results. Finally, numerical simulations illustrate the effectiveness of the proposed approaches.

Secure Frequency Regulation of Electric Vehicle-connected Microgrid System under Multiple Latency Attacks

Occurring attacks in communication links of interconnected alternating current (AC) microgrids (MGs) is inevitable and interrupts the grid operation. If they are not tolerated, the stability of the overall AC MG may ruin. This paper deals with a robust (mixed) μ-synthesis-based controller to regulate the frequency in an AC MG system with vehicle-to-grid (V2G) technology. In the developed control method, the system uncertainties and external disturbance inputs are considered and the robust controller is designed offline based on a numerical method. The AC MG involves a load, a wind turbine, a photovoltaic cell, a gas turbine, a diesel generator, and a battery. The designed controller manipulates the diesel generator to mitigate the destructive effects of load, wind turbine, and photovoltaic cell power variations. By using the Pade approximation technique, the control input time delay is augmented to the state-space representation. Numerical comparisons are given to illustrate the superiority of the proposed control method.

Discrete State Predictive Control for System with Input Time-delay by Subspace System Identification

This paper proposes a discrete state predictive control by introducing a virtual system. To determine the state-space model and the time delay, the subspace identification method, called CCA(Canonical correlation analysis) method, is applied. The CCA method can judge orders of the system by checking how many singular values of a covariance matrix among input-output data are near 1. First, the time system is shown to be identified by a higher-dimensional system, and this model can be used to the LQG control for the time delay system. After that, by confirming the number of singular values near 1 according to time-shift operations between input-output data, the time delay can be identified and used it for the discrete state predictive control. The proposed method is applied to the stable vibration cart type pendulum with time delay inserted in artificially.

Dynamic control for LNG carrier with output constraints

This paper addresses constrained robust control for dynamic positioning of the Liquefied Natural Gas (LNG) Carrier in side-by-side offloading operations subject to input time delay. During the LNG offloading operation, the relative motions of the multibody system are connected by the LNG offloading arm. To ensure the operation safety, robust control with asymmetric Barrier Lyapunov Function is proposed considering predefined output constraints under the unknown dynamics and external disturbances. In offshore engineering, due to the mechanical effects, the thrusters of the LNG carrier in the presence of time-delay should be investigated to guide the design practice. The predictor-based method is employed to deal with the time delay induced by the control inputs. It is proven that the proposed scheme can guarantee semi-global uniform ultimate boundedness. The performance and feasibility of the proposed control are further verified by simulation studies.

Adaptive output feedback control of large-scale nonlinear time-delay systems with uncertain output equations

For a class of large-scale nonlinear time-delay systems with uncertain output equations, the problem of global state asymptotic regulation is addressed by output feedback. The class of systems under consideration are subject to feedforward growth conditions with unknown growth rate and time delays in inputs and outputs. To deal with the system uncertainties and the unknown delays, a novel low-gain observer with adaptive gain is firstly proposed; next, an adaptive output feedback delay-free controller is constructed by combining Lyapunov-Krasovskii functional with backstepping algorithm. Compared with the existing results, the controllers proposed are capable of handling both the uncertain output functions and the unknown time delays in inputs and outputs. With the help of dynamic scaling technique, it is shown that the closed-loop states converge asymptotically to zero, while the adaptive gain is bounded globally. Finally, the effectiveness of our control schemes are illustrated by three examples.

Robust adaptive backstepping control of uncertain fractional-order nonlinear systems with input time delay

In the present work, a fractional adaptive backstepping control approach is proposed for controlling a class of uncertain fractional-order nonlinear systems subjected to unknown external disturbance and input delay. In control design, by introducing fractional command-filter, the key issue of the common backstepping method called the “explosion of complexity” is addressed. Furthermore, the Szász–Mirakyan operator is used as a simple but efficient universal approximator to approximate uncertain or unknown terms and reduce the design complexity. In addition, to enhance the capability of the proposed controller in dealing with the approximation error and the unknown disturbance, an efficient robust control term is also incorporated into it. One advantage of the suggested control approach is that the input-delay fractional-order system is effectively treated by introducing a new variable as a non-delayed fractional-order system. The other advantage is that the number of tuning variables is considerably low; specifically, for an n-order fractional nonlinear system, only n adaptive parameters are adjusted online. This makes the implementation of the proposed approach simpler. The Lyapunov stability theorem is used to prove that all of the closed-loop system’s signals are semi-globally uniformly ultimately bounded. The feasibility of the suggested control approach is shown by comparing the simulation results obtained with the fuzzy system.

Event-Triggered Impulsive Optimal Control for Continuous-Time Dynamic Systems with Input Time-Delay

Time-delay is an inevitable factor in practice, which may affect the performance of optimal control. In this paper, the event-triggered impulsive optimal control for linear continuous-time dynamic systems is studied. The event-triggered impulsive optimal feedback controller with input time-delay is presented, where the impulsive instants are determined by some designed event-triggering function and condition depending on the state of the system. Some sufficient conditions are given for guaranteeing the exponential stability with the optimal controller. Moreover, the Zeno-behavior for the impulsive instants is excluded. Finally, an example with numerical simulation is given to verify the validity of the theoretical results.

A simple robust method of fractional time-delay estimation for linear dynamic systems

This paper is concerned with estimating the parameters of single-input, continuous-time systems from sampled input–output data, where any input time delays may be a fraction of the sampling interval. The proposed method estimates the parameters by minimizing a cost function defined by the sum of squared errors between the predicted and measured outputs using the optimal Refined Instrumental Variable method for Continuous-time models (RIVC). Potential difficulties may be encountered when standard gradient-based optimization is used for solving this optimization problem directly. These arise because the cost function is normally multi-modal with respect to the fractional time delay and they can occur for several reasons, such as aliasing errors, the nature of the system dynamics, and the selection of the excitation signal. In order to avoid the problems caused by these local minima, a two-stage procedure is proposed combining RIVC estimation of the model parameters with a grid search for the fractional time delay. Although this algorithm is not quite as computationally efficient as standard gradient-based optimization, it is simple, robust, and more widely applicable, as illustrated by numerical examples.

Reinforcement Learning-Based Optimal Tracking Control for Levitation System of Maglev Vehicle With Input Time Delay

The running environment of a magnetic levitation (maglev) vehicle is complex, with problems such as track irregularity, external disturbance, varying system parameters, and time delays, which bring great challenges to the design of a high-performance levitation controller. In this article, an adaptive neural network controller with input delay compensation and a control parameter optimization scheme is proposed for the electromagnetic levitation system of a maglev vehicle, which can solve the key engineering problems of external disturbance, input time delay, and time-varying mass. Aiming at the problem of input time delay, a sliding-mode surface with time-delay compensation is constructed, and a double-layer neural network and adaptive law are utilized to approximate the uncertain dynamics; thus, a finite time adaptive tracking control law is proposed. Based on the Lyapunov method, the stability of the proposed controller in finite time is analyzed. The proposed method does not only update the input and output weights of the neural network online, but also introduces reinforcement learning (Actor–Critic network) to optimize the key controller parameter in real time and enhance system robustness. Simulation and experimental results show that the proposed controller can effectively suppress the air gap vibration with time delay and uncertain dynamics, and significantly improve the performance of levitation control.