Variable Time Delay System Research Articles

Sliding-mode fault-tolerant control of the six-rotor UAV with dead-zone-input under event-triggered mechanism

This paper investigates the problem of event-triggered mechanism(ETM)-based sliding-mode fault-tolerant control (FTC) for a six-rotor Unmanned Aerial Vehicle (UAV) with dead zone input (DZI) cases, considering potential actuator and sensor faults. Initially, a dynamic ETM is designed, followed by the development of a non-fragile observer utilizing this designed ETM. An integral sliding surface (SS) is then designed in the observation space, and the system is augmented and treated as a variable time delay system. Subsequently, sufficient conditions to ensure the stability of the augmented system with an H∞ performance index γ are obtained using the Lyapunov-Krasovskii function. Next, a sliding mode control (SMC) law is formulated to guide the sliding variables to the SS in finite time. Furthermore, sufficient conditions for ensuring system stability with an H∞ performance index γ are decoupled, and the calculation methods for the non-fragile observer gain matrix and the sliding mode gain matrix are obtained. Finally, to validate the effectiveness of the proposed method in this paper, simulation experiments are conducted.

State estimation and sliding-mode fault-tolerant control of a class of nonlinear systems with actuator faults under the event-triggered mechanism

The current work is an analytical study of the problem of state estimation and fault-tolerant control (FTC) based on dynamic event triggered mechanism (ETM) in the event of actuator fault for a class of nonlinear systems in a network environment. First, a state estimator module is designed in conjunction with the designed dynamic ETM, and an integral sliding surface (SS) is designed in the estimation space to obtain a variable time delay system after augmenting the system by combining the state estimator module and the SS. Second, the sufficient conditions that can make the augmented system stable under the ETM with H∞ performance index are obtained by the Lyapunov–Krasovskii function. The sufficient conditions are decoupled after the design of the sliding mode control (SMC) law that can stabilize the system, and the calculation of the state estimation gain matrix and the SMC gain matrix are obtained. Finally, the effectiveness of the method proposed in this study is verified with two simulation comparison experiments.

Fault diagnosis and fault-tolerant control design for neutral time delay system

This paper presents a new approach of fault-tolerant control (FTC) for the transmission line as a neutral variable time-delay system. The main goal of this work guarantees faulty neutral variable time delay system stabilization using the state feedback control design based on Lyapunov function and the Linear Matrix Inequality resolution. The use of the FTC method is to achieve actuator and sensor fault compensation. This method is based on two steps. The first one is the synthesis of a nominal control, which remains to maintain the closed-loop system stability. The second step is based on adding a new control law to the nominal one to compensate the fault effect on system behaviour and maintain the desired performance in the closed loop system. Then, a conception of an adaptive observer is used to detect and estimate the fault. Finally, the developed approach is applied for the transmission line. The given results are presented to prove the effectiveness of this approach.

Observer design for a class of nonlinear systems under a persistent excitation

The problem of state reconstruction from input and output measurements for nonlinear time delay systems remain open in many cases. In this paper we propose an adaptive observer to solve this problem for a class of unknown variable time-delay nonlinear systems where the state matrix depends on the input persistency excitation. To achieve this we combine the use of a Kalman-like observer with a suitable choice for the Lyapunov-Krasovskii functional. This is done under a sufficient number of hypothesis to guarantee the convergence of the observer inside a sphere depending of the delay upper bound. The proposed strategy is tested in simulation by considering a mixed piece-wise and sinusoid time delay function and its efficiency when the problem of persistency excitation occurs.

Synchronizing a class of uncertain and variable time-delay fractional-order hyper-chaotic systems by adaptive sliding robust mode control

In view of a class of synchronization problems about uncertain and variable time-delay systems, this paper puts forward a method of adaptive sliding robust control. Based on the Lyapunov stability theory and adaptive sliding mode control methods, the adaptive sliding robust controllers and the parameter adaptive rate are designed. A single controller designed by the synchronous control method is applicable to the synchronizing of a class of fractional-order hyper-chaotic systems, and it has a great ability to resist noise-perturbed. What is more, it can also well control the time-varying time-delay systems. So the controller is of highly practical value. Furthermore, by introducing a certain amount of compensation into the system, the influences of the uncertainty and the noise-disturbance can be eliminated, thus the synchronization of the uncertainty fractional-order hyper-chaotic system is realized. In addition, the control of the synchronous errors of the systems can be stable in arbitrarily small domain. Finally, time-varying and time-delay fractional-order Chen's hyper-chaotic systems with the external noisy disturbances and uncertain parameters are numerically simulated, and the effectiveness of the proposed control method is verified.

Inverse chaos synchronization between bidirectionally coupled variable multiple time delay systems

We make first report on inverse chaos synchronization between bidirectionally non-linearly and linearly coupled variable multiple time delay laser systems governed by the Ikeda model. The results are of certain importance in secure chaos-based communication systems.

Closed-loop identification using Laguerre orthogonal functions for a virtual diesel engine

This paper provides a paradigm consisting of a closed-loop system identification algorithm in terms of Laguerre orthogonal functions to handle variable transport time delay system. The identification algorithm does not require any special excitation signal. Two-closed-loop transfer functions (time domain and frequency domain) from the set point signal to the control input and output are identified using Laguerre orthogonal functions. A plant model is then computed based on the two-closed-loop transfer functions. We perform the entire design and simulation on a virtual diesel engine developed by Cummins Engine Company.

Generalized projective synchronization in time-delayed systems: Nonlinear observer approach

In this paper, we consider the projective-anticipating, projective, and projective-lag synchronization in a unified coupled time-delay system via nonlinear observer design. A new sufficient condition for generalized projective synchronization is derived analytically with the help of Krasovskii-Lyapunov theory for constant and variable time-delay systems. The analytical treatment can give stable synchronization (anticipatory and lag) for a large class of time-delayed systems in which the response system's trajectory is forced to have an amplitude proportional to the drive system. The constant of proportionality is determined by the control law, not by the initial conditions. The proposed technique has been applied to synchronize Ikeda and prototype models by numerical simulation.

Performance Analysis of EWMA Controllers Subject to Metrology Delay

Metrology delay is a natural problem in the implementation of advanced process control scheme in semiconductor manufacturing systems. It is very important to understand the effect of metrology delay on performance of advanced process control systems. In this paper, the influences of metrology delay on both the transient and asymptotic properties of the product quality are analyzed for the case when a linear system with an initial bias and a stochastic autoregressive moving average (ARMA) disturbance is under an exponentially weighted moving average (EWMA) run-to-run control. Tuning guidelines are developed based on the study of numerical optimization results of the analytical closed-loop output response. In addition, effective metrology delay of a variable time delay system is analyzed based on the resampling technique implemented to a randomized time delay system. A virtual metrology technique is a possible solution to tackle the problem of metrology delay. The tradeoff between additional error of virtual metrology and reduction in time delay is studied. The results are illustrated using an example of control of the tungsten deposition rate in a tungsten chemical-vapor deposition reactor. The basic conclusion is that metrology delay is only important for processes that experience nonstationary stochastic disturbance. In such a case, use of virtual metrology is justified if the error of the virtual metrology method is less than the error caused by stochastic process noise. The accuracy of the virtual metrology noise with respect to the traditional metrology is not critical, provided that the error due to metrology is much less than that due to process disturbances.

Variable time-delay system for broadband phased array and other transversal filtering applications

A variable time-delay system for broadband phased array receiving and other transversal filtering applications is presented. The approach uses a segmented mirror device (SMD) and a linear fiber array to realize a quantized variable delay line. The use of the SMD allows for extremely high packing density withoutthe large losses usually associated with switched fiber schemes. The system presented is compatible with a SMD-based true time-delay transmitter that has been developed. Experimental results are presented.

Robust Self Tuner for Variable Time Delay Systems

A robust self tuner is presented for systems with unknown or variable time delay systems. A stability protection function is included in the controller to safeguard against instability caused by changes in the time delay of the process. Based on the behaviour of the self tuner in variable time delay systems, a simple time delay tracking technique is used to track the estimated process time delay parameter d0 every r sampling periods. Robustness of the proposed self tuner is achieved by combining the above two techniques. A simulation example will be presented to illustrate the proposed self tuner

Robust Protection-time Delay Tracing Adaptive Control and its Application

In this paper, Robust protection–Time delay tracing Adaptive Control (RTAC) is presented. A large number of Simulation results Show that RTAC can be effectively applied to control systems with variable time—delay and unknown parameters, and that its control properties can perform minimum variance, thus proving superior to those of the classical adaptive algorithms for the above systems. Especially in cement manufacture, RTAC has successfully been applied to the microcomputer control system of the ball mill, which has a variable and overlong delay. In this way, cement production has been largely increased. Application and simulation experiments all demonstrate that this method has satisfactorily solved the control problems of variable time—delay systems, and that it has possessed a strong robustness and the ability to identify the process time—delay. Therefore it has avoided the main disadvantages of many adaptive control techniques.

Analysis of time-delay systems using the Galerkin method

This paper is concerned with the analysis of a time-varying, variable time-delay system using the Galerkin method. The approximate solution is expanded in a set of shifted Legendre polynomials with unknown expansion coefficients. A delay matrix is derived to manipulate the time delay. The original delay-differential equation is converted to a set of algebraic equations through setting the weighted integrals of the residual to zero. An approximate shifted Legendre series solution to the time delay system is thus obtained by solving the resultant algebraic equations. Numerical results are provided to illustrate the applicability of the method.

AN OPTIMAL CONTROLLER FOR DISCRETE TIME DELAY SYSTEMS REQUIRING NO PREDICTION

The fact that the most popular techniques available for handling time delay problems in process control involve prediction, coupled with the very notion of a time delay, and its unique effect on process dynamics, have led to the following general consensus: that any systematic treatment of the controller design problem for time delay systems must result in controllers that require prediction. The traditional problem faced by these controllers in practice however, has been that of obtaining acceptable predictions using unavoidably imperfect mathematical models of the plant's dvnamic behavior. While this may not necessarily constitute an insurmountable barrier, a means by which the prediction problem may be totally circumvented is presented in this paper. An optimal controller which does not require prediction is derived for a discrete, single variable time delay system. The controller is compared with others which handle time delay problems and its performance tested on a simulation example of practical engineering interest. It is also shown how time varying time delay problems may be handled by this controller

An Implicit Self-Tuning Controller for Variable Time Delay Systems

Abstract Implicit self-tuning controllers which incorporate prediction over the maximum time delay of the process being controlled run into difficulties when significant variations in the process delay occur. This paper shows how these difficulties arise and propose a self-tuning algorithm which can cope with wide variations in process delay requiring only a knowledge of the maximum delay value. The capability of the proposed technique is demonstrated by its application to the temperature control loop of a research nuclear reactor.

Stability of a system with variable time delay

In this paper the stability problem of a first-order system with time- or state-variable time delay is investigated and the proposition that the time-varying system is not always stable (unstable) even if the frozen-time system is stable (unstable) is verified for a variable time delay system by several examples.

Optimal periodic control of variable time-delay systems

Periodic control of a general class of dynamic systems involving state and control dependent time delays is considered. Variational analyses yield a necessary condition for optimality and a sufficient condition for proper periodicity. The latter result is applied to analyse a single input-single output example.

A Highly Stable Variable Time-Delay System

This paper describes a variable time-delay system having time jitter less than 0.00025 μsec, which is equivalent to 2.5 parts per million of its maxmum time delay. To achieve this stability, time delay in this system is accomplished exclusively by means of linear bilateral elements. A distributed amplifier is used to compensate the losses in the delay elements. Due to the fact that only a limited number of elements can be installed in a practical circuit, the signal pulse is permitted to travel through each delay element many times in order to increase the amount of total time delay. One of the experimental units having a total time delay up to 100 μsec in step of 1 μsec has been found to be satisfactory. The usual causes of time jitter in conventional time-delay circuits such as, variations of cut-off characteristics, noise, hum, and fluctuations of supply voltages, cannot affect the stability of this system. Practical circuits as well as experimental results are described.