Control Of Time-delay Systems Research Articles

On the initial function space of time-delayed systems: A time-delayed feedback control perspective

We address the problem as if the initial function space of a time-delayed system can be finite-dimensional. We argue that the dimension of the initial function space of a time-delayed feedback control system is just identical to that of the corresponding plant which is to be controlled, and so is finite-dimensional in many cases. We prove this property by constructing an injection map between the two spaces. We anticipate that this may also be applied to some other systems, such as ecological processes involving time delays without control. We believe that the significance of this discovery not only makes available the physical interpretation and intuitional explanation of the basins of attraction associated with time-delayed feedback control, but also suggests the principle as how to evaluate the robustness of the time-delayed feedback control schemes to external disturbances. We finally visualize and illustrate such basins of attraction via numerical simulation for the classical Duffing system by equipping it with the velocity time-delayed feedback control.

Tutorial on Lyapunov-based methods for time-delay systems

Time-delay naturally appears in many control systems, and it is frequently a source of instability. However, for some systems, the presence of delay can have a stabilizing effect. Therefore, stability and control of time-delay systems is of theoretical and practical importance. Modern control systems usually employ digital technology for controller implementation, i.e. sampled-data control. A time-delay approach to sampled-data control, where the system is modeled as a continuous-time system with the delayed input/output became popular in the networked control systems, where the plant and the controller exchange data via communication network. In the present tutorial, introduction to Lyapunov-based methods for stability of time-delay systems is given together with some advanced results on the topic.

An Improved Receding Horizon Control for Time-Delay Systems

In this paper, we propose an improved version of receding horizon control for systems with state delays. The proposed control guarantees closed-loop stability for a wider class of state-delay systems than the existing one. For expanded applications, a more generalized cost function, with three terminal weighting terms, is employed and minimized. Terminal weighting matrices are chosen to achieve the property that the optimal cost monotonically decreases with time. It turns out that the stability condition depends on the delay size and then it is less conservative than the existing delay-independent one. The simulation study shows that the proposed control scheme guarantees closed-loop stability even for state-delay systems that cannot be stabilized by the existing receding horizon control.

Design of Fractional–order PID Controllers for Time Delay Systems using Differential Evolution Algorithm

This paper aims to club on the scheme of Fractional-Order Proportional-Integral-Derivative (FOPID) controllers for time delay systems. The way is based on a composition of the DE algorithm and the Smith predictor control method to arrive meliorated control efficiency of the time delay process. Lately, Differential Evolution (DE) has been transpired as an ordinary but very powerful materiel for real parameter optimization. Parameters of FOPID controllers consisted proportionality constant, integral constant, derivative constant, derivative order and integral order, thus its scheme is more intricate than that of conventional integer-order Proportional-Integral-Derivative (PID) controller. Manufacturing of the controller portrayed here is based on user- specified peak overshoot and settling time and has been formulated as a single objective optimization issue. Finally, better simulation results and control performance of the Fractional-Order PID (FOPID) will be showed in these controllers in collation with those of the integer-order PID controllers. Keywords: Differential Evolution, Fractional Order Controller, Smith Predictor Control, Time Delay System

Design of Fractional-order PID Controllers for Time Delay Systems Using Differential Evolution Algorithm

This paper aims to club on the scheme of Fractional-Order Proportional-Integral-Derivative (FOPID) controllers for time delay systems. The way is based on a composition of the DE algorithm and the Smith predictor control method to arrive meliorated control efficiency of the time delay process. Lately, Differential Evolution (DE) has been transpired as an ordinary but very powerful materiel for real parameter optimization. Parameters of FOPID controllers consisted proportionality constant, integral constant, derivative constant, derivative order and integral order, thus its scheme is more intricate than that of conventional integer-order Proportional-Integral-Derivative (PID) controller. Manufacturing of the controller portrayed here is based on user- specified peak overshoot and settling time and has been formulated as a single objective optimization issue. Finally, better simulation results and control performance of the Fractional-Order PID (FOPID) will be showed in these controllers in collation with those of the integer-order PID controllers.

Optimal sign inverting control for time-delayed systems, a concept study with experiments

An intriguing control logic, sign inverting control (SIC) is considered for control systems with delayed feedback. It starts with a nominal control law formulated for non-delayed case and simply inverts the sign of the control gains for some surprising benefits when used with the delays. This operation sounds paradoxical as the sign inversion potentially harms the stability of the non-delayed dynamics. However, SIC with large delays may yield some complementary benefits to the nominal control logic from delay robustness perspective. The main question we address in this paper is ‘How to select the nominal control law so that such a contribution can be (a) feasible, (b) optimal in some sense?’ A structured methodology is proposed to achieve this, starting with a linear quadratic regulator based controller. A single scaling factor on the corresponding control gains is used for one-dimensional optimisation. Experimental validation of the concept of this optimal SIC procedure is also reported on a single-axis manipulator.

H∞ state-feedback control of time-delay systems using reciprocally convex approach

In this paper, state-feedback H∞ control of systems with time-varying delay is considered. The time-delay is assumed to be a time-varying continuous function which is bounded below and above by positive constants. The reciprocally convex approach based on linear matrix inequality (LMI) optimization is adapted to design the H∞ state feedback control law. For the illustrative examples the physical model of liquid monopropellant rocket motor with a pressure feeding system and the problem of controlling the yaw angles of a satellite system with delays are considered along with their numerical simulations to show effectiveness of derived results. Furthermore few other numerical examples are also given to illustrate the advantages of the derived results.

New delay-dependent stability criteria and robust control of nonlinear time-delay systems

This paper investigates the stability analysis and H∞ control for a class of nonlinear time-delay systems, and proposes a number of new results. Firstly, an equivalent form is given for this class of systems by means of coordinate transformation and orthogonal decomposition of vector fields. Then, based on the equivalent form, some delay-dependent results are derived for the stability analysis of the systems by constructing a novel Lyapunov functional. Thirdly, the authors use the equivalent form and the obtained stability results to investigate the H∞ control problem for a class of nonlinear time-delay control systems, and present a control design procedure. Finally, an illustrative example is given to show the effectiveness of the results obtained in this paper. It is shown that the main results of this paper are easier to check than some existing ones, and have less conservatism.

Linear quadratic Gaussian control for linear time‐delay systems

This study investigates a separation principle for the H 2 control of time-delay systems with partial observations. The authors first consider the linear quadratic regulation problem for time-delay systems. Based on the dynamic programming technique, the solution to the controller is given in terms of a backward partial difference Riccati equation. Then the estimation problem is investigated for linear discrete-time systems in the presence of time-delays. By employing the innovation analysis approach, the linear minimum-mean-square error (LMMSE) estimator is developed in terms of a forward partial difference Riccati equation. The Riccati equation is of the same dimension as the plant. Therefore compared with the conventional augmented approach, the presented approach greatly lessens the computational demand when the delay is large. Finally, they show that the separation principle holds in the following sense: an optimal controller can be obtained from two parts, one associated with the optimal control problem when state variable is available, and the other one associated with the LMMSE estimation problem.

A Singular System Approach to Output Feedback Sliding Mode Control for Time-delay Systems

摘要: 利用一种奇异系统方法讨论了时滞系统的输出反馈滑模控制问题. 时滞系统的非线性项满足范数有界约束.首先,将滑动模态与线性切换面作为一个奇异时滞系统,基于奇异时滞系统的稳定性理论, 给出滑动模态稳定及切换面存在的线性矩阵不等式(Linear matrix inequality, LMI)充分条件.然后,给出使得系统闭环渐近稳定的静态输出反馈滑模控制器的设计方法,此控制器保证闭环 系统有限时间到达切换面.最后,用数值算例验证本文方法的有效性和正确性. 关键词: 时滞系统 / 滑模控制 / 奇异系统方法 / 静态输出反馈 / 线性矩阵不等式

Approximation of distributed delays

In this paper, we address the approximation problem of distributed delays. These elements are convolution operators with kernel having bounded support and appear in the control of time-delay systems. From the rich literature on this topic, we propose a general methodology to achieve such an approximation. For this, we enclose the approximation problem in the graph topology, and working on the convolution Banach algebra, a constructive approximation is proposed. Analysis in time and frequency domains is provided. This methodology is illustrated on the stabilization control for time-delay systems.

A Matter of Timing

A regulatory circuit controlling plant flowering genes leads the way to reconstruction of a time-delay control system.

A modified bacterial foraging optimised PID controller for time delay systems

This paper presents design of an optimised PID controller for single input single output (SISO) systems with time delay. The three control parameters K

Fault Diagnosis and Fault Tolerant Control for Non-Gaussian Singular Time-Delayed Stochastic Distribution Systems

New integrated fault diagnosis (FD) and fault tolerant control (FTC) algorithm for non-Gaussian singular time-delayed stochastic distribution control (SDC) system is proposed in the paper. Different from general SDC systems, in singular time-delayed SDC systems, the relationship between the weights and the control input is expressed by a singular time-delayed state space model, which largely increases the difficulty in the FD and FTC design. An iterative learning observer (ILO) is designed to carry out the fault estimation. The influence of the time delay term is eliminated in the process of the proof of the observation error stability. The fault may be constant, slow varying, or fast varying. Combined with the switching control theory, based on the estimated fault information, the fault tolerant controller can be designed to make the postfault probability density function (PDF) still track the given distribution. Simulations are given to show the effectiveness of the proposed integrated FD and FTC algorithms.

Computation of Stability Delay Margin of Time-Delayed Generator Excitation Control System with a Stabilizing Transformer

This paper investigates the effect of time delays on the stability of a generator excitation control system compensated with a stabilizing transformer known as rate feedback stabilizer to damp out oscillations. The time delays are due to the use of measurement devices and communication links for data transfer. An analytical method is presented to compute the delay margin for stability. The delay margin is the maximum amount of time delay that the system can tolerate before it becomes unstable. First, without using any approximation, the transcendental characteristic equation is converted into a polynomial without the transcendentality such that its real roots coincide with the imaginary roots of the characteristic equation exactly. The resulting polynomial also enables us to easily determine the delay dependency of the system stability and the sensitivities of crossing roots with respect to the time delay. Then, an expression in terms of system parameters and imaginary root of the characteristic equation is derived for computing the delay margin. Theoretical delay margins are computed for a wide range of controller gains and their accuracy is verified by performing simulation studies. Results indicate that the addition of a stabilizing transformer to the excitation system increases the delay margin and improves the system damping significantly.

Design of Stable and Robust Controllers for Time-Delay Systems

Design of Stable and Robust Controllers for Time-Delay Systems

New Results on Robust Model Predictive Control for Time-Delay Systems with Input Constraints

This paper investigates the problem of model predictive control for a class of nonlinear systems subject to state delays and input constraints. The time-varying delay is considered with both upper and lower bounds. A new model is proposed to approximate the delay. And the uncertainty is polytopic type. For the state-feedback MPC design objective, we formulate an optimization problem. Under model transformation, a new model predictive controller is designed such that the robust asymptotical stability of the closed-loop system can be guaranteed. Finally, the applicability of the presented results are demonstrated by a practical example.

Quasipolynomial Approach to Simultaneous Robust Control of Time-Delay Systems

A control law for retarded time-delay systems is considered, concerning infinite closed-loop spectrum assignment. An algebraic method for spectrum assignment is presented with a unique optimization algorithm for minimization of spectral abscissa and effective shaping of the chains of infinitely many closed-loop poles. Uncertainty of plant delays of a certain structure is considered in a sense of a robust simultaneous stabilization. Robust performance is achieved using mixed sensitivity design, which is incorporated into the addressed control law.

Fault diagnosis and fault tolerant control for the non-Gaussian time-delayed stochastic distribution control system

The purpose of fault diagnosis of stochastic distribution control (SDC) systems is to use the measured input and the system output probability density functions (PDFs) to obtain the fault information of the SDC system. When the target PDF is known, the purpose of fault tolerant control of stochastic distribution control system is to make the output PDF still track the given distribution using the fault tolerant controller. However, in practice, time delay may exist in the data (or image) processing, the modeling and transmission phases. When time delay is not considered, the effectiveness of the fault detection, diagnosis and fault tolerant control of stochastic distribution systems will be reduced. In this paper, the rational square-root B-spline is used to approach the output probability density function. In order to diagnose the fault in the dynamic part of such systems, it is then followed by the novel design of a nonlinear neural network observer-based fault diagnosis algorithm. The time delay term will be deleted in the stability proof of the observation error dynamic system. Based on the fault diagnosis information, a new fault tolerant controller based on PI tracking control is designed to make the post-fault probability density function still track the given distribution, which is dependent of the time delay term. Finally, simulations for the particle distribution control problem are given to show the effectiveness of the proposed approach.

Optimal control of time-varying linear delay systems based on the Bezier curves

In this paper, time-delay control systems with quadratic performance are solved by applying the least square method on the Bezier control points. The approximation process is done in two steps. First, the time interval is divided into $$2k$$ subintervals, then in each subinterval the trajectory and control functions are approximated by the Bezier curves. We have chosen the Bezier curves as piecewise polynomials of degree $$n$$ and determined the Bezier curves on any subinterval by $$n+1$$ control points. By considering a least square optimization problem, the control points can be found, then the Bezier curves that approximate the action of control and trajectory can be computed as well. Some numerical examples are given to verify the efficiency of the proposed method.