Control Of Time-delay Systems Research Articles

Robust predictive regulation of uncertain time-delay control systems with non-zero references and disturbances

Robust regulation is predictively investigated in time-delay models including uncertainties, non-zero reference, and disturbance. Hence, to handle the complexities induced because of the time-delays, disturbances, and uncertainties, enhancing the transient performance would be a main control goal. To this purpose, the required transient and steady-state specifications are achieved through an integral control structure with adjustable gains. The constraints on the signals and aims of the control algorithm are also described by some linear matrix inequalities. Guaranteeing the stability, a minimisation procedure is found to specify the predictive controller. Several simulations are performed to establish the effectiveness of the introduced plan in comparison with the similar strategy.

Design of Optimal FOPI Controller for Two-Area Time-Delayed Load Frequency Control System with Demand Response

Design of Optimal FOPI Controller for Two-Area Time-Delayed Load Frequency Control System with Demand Response

Boosted Incremental Nonlinear Dynamic Inversion for Flexible Airplane Gust Load Alleviation

Active gust load alleviation is an important technology for reducing loads on future commercial airplanes so that the structure can be designed to be lighter in order to save fuel. For the intense reduction of gust loads, a highly reactive control system of sensors, control algorithms, and actuators is required, which is not yet available. In this paper, a control algorithm based on incremental nonlinear dynamic inversion is extended so that actuators respond faster. The control algorithm is applied to a future medium-range aircraft with distributed trailing-edge flaps. It is assumed that the vertical acceleration of the center of gravity and the displacement, velocity, and acceleration of the first wing bending mode are available as feedback variables. To allow comparability with other actuator and sensor setups, the authors abstract the actuator dynamics and sensor filter as control system time delay. The feedback gains are adjusted automatically to the control system time delay. In simulation, the authors investigate the influence of the control system time delay on the peak gust loads. They show that gust loads can indeed be intensely reduced with sufficiently small control system time delay in simulation.

Vibration control of an eleven-story structure with MR and TMD dampers using MAC predictive control, considering nonlinear behavior and time delay in the control system

In the last two decades, model predictive control has made significant progress in research and industrial process control. This achievement is through the high ability of model predictive control to solve industrial process control problems in the time domain. It is applicable in many control systems, such as delayed systems, univariate and multivariable systems, non-minimum phase systems, and unstable systems. This strategy is essentially for controlling delayed systems. It is possible to create a time delay in transmitting structure movement data in the systems that use sensors and receivers of sensor-recorded data, which is a factor to reduce the efficiency of the control system and even the instability of the structure. In this study, to investigate and compensate the effect of time delay in the hybrid vibration control system, an 11-story structure with a tuned mass damper and an MR damper was used by model algorithmic control (MAC) and nonlinear behavior of the structure in the control process. The linear and nonlinear structural models are created in OpenSEES, the control system in MATLAB; and the TCP/IP connection method was used to connect two programs. The fuzzy decision system is based on accelerating and decelerating movement. The structure has been subjected to seven earthquakes with maximum accelerations of 0.1 g to 1.0 g with an incremental step of 0.1 g. According to the results of incremental dynamic analysis, the average percentage of the fuzzy control system performance reduction, considering the time delay, is 15.28% and 38.57% for the maximum displacement and base shear in the linear structure, and 8.04% and 5.97% for the nonlinear structure, respectively. The assumed time delays have been effectively overcome using the model algorithmic control system (MAC), determining the prediction horizon of the structural behavior, and optimizing the control force in the control horizon. The performance of the MAC control system has been better than the fuzzy control system and the passive control with TMD. The average improvement percentage of the results of the maximum linear and nonlinear structural displacement response is respectively equal to 10.2 and 11.8 with the MAC control system, compared to the fuzzy control system without time delay. For the maximum base shear, it is equal to 8.32 and 2.49, respectively.

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.

PI CONTROLLER DESIGN FOR TIME DELAY SYSTEMS USING DIFFERENT MODEL ORDER REDUCTION METHODS

This study focuses on designing PI controllers for time-delay systems using various model order reduction techniques to reduce complexity. The stability boundary locus method was used to determine PI parameters that stabilizing reduced order models. After the PI parameters have been determined using the weighted geometric center method, the calculated controller parameters have been implemented in the original system. In this way, the efficiency of the controller design is effectively demonstrated through the reduction techniques. In addition, the study investigated the effectiveness of reduction methods with increasing time delay and adding an integrator to the system. The importance of these results is that they demonstrate the use of model order reduction techniques in the design of controllers for time-delay systems and reveal the advantages of these methods.

Active Disturbance Rejection Fractional-Order Independent Control of Time Delay Systems With Application to Air Floating Motion Platform

Active Disturbance Rejection Fractional-Order Independent Control of Time Delay Systems With Application to Air Floating Motion Platform

Mechanism of time-delay feedback control of suspension damping with an annular vibration-absorbing structure

With the aim of enhancing both the ride comfort and the safety of the vehicle, we propose a new type of suspension with an annular vibration-absorbing structure, and establish a 3-DOF 1/4 vehicle model. The structure parameters and time-delay feedback control parameters are determined by particle swarm optimization algorithms, which take the root mean values of body acceleration, suspension dynamic deflection, and tire dynamic displacement as their optimization objectives. We analyze the stability of the suspension control system to ensure the stability of the time-delay control system through the Routh-Hurwitz stability criterion, characteristic root method, and stability switching method. Then, we compare and analyze the response characteristics of conventional suspension, new suspension without time-delay feedback control, and new suspension with time-delay feedback control under simple harmonic excitation and random excitation. The results show that the new suspension with time-delay feedback control has a significant damping effect on the body under the premise of ensuring the stability of the system.

ADRC for a piezoelectric plate with delays and disturbances via frequency response method: Design, analysis and experiments

A large number of uncertainties such as external excitement, model parameter perturbation, complex boundary conditions, time delays, seriously impact the operation of the piezoelectric plate structure. Therefore, an active disturbance rejection controller is designed and implemented based on an extended state observer to address such issues. The controller designed is analyzed in frequency-domain to address the time delays introduced by the sensors, actuators, communicational networks, computational delays, etc. Knowing that the accurate models are difficult to build, the Lissajous graphics and frequency test methods, hence, are implemented to estimate the delay and model parameters of the system. The stability characteristics and performance are verified via two intuitive frequency response methods, the small gain theorem and the Nyquist diagram. Bedsides, the relationship between time delays and control parameters is quantified, which enables controller parameters to be adjusted according to frequency index. This is the first attempt to use the small-gain theorem, which is favored for its numerical precision and computational efficiency, to analyze the active disturbance rejection control of time-delay systems. A case of a disturbed all-clamped piezoelectric plate with delays is, in particular, tested under a hardware-in-the-loop benchmark. Theoretical and experimental results show the effectiveness of the proposed approach to suppress the structure vibration in the presence of delays and disturbances.

Retracted: Application Research of Time Delay System Control in Mobile Sensor Networks Based on Deep Reinforcement Learning

Retracted: Application Research of Time Delay System Control in Mobile Sensor Networks Based on Deep Reinforcement Learning

Event-triggered [formula omitted]-gain control for networked systems with time-varying delays and round-robin communication protocol

This paper studies the event-triggered (ET) L2-gain control issues for time-delay networked control systems (NCSs) subject to round-robin protocol. The considered NCS consists of n sensor nodes, where the communication from the sensors to the controller is scheduled by round-robin protocol. This protocol requires that, at every sampling instant, only one sensor is chosen to use the sensor/controller network and transmits its measurement information toward the controller. On the other hand, the ET strategy is adopted in the controller/actuator network, which means that the actuator will receive the updated control input signal in the situation that the predefined ET conditions are satisfied. The utilization of round-robin protocol and ET strategy will help to relieve the burden of network transmission. The network resources and bandwidth will be saved. By developing appropriate Lyapunov functional, sufficient conditions in matrix inequalities are established in order to achieve the stability and L2-gain of the studied systems. Then, a novel iterative algorithm is presented to solve the derived stability conditions so as to design the controllers and obtain the minimal L2-gain simultaneously. Two examples are executed at last to demonstrate the validness and benefits of our results.

Lyapunov-based robust optimal control for time-delay systems with application in milling process

In this paper, we propose an optimal delay-independent robust controller based on the Lyapunov–Krakovskii theorem for the milling process as a time-delay system in the presence of varying axial depth of cut and different parametric uncertainty, such as stiffness, damping, etc. Milling is widely used in the manufacturing processes for the production of complex-shaped workpieces with high accuracy. However, chatter is a self-excited vibration that may cause adverse effects, such as tool damage, poor surface quality, excessive noise, etc. The dynamic model of the milling process is considered a two-dimensional time-delay system. A nonlinear programming with linear matrix inequality constraints is solved in order to obtain the controller gain where the objective function is corresponding to the norm-2 of controller gain, and the constraints guarantee robust stability. Using the semi-discretization method, stability lobes are shown in both uncontrolled and controlled plants to illustrate the improvement of the stable region via the proposed controller. Bifurcation phenomena have been improved with this controller by postponing the adverse effects to the higher values of the axial depth of cut, reducing the amplitude of limit cycles, and changing the type of bifurcation. Finally, we will compare the proposed controller with an intelligent controller in order to show the efficiency of the proposed method. It is shown that the proposed controller has improved the integral absolute error index by about 3.65 times compared with the intelligent controller.

Control of time-delay systems through modified Smith predictor using sliding mode controller

Smith-Predictor (SP) is used as a dead-time compensating tool for chemical processes as they are Integrating-Plus-Dead-Time (IPDT), pure integrating-type process, and higher-order-integrating-process. The performances of these processes can be improved by modifying SP. The present work deals with the control of dead-time by integrating the first-order-plus-dead-time (IFOPDT) or first-order-plus-dead-time process (FOPDT), and a modified sliding-mode-controller (SMC) in the proposed modified-Smith-predictor (MSP) structure. Here, a modified novel SMC discontinuous tuning-parameter is derived analytically to satisfy performance criteria such as speed adjustment, reducing overshoot and chattering effects. Furthermore, the MSP-SMC structure is implemented in six different processes. This is done to counteract time-delay and constant load-disturbance for integrating processes and a nonlinear system separately. Also, the proposed work is implemented in the real-time lab setup of a neutralisation process. Furthermore, the robustness and invariance properties of the SMC have been analysed against parametric uncertainty. The optimality of the proposed controller parameters is tested by giving uncertainty in the dead time of the process parameters. The proposed design is also implemented in the non-linear and Multi-Input-Multi-Output processes. The performance metrics, IAEs, of 6 case studies have been obtained using MATLAB and the peak overshoots are compared with similar kinds of works.

Delay Compensation of Neutral-Type Time-Delay Control Systems by Cascaded-Observers

Delay Compensation of Neutral-Type Time-Delay Control Systems by Cascaded-Observers

Control barrier functionals: Safety‐critical control for time delay systems

AbstarctThis work presents a theoretical framework for the safety‐critical control of time delay systems. The theory of control barrier functions, that provides formal safety guarantees for delay‐free systems, is extended to systems with state delay. The notion of control barrier functionals is introduced, to attain formal safety guarantees by enforcing the forward invariance of safe sets defined in the infinite dimensional state space. The proposed framework is able to handle multiple delays and distributed delays both in the dynamics and in the safety condition, and provides an affine constraint on the control input that yields provable safety. This constraint can be incorporated into optimization problems to synthesize pointwise optimal and provable safe controllers. The applicability of the proposed method is demonstrated by numerical simulation examples.

Design and analysis of active disturbance rejection control for time-delay systems using frequency-sweeping

For the typical first-order systems with time-delay, this paper explors the control capability of linear active disturbance rejection control (LADRC). Firstly, the critical time-delay of LADRC is analyzed using the frequency-sweeping method and the Routh criterion, and the stable time-delay interval starting from zero is accurately obtained, which reveals the limitations of general LADRC on large time-delay. Then in view of the large time-delay, an LADRC controller is developed and verified to be effective, along with the robustness analysis. Finally, numerical simulations show the accuracy of critical time-delay, and demonstrate the effectiveness and robustness of the proposed controller compared with other modified LADRCs.

An Approach for the Stability of Communication Constrained Networked Time-delay Control Systems

An Approach for the Stability of Communication Constrained Networked Time-delay Control Systems

The Effect of Virtual Inertia and Damping Control on the Stability Region of Load Frequency Control Systems with Time Delays

This article examines the effect of virtual inertia and damping (VID) control on the stability regions of time-delayed load frequency control (LFC) systems. Because of the substantial integration of renewable energy sources (RES) and the utilization of an open communication network for sending/receiving data and control signals, the system inertia significantly decreases, and inevitable delays are observed, both of which adversely affect the controller performance and frequency stability. For improving the stability of LFC systems including RES and delays, this study proposes the integration of the VID control and determines stability regions using the method of stability boundary locus. The regions’ boundaries are substantiated by time-domain simulations and a quasi-polynomial mapping-based root finder (QPmR) algorithm. A wide-ranging evaluation of the VID coefficients’ effects on the stability region and the system’s frequency response are presented. Results evidently divulge that with the integration of the VID control, stability regions get larger, the frequency dynamic is improved, and unstable LFC systems with delays are stabilized.

Application of Empirical Bode Analysis for Delay-Margin Evaluation of Fractional-Order PI Controller in a Renewable Distributed Hybrid System

For an uninterrupted power supply, renewable energy promises to be a suitable alternative compared to the conventional sources. System delays or communication delays may cause significant synchronization imbalances between various components in big electrical grids. Since the properties of solar and wind generation constantly change with climatic circumstances, engineers encounter many difficulties when substituting sustainable power with conventional electricity. The computation delay margin may be leveraged to handle a time-delayed automatic generation control (AGC) system. In order to regulate a distributed hybrid renewable energy system in a three-area AGC configuration, this paper investigates the influence of the fractional integral order on the stable system’s delay parameter region. By changing the fractional order range, the delay margin can be increased, potentially broadening the time-delayed system’s stability region. The controller’s stability region has dependency on the order of fraction and the time delay. For this purpose, the asymptotic Bode diagram of the time-delayed fractional proportional-integral controller is determined. The gain and phase margins are used to calculate the delay margin for the application in discussion. The Honey Badger algorithm helps to adjust the controller parameters. It is also confirmed that the suggested controller is resilient to random load perturbations, nonlinearities, and parameter variations.

Predictive Extended State Observer-Based Active Disturbance Rejection Control for Systems with Time Delay

The latest research on disturbance rejection mechanisms has shown active disturbance rejection control (ADRC) to be an effective controller for uncertainties and nonlinear dynamics embedded in systems to be controlled. The significance of the ADRC controller is its model-free nature, as it requires minimal knowledge of the system model. In addition, it can actively estimate and compensate for the impact of internal and external disturbances present, with the aid of its crucial subsystem called the extended state observer (ESO). However, ADRC controller design becomes more challenging owing to different system disturbances, such as output disturbances, measurement noise, and varying time-delays persistent in the system’s communication channels. Most disturbance rejection techniques aim to reduce internal perturbations and external disturbances (input and output disturbance). However, output disturbance rejection with measurement noise under time-delay control is still a challenging problem. This paper presents a novel predictive ESO-based ADRC controller for time-delay systems by employing predictive methods to compensate for the disturbances originating from time delay. The prediction mechanism of the novel (proposed) controller design is greatly attributed to the extended state predictor observer (ESPO) integrated with the delay-based ADRC inside the proposed controller method. Thus, the proposed controller can predict the unknown system dynamics generated during the delay and compensate for these dynamics via disturbance rejection under time-delay control. This approach uses the optimization mechanism to determine controller parameters, where the genetic algorithm (GA) is employed with the integral of time-weighted absolute error (ITAE) as the fitness function. The proposed controller is validated by controlling second-order systems with time delay. Type 0, Type 1, and Type 2 systems are considered as the controlled plants, with disturbances (unknown dynamics due to delay and external disturbance), along with measurement noise present. The proposed controller method is compared with state-of-the-art methods, such as the modified time-delay-based ADRC method and the ESPO-based controller method. The findings indicate that the method proposed in this paper outperforms its existing competitors by compensating for the dynamics during the time delay and shows robust behaviour, improved disturbance rejection, and a fair extent of resilience to noise.