Time Delay Uncertainties Research Articles

Exponential stability of fractional-order asynchronous switched impulsive systems with time delay and mode-dependent parameter uncertainty

Distinguished from asymptotic stability or Mittag–Leffler stability of fractional-order synchronous switched impulsive systems, the exponential stability, implying explicit and faster convergence rate, is investigated in this paper for the fractional-order asynchronous switched impulsive systems with time delay and mode-dependent parameter uncertainty, where the addressed impulsive functions depend on not only switching modes but also impulsive sequences. Some novel criteria are developed via fractional differential delayed inequalities and LMIs technique, as well as the methods of induction and Lyapunov function, which establish a connection between fractional order, impulsive interval, impulsive function, time delay and average dwell time. In addition, our results extend the ones of fractional-order synchronous switched impulsive systems, and fractional-order asynchronous switched impulsive systems without time delay, which include the exponential stability of integer-order asynchronous switched impulsive systems with time delay as a special case. Finally, four numerical examples are presented to testify the theoretical achievements.

Set‐membership state estimation for delayed switched systems with interval uncertainty: A zonotopic approach

SummaryConsidering the existence of time delay and interval uncertainty, a set‐membership state estimation problem based on zonotopes is studied for discrete‐time switched systems subject to unknown but bounded noises. To conform the actual situation, a state observer asynchronous with the subsystem is designed. The performance is introduced to attenuate the effect of noises in the observer design. By dealing with the interval uncertainty, the design approach of observer is given and transformed into a convex optimization problem which can be solved off‐line. The zonotope and the estimation interval containing state are provided based on the observer. Finally, a numerical example is given to verify the effectiveness of the proposed algorithm.

Synchronization of heterogeneous discrete-time fractional-order quaternion-valued neural networks with time delay and parameter uncertainty using the impulsive method

This paper presents theoretical results on the impulsive synchronization of discrete-time fractional-order quaternion-valued neural networks (DFQVNNs) with time delay and parameter uncertainty. First, a useful assumption for parameter uncertainty is put out, predicated on the observation that it is typically brought about by a very tiny disruption. Next, we realize impulsive synchronization for DFQVNNs with the same structure by utilizing the nabla discrete Mittag–Leffler function. We put out a novel synchronization theory for more intricate scenarios in which the architectures of the DFQVNNs are heterogeneous. Finally, the applicability of the theoretical results is demonstrated through numerical examples.

Robust fractional-order PID controller assisted by active disturbance rejection control for the first-order plus time-delay systems

Time-delay characteristics of various industrial processes may degrade the stability and dynamic performance of the control systems. Aiming at the problems of the existing methods in dealing with the time delay plant, a modified fractional-order proportional–integral–derivative (FOPID) controller for the first-order plus time-delay (FOPTD) system is developed. Assisted by a modified active disturbance rejection control (ADRC) scheme with increased observer bandwidth, the proposed FOPID controller inherently obtains good robustness to time-delay uncertainties and external disturbances. In addition, taking advantage of the fractional-order operator, the proposed controller can provide larger stability margin over the proportional–integral–derivative (PID) controller. By suitably establishing the relation between ADRC and FOPID controller parameters, the proposed controller can be analytically tuned based on the common design indices. A practical tuning guideline is developed according to frequency-domain characteristic analysis, making the proposed controller more acceptable to industrial application. The performance of the ADRC-based FOPID controller is tested by the control simulation of some typical FOPTD systems and a diesel engine speed regulation system. The efficiency of the ADRC-based FOPID controller is demonstrated by the comparisons with some existing controllers.

GESO based RISE Controller for Active Flutter Suppression for Aeroelastic System

Abstract The paper presents a Robust Integral of Signum of Error (RISE) controller for active suppression of flutter of a two dimensional aerofoil and it is integrated with a General Extended State Observer (GESO). Towards this, aerofoil model in state space is first changed into a canonical form. Then, the controller is designed using RISE control technique. As equations of system dynamics are not into integral chain form, a GESO is formulated to observe system states and disturbances. The controller is implemented using estimated states and it is robustified using estimated disturbance. Stability of the proposed GESO-RISE controller is established using the Lyapunov theory. Simulations are performed to check the proposed controller's performance against variations in airspeed, uncertainties in model parameters, external disturbances, time delay and unmodeled dynamics. Comparison of the proposed GESO-RISE controller is carried out with existing controllers using two performance criteria i.e. Control Efforts and Integral of Absolute Error (IAE). It is discovered from simulations that the proposed GESO-RISE controller significantly reduces IAE and control efforts. Additionally, Monte Carlo method is utilized to check robustness of the proposed GESO-RISE controller. The proposed GESO-RISE controller significantly enhances flutter boundary of aerofoil and is completely implementable.

Delayed non‐fragile robust control of civil structure considering structural uncertainties, actuator faults, and control force time delays

Active control is an effective strategy for suppressing unwanted structural vibrations. The uncertainties in computational models, actuator faults, and time delays in control forces are the potential threats for control performance improvements. These factors are interconnected and may lead to control system instability and poor control effectiveness. The paper presents a delayed non-fragile robust control (DNR) algorithm for uncertain systems with consideration of actuator faults and time delays. To this end, the existence conditions for the DNR multi-objective controller are derived by utilizing the Lyapunov stability proof and introducing a pole constraint inequality. Then, a dynamic output feedback DNR algorithm is further developed. Finally, two numerical simulation examples are discussed for several ground motions. The results show that the control system based on the proposed algorithm exhibits better stability, robustness, and fault tolerance than the linear quadratic Gaussian (LQG) algorithm. Furthermore, there is no need for additional control energy. Significantly, the control performance of the proposed algorithm can be further enhanced with the decentralized control strategy.

A Simulation-Based Bayesian Network Approach to the Joint Decision of the International Transportation Mode and Safety Inventory Policy

Uncertainty in international transportation can have a significant impact on inventory costs and customer service levels in a global supply chain network. A very limited number of studies in the literature have addressed the international transportation mode and safety inventory policy (ITM-SIP) issues simultaneously. This study formulates the problem and proposes a simulation-based Bayesian network (SBN) approach for the joint decisions on ITM-SIP, where Bayesian networks are used to dynamically estimate international replenishment lead times for railway and maritime transportation modes. We implement our approaches in an international automotive spare parts supply chain experiencing fluctuations in its shipping supply market and with dynamic demand. For this joint decision problem, we build an international supply chain network simulation model in which the time-delay uncertainties of key bottleneck nodes in maritime and railway transportation routes are considered. The simulation experiment results show the performance improvement of the SBN approach in substantially reducing total costs and achieving service levels. We also provide insights into the value of decision tactics for responding to different fluctuation modes in the shipping supply market in the global supply chain network.

Disinfection scheduling in water distribution networks considering input time-delay uncertainty

Abstract A significant challenge when attempting to regulate the spatial-temporal concentration of a disinfectant in a water distribution network is the large and uncertain delay between the time that the chemical is injected at the input node and the time that the concentration is measured at the monitoring output nodes. Uncertain time delays are due to varying water flows, which depend mainly on consumer water demands. Existing approaches cannot guarantee that the concentration of the disinfectant will remain within a specified range at the output, even though bounds on time-delay uncertainty may be known. In this work, given bounded water-flow uncertainty, we use the input–output modeling approach to develop a disinfectant scheduling methodology that guarantees a bounded output disinfectant concentration. The proposed methodology creates an input–output model uncertainty characterization by utilizing estimated bounds on water-quality states using the backtracking approach. An optimization problem is formulated and solved to find an input schedule that keeps the disinfectant concentration within predefined bounds for a specified time horizon. Simulation results in two case studies where water demands varied between ±20% of their nominal value show that the proposed scheduler is able to avoid lower bound violations of disinfectant concentration.

Predictive State Observer-Based Aircraft Distributed Formation Tracking Considering Input Delay and Saturations

This paper investigates a fully distributed time-varying formation tracking problem for a group of fixed-wing aircraft. The fixed-wing aircraft formation control system consists of an outer-loop trajectory control subsystem and an inner-loop attitude control subsystem. For fixed-wing aircraft, it is crucial to consider the time delay of the engine response, the model uncertainties, the tracking capability of the attitude commands in the inner loop, and other agility performances of the aircraft. To address the problems related to the input time delay and model uncertainties, a predictive extended state observer-based fully distributed time-varying formation tracking control (PESO-TVFTC) protocol is proposed. To satisfy the constraints set by the attitude tracking quickness and the trajectory tracking smoothness, the low gain feedback technique is introduced in the protocol to keep the control inputs for the outer loop within the desired saturation constraints. Through theoretical analysis, it is proved that the multiple aircraft systems can achieve time-varying formation tracking consensus under specific initial conditions and feasibility conditions, and it is shown that the upper bounds of the PESO gains are restricted by the time delay. Numerical simulations are used to demonstrate the effectiveness of and the improvements in the proposed method.

Optimized robust control for improving frequency response of delay dependent AC microgrid with uncertainties

Converter-interface-based renewable energy incorporated into modern power systems causes deterioration in power system stability and it is proving to be a main challenge for operators using sluggish traditional generation with a growing share of converter-interface generation, and there is a need for an alternative means to deliver rapid frequency control. This paper proposes two control loops as secondary frequency control, first is an improved optimized delay-dependent frequency control to ensure robust frequency control under daily changes in system parameters that may occur in prospective, renewable-rich future AC microgrids. For a variety of operating conditions, the design process employs a mixed H2/H∞ robust control based on linear matrix inequality (LMI). In second, a speedy-acting improved power stability control loop is utilized as the proposed secondary frequency control, because demand response aggregators can be beneficial for frequency control. Robustness is evaluated against several perturbations and communication delay attacks through dynamic simulation and stability is evaluated by small-signal analysis. Different case studies subject to generation\\load loss, multiple time delay and parameter uncertainties are demonstrated on an interconnected AC microgrid system to verify the performance of the proposed control technique.

Adaptive Iterative Learning Control for a Class of Nonlinear Strict-Feedback Systems With Unknown State Delays.

In this article, an adaptive iterative learning control scheme is presented for a class of nonlinear parametric strict-feedback systems with unknown state delays, aiming to achieve the point-wise tracking of desired trajectory in a finite interval. The appropriate Lyapunov-Krasovskii functions are established to compensate the influence of time-delay uncertainties on the control systems. As the main features, the proposed approach integrates the command filter into the backstepping procedure to avoid the differential explosion problem that may occur with the increase of system order, and introduces the hyperbolic tangent functions into the learning controller to handle the singularity problem thus maintaining the continuity of input signal. The results of theoretical analysis and numerical simulation demonstrate that the tracking errors at the entire period will converge to a compact set along the iteration axis. Compared with the existing works, the proposed control scheme is promising to manifest the better performance and practicability owing to the learning mechanism, the dynamic model, as well as the implementation of controller.

Robust control strategy for networked vehicle system with fake data injection attack

This article investigates the safety control problem of intelligent networked vehicle and utilizes the sliding-mode control to solve the system with time delay, system disturbance, and parameter uncertainty. First, the modeling of automobile system is introduced. What’s more, time delay, parameter uncertainty, disturbance, and attack are added to the original model. Then, designed an integral sliding-mode surface and given the sufficient conditions for system stability using linear matrix inequalities. Furthermore, the controller is designed according to the slide approach rate, and it is proved that the designed controller can make the system state reach the sliding surface in finite time. Finally, the simulation is used to verify the effectiveness of the arithmetic.

Intelligent Controller Design and Fault Prediction Using Machine Learning Model

In a solar power plant, a solid phase transformer and an optimization coordinated controller are utilized to improve transient responsiveness. Transient stability issues in a contemporary electrical power system represent one of the difficult tasks for an electrical engineer due to the rise in uncertain renewable energy sources (RESs) as a result of the need for green energy. The potential for terminal voltage to be adversely impacted by this greater RES raises the possibility of electrical device damage. It is possible to use a solid state transformer (SST) or smart transformer to address a transient response issue. These devices are frequently employed to interact between RES and a power grid. SST features a variety of regulated converters to maintain the necessary voltage levels. This method can therefore simultaneously lessen power fluctuations and transient responsiveness. In order to improve the quality of RES power injections and the electrical system’s transient stability, this work provides a controller design for a solar photovoltaic (SPV) system that is connected to the grid by SST. The optimization of a controller model is proposed by modifying a PI controller taken from a commercial one. With the use of IEEE 39 standard buses, the proposed controller is tested. When evaluating the effectiveness of a suggested controller, it is important to take into account a variety of solar radiation patterns as well as a time delay uncertainty that can range from 425 ms to 525 ms. According to simulation results, the proposed controller can be employed to lessen power fluctuation brought on by unpredictable RES. Additionally, the proposed coordinated regulation of SPV and SST can prevent catastrophic damage in the event of substantial disturbances like a circuit breaker collapsing to expand a power line due to a fault by inhibiting significant voltage cycles within an electronic appliance’s rated voltage limit. The results indicate that a transitory stability issue in a modern power system caused by an unforeseen increase in RES may be addressed utilizing the suggested controllers as alternatives.

Interacting Multiple Model Strategy Based Adaptive Wide-Area Damping Controller Design for Wind Farm Embedded Power System

The intermittent nature of Wind Turbine Systems (WTSs) can severely affect the Low-Frequency Oscillations (LFOs) in the power system. Hence, a Wide-Area Damping Controller (WADC) is designed in this paper to provide adequate damping to critical LFO modes. This WADC utilizes a modal-based prescribed degree approach, ensuring the specified shift of concerned modes from their existing position. However, the design of WADC at a fixed operating point and time delay in feedback signals does not provide robust performance as these uncertainties may vary for different time intervals. Specifically, time-varying delays should be tackled appropriately, or the system's damping performance will be severely hampered. Keeping this in view, an Interacting Multiple Model (IMM) infrastructure is employed to provide robust damping performance for such uncertainties. The IMM strategy utilizes the deviation of output error between actual and probable plants, through which weights are assigned to corresponding probable WADCs via the Bayesian framework. The simulations are performed on the nonlinear 4-machine, 11-bus system and the complex 16-machine, 68-bus system using MATLAB/Simulink platform. The results demonstrate that the proposed IMM-based WADC furnishes adequate damping to critical LFO modes for operating point and time delay uncertainties.

Control–Communication–Computing Co-Design in Cyber–Physical Production System

The cyber–physical production system (CPPS) has practical requirements, such as distributed, reconfigurable, and high-performance, which bring a new challenge to performance guarantee of remote manufacturing with time delay under shared resources. Time delay has a great influence on system performance, and the mainstream methods mainly reduce its influence by optimizing control. However, due to the uncertainty of time delays, the existing methods have great limitations, and the configuration complexity is high. To address this issue, we take teleoperation as the control model, then we introduce 5G slicing and edge computing technologies to turn this control problem into a control–communication–computing co-design problem. An industrial teleoperation testbed is implemented to help clarify this problem and explore the key points in solving it. Then, a novel co-design teleoperation platform (CdTP) is designed that can quantitatively describe the relationship between the time delay and system configuration. Based on CdTP, system performance assurance does not have to be achieved by blindly increasing the total amount of resources, but can be achieved by improving the utilization of shared control–communication–computing resources. In addition, CdTP can dynamic configure resources based on changing requirements, which make it combines flexibility, real time, and reliability. Finally, we propose a resource allocation method to minimize the maximum job delay. The evaluation and experimental results indicate that our platform can achieve an all-in-one configuration, and validation of the proposed method is conducted to provide deterministic delay guarantees.

Robust Stability Analysis of Smith Predictor Based Interval Fractional-Order Control Systems: A Case Study in Level Control Process

The robust stability study of the classic Smith predictor-based control system for uncertain fractional-order plants with interval time delays and interval coefficients is the emphasis of this work. Interval uncertainties are a type of parametric uncertainties that cannot be avoided when modeling real-world plants. Also, in the considered Smith predictor control structure it is supposed that the controller is a fractional-order proportional integral derivative (FOPID) controller. To the best of the authors' knowledge, no method has been developed until now to analyze the robust stability of a Smith predictor based fractional-order control system in the presence of the simultaneous uncertainties in gain, time-constants, and time delay. The three primary contributions of this study are as follows: i) a set of necessary and sufficient conditions is constructed using a graphical method to examine the robust stability of a Smith predictor-based fractional-order control system—the proposed method explicitly determines whether or not the FOPID controller can robustly stabilize the Smith predictor-based fractional-order control system; ii) an auxiliary function as a robust stability testing function is presented to reduce the computational complexity of the robust stability analysis; and iii) two auxiliary functions are proposed to achieve the control requirements on the disturbance rejection and the noise reduction. Finally, four numerical examples and an experimental verification are presented in this study to demonstrate the efficacy and significance of the suggested technique.

Networked Control System Based on PSO-RBF Neural Network Time-Delay Prediction Model

To satisfy the requirement of real-time and accurate control of the system, a time-delay prediction control system based on the PSO-RBF neural network model is established to solve the effect of time delay on the control system’s performance. Firstly, a network control model with a time delay is established to predict the control system’s output to solve the uncertainty of the output time delay. Secondly, an improved offline prediction model of RBF networks is proposed to solve the problem of the low accuracy of time-delay prediction in PSO-RBF networks. To solve the problem that the PSO algorithm is prone to fall into local optimality, a nonlinear adjustment formula for the parameters of the PSO algorithm based on the number of iterations is proposed, and the TS algorithm is used to make the optimal global solution. Finally, in order to compensate for the problem of time delay, an online RBF network prediction controller is designed, the parameters of the online RBF network are adjusted by the gradient descent method, and a target function with the differential component is proposed to evaluate the optimization effect of the rolling optimization stage. The results from the true-time simulation platform show that the delay prediction control system based on the PSO-RBF network model proposed in this paper improves the IAE by 59.9% and 31.7%, respectively, compared to the traditional PID controller and fuzzy PID control under the influence of uncertainty disturbances. Therefore, the time-delay prediction control system proposed in this paper has good control capability for the time-delay compensation problem and system output.

Adaptive event‐triggered quantized H∞ fuzzy filtering for T‐S fuzzy systems via fuzzy Lyapunov–Krasovskii functional method

SummaryThis article is concerned on the problem of adaptive event‐triggered quantized fuzzy filtering for networked T‐S fuzzy control systems under imperfect premise matching. First, a novel adaptive event‐triggered communication scheme for networked fuzzy control systems is built to save more limited network bandwidth, where the event‐triggered parameter is changed with the output fluctuation. Second, a fuzzy filter with the imperfect premise matching is designed. Under consideration of event‐triggered scheme and quantization method, an unified filtering error model is well constructed, which contains time delay and parameter uncertainties. Then, a new augmented fuzzy Lyapunov–Krasovskii functional including a fuzzy Lyapunov matrix and a delay product term is established, and sufficient conditions are derived to guarantee the asymptotic stability of the filtering error system with a given performance. Moreover, the corresponding filter can be designed by solving a set of linear matrix inequalities. Finally, a numerical example is put forward to illustrate the effectiveness and advantages of the proposed method.

Adaptive control of time delay teleoperation system with uncertain dynamics.

A bilateral adaptive control method based on PEB control structure is designed for a class of time-delay force feedback teleoperation system without external interference and internal friction to study the uncertainty of dynamic parameters and time delay. The stability and tracking performances of the closed-loop constant time delay teleoperation system are analyzed by Lyapunov stability theory. Finally, the controller designed in this paper is successfully applied to the teleoperation system composed of a two-degree of freedom rotating manipulator as the master robot and the slave robot. The simulation is carried out in no operator and environment force or with operator and environment force. The adaptive bilateral control method's control performance is compared with that of the traditional time-delay teleoperation system. Finally, it is verified that the method has good control performance.

Lyapunov-Krasovskii passivity based stability analysis of grid-tied inverters

The non-linear dynamics of a grid-interfaced inverter (GII) in a distributed generation system results in dynamic instability and power quality issues. The conventional linear methods depend on parametric variations in controller parameters hence, tuning should be proper. Also, linearization of dynamical states around steady-state operating point works only if the controllers operate around a fixed operating point thus, only ensuring local stability. The feedback and feedforward damping methods can address some of the above challenges but requires additional sensors and also incapable of maintaining robustness against grid impedance variations and system parametric changes. To address aforementioned issues, this journal presents a non-linear Lyapunov Krasovskii Passivity (LK-PBC) based dynamic controller for Grid-interfaced Voltage Source Converters (VSCs). A generalized admittance model is derived which is used to calculate Non-passive regions of the VSC where the output admittance will have a negative real part. The damping provided by the proposed controller also eliminates the resonance instability issues in the concerned frequency scale regardless of the admittance seen at the inverter terminals. It also takes care of time delay and norm-bounded state uncertainties. The evaluation of the theoretical studies and efficacy of the proposed LK-PBC controller is confirmed by hardware in loop analysis on a laboratory experimental setup.