Input Time Delay Systems Research Articles

Passive and H ∞ control based on non-fragile observer for a class of uncertain nonlinear systems with input time-delay

In this paper, passive control and H ∞ state feedback based on non-fragile observer are presented for a class of uncertain, nonlinear and input time-delay systems. Firstly, taking uncertainties, nonlinearities and input time-delay into account, non-fragile observer and controller are designed and the perturbations of controller gain and observer gain are processed. Secondly, for the dynamic disturbances, an appropriate non-fragile state feedback controller based on the observation is selected to prove that the states of closed-loop system can be passive and stabilized with H ∞ performance for continuous time system. Moreover, the problems such as time-delay are handled in virtue of Lyapunov method and linear matrix inequalities (LMIs). Finally, the simulation results demonstrate the validity of the proposed control design method.

Predictive Feedback Control for Inventory Systems Subject to Delays and Constraints

In this paper, we discuss the inventory regulation problem of a logistic system composed of a production unit and inventory unit. The production system is characterized by a constant lead time, and the storage unit presents fixed losses due to perishable products. In this study, the system is subject to finite production resources, limited storage capacities, and the customer demands are uncertain in a given range. We address a control strategy to the input time delay system that is subject to positive and saturation constraints and to bounded disturbances. We apply a linear prediction feedback control strategy, in order to stabilize the closed-loop system and to fulfill the system constraints, so that necessary and sufficient conditions for the existence of an admissible control law are formulated.

Predictive disturbance-observer-based controller design for a class of input time-delay mechanical systems with input constraints

A predictive disturbance-observer-based controller (DOBC) is proposed for a class of input time-delay mechanical systems with input constraints. A predictive disturbance observer is developed for external disturbance and proof for exponential convergence of estimation error is provided. In the controller design process, the input integral is fed back into the controller to eliminate the effect of input delay, and the input integral method and hyperbolic tangent function are firstly combined to solve the problem of input delay and limit the control input simultaneously. The optimisation function FMINCON of MATLAB is used to obtain control parameters. Control goal realisation and the exponential stability of the closed-loop system are proven via the Lyapunov direct method. Simulation results verify the effectiveness of the proposed controller.

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.

Robust stabilization of an elementary logistic system with an input delay

In this paper, we are interested in the robustness analysis of an elementary logistic system having a fixed loss factor on the inventory level and uncertainties on the production delay. The problem is treated in control theory domain, where the model is considered as an input time delay system characterized by positivity and saturation constraints, and an external disturbance. Indeed, we apply a prediction state feedback control strategy using an affine control law, where the prediction of the future inventory level is based on a delay estimation of the delay uncertainty. Hence, the objective of the study is to quantify the impact of the uncertainty induced by this estimation on the performance of the controlled system. First, we use a frequency-domain technique to identify the robust stability condition in the set of parameters. In particular, we specify the range of the delay deviation such that the closed-loop system stability is guaranteed. Then, we move on to define the input-output flow variations that allows to check the system constraints, based on the invariance properties. Finally, a comparative simulation is provided to highlight the advantages of this study.

Disturbance‐prediction–based control of input time delay systems for rejection of unknown frequency disturbances

SummaryIn this paper, a novel disturbance rejection approach is presented for a class of input time‐delay systems subject to sinusoidal disturbances with unknown frequency. In particular, an auxiliary observer is proposed to represent the periodic disturbance in a parametric uncertainty form, where the unknown factor related to disturbance frequency can be estimated. Furthermore, the correlation between the future disturbance and the auxiliary observer output is analyzed, such that the future disturbances can be predicted and rejected through the input channel. Based on the aforementioned observer and predictor structure, the overall control architecture can be established as a framework of disturbance‐prediction–based control for systems with input time delays, where the conditions on the asymptotic stability of the closed‐loop systems are also derived. Finally, numerical examples are provided to illustrate the effectiveness of the proposed control approach.

Improved Synchronization Criteria for Coronary Artery Input Time-Delay System

This paper investigates the synchronization problems of the coronary artery input time-delay systems with disturbances based on $H_{\infty }$ control. By constructing novel Lyapunov–Krasovskii functionals and developing delay-partitioning methods, the synchronization criteria are established in view of a free-matrix-based integral inequality and an extended reciprocally convex matrix inequality, which further reduce the conservativeness. Then, a state feedback controller is designed to ensure the robust synchronization of the systems through the proposed matrix inequality. Finally, the simulation results for synchronization are presented to demonstrate the effectiveness of the proposed schemes.

H∞ Control of Coronary Artery Input Time-Delay System via the Free-Matrix-Based Integral Inequality

The issue of H∞ control for the coronary artery input time-delay system with external disturbance is of concern. To further reduce conservation, we utilize the free-matrix-based integral inequality, Wirtinger-based integral inequality, and reciprocal convex combination approach to construct Lyapunov-Krasovskii function (LKF). Then a sufficient condition for controller design which can guarantee robust synchronization the coronary artery system is represented in terms of linear matrix inequality (LMI). Finally, a numerical example is exploited to show the effectiveness of the proposed methods.

EID‐Estimation‐Based Periodic Disturbance Rejection for Sintering Ignition Process with Input Time Delay

AbstractSintering plays a key role in generating blast furnace burden in metallurgical processes. The continuous production and stable quality of sintering significantly depends on the stable and precise control of sintering ignition, which, however, is achieved through an input time delay system, and suffers from different and unknown disturbances. To reject disturbances and enhance the control precision of ignition temperature, this paper introduces a modified equivalent input disturbance (EID)‐based disturbance compensation that is suitable for controlling sintering ignition. First, the periodic properties of disturbances induced by gas pressure fluctuations are obtained based on spectral density decomposition. Second, to obtain the dynamics of sintering ignition, an iterative subspace modeling method is developed, which estimates not only the model parameters but also the length of time delay. By considering the periodic property, a control structure of sintering ignition based on the modified EID‐based compensation is proposed, in which an additional time‐delay element is designed to make the phase difference between EID estimation and real disturbance close to zero. Finally, the validity of the proposed method is verified by a simulation.

ADRC based control for a class of input time delay systems

ADRC based control for a class of input time delay systems

Robust Predictive Control for a Class of Multiple Time Delay Uncertain Systems with Nonlinear Disturbance

摘要: 针对一类具有非线性扰动且同时存在多重状态和输入时滞的不确定系统, 提出 一种鲁棒预测控制器设计方法. 基于预测控制滚动优化原理, 运用Lyapunov稳定性 理论和线性矩阵不等式 (Linear matrix inequalities, LMIs)方法, 首先近似求解无限时域二次性能指标优化问题, 然后优化非 线性扰动项所应满足的最大上界, 定量地研究鲁棒预测控制在范数有界意义下的扰动抑制 问题, 并给出了鲁棒预测控制器存在的充分条件. 最后通过仿真验证了所提方法的有效性. 关键词: 非线性扰动 / 鲁棒预测控制 / 线性矩阵不等式 / 时滞 / 不确定系统

Frequency domain subspace identification of commensurate fractional order input time delay systems

A frequency domain subspace identification of fractional order systems with input timedelay is studied in this paper. A new identification method, which combines the merits of differential evolution (DE) algorithm and subspace identification algorithm in frequency domain, is presented. For the optimal search of fractional commensurate differential order and time delay parameters, the DE algorithm is applied. For fixed fractional commensurate differential order and time delay, subspace method is performed to obtain the state space model. Simulation results validate the proposed fractional order system identification method.

Iterative design using IMC for input time-delay systems with disturbance observer

AbstractThis paper discusses the iterative design method of closed-loop identification and internal model control (IMC) for input time-delay systems with a disturbance observer. The IMC is known as an effective control method for time-delay systems; however, a precisely identified model is required for achieving effective control performance. High closed-loop performance is achieved by the iteration of the IMC and the closed-loop identification. Moreover, the disturbance observer requires the same precise model as the IMC. In this paper, an iterative design method for the IMC combined with a disturbance observer for the time-delay system is proposed and confirmed by experimental results.

Identification and Fuzzy Controller Design for Nonlinear Uncertain Systems with Input Time-Delay

This paper considers the identification and fuzzy controller design for nonlinear uncertain systems in presence of unknown input time-delay. Firstly, a time-delay Takagi-Sugeno-Kang (TSK) type fuzzy neural system (TDFN) is proposed to identify a class of nonlinear input time-delay systems. The input- output signals of nonlinear systems are used to identify the system dynamics and unknown time-delay, and then construct the system in the form TSK-fuzzy time-delay model. Each fuzzy rule has a corresponding linear system with an input time-delay as the consequent part. Based on parallel distribution compensation (PDC) approach, the Smith predictor compensation and dominate pole assignment technique are then adopted to design the fuzzy PID controller. Several simulations are shown to demonstrate the effectiveness and control performance of the proposed approach.

Discrete Time Models of Unilateral Time Delay Systems

Time delay systems have the mathematical difficulties for the controller design, the modeling and so on. In the continuous time approach, a time delay system has an infinite dimension. On the other hand, in the discrete time approach, an input time delay system has finite dimension and many controller design methods for the finite dimensional systems can be applied. But, for the case that the length of a time delay is not multiples of a discrete time, some additional methods are needed. The modeling and controller design methods have been studied by some authors for this case.In this paper, we focus on the case that the delay length is not multiples of a discrete time. Then the discrete time model is derived for the input and unilateral time delay systems without any approximations.

Iterative design of state predictive LQG controller for inertia rotor with time delay

Abstract It is known that LQG controller can be composed by using the state predictor for the input time delay system. Iterative design that improves the control performance of the closed-loop system has been proposed by repeating LQG control and closed-loop identification. In this research, the theory is verified by experiment of the swing control for the inertia rotor with an artificial time delay.

Second order hold and taylor series based discretization of SISO input time-delay systems

Second order hold is a method that enables the discretization of input-driven nonlinear systems to be carried out with high precision. A new discretization scheme combining second order hold with the Taylor-series is proposed. The sampled-data representation and mathematical structure are explored. Both exact and approximate sampled-data representations are described in detail. The performance of the proposed algorithm is evaluated for three different systems. Various sampling rates, delay times and truncation orders of the Taylor-series are considered to investigate the proposed method. The results demonstrate that the proposed scheme is practical and easy to use for time-delay systems. Comparisons between the second, first and zero orders are given to show the advantages of the proposed method.

Optimal digital controller and observer design for multiple time-delay transfer function matrices with multiple input–output time delays

In this article, we address the optimal digital design methodology for multiple time-delay transfer function matrices with multiple input–output time delays. In our approach, the multiple time-delay analogue transfer function matrix with multiple input–output time delays is minimally realised using a continuous-time state-space model. For deriving an explicit form of the optimal digital controller, the realised continuous-time multiple input–output time-delay system is discretised, and an extended high-order discrete-time state-space model is constructed for discrete-time LQR design. To derive a low-order optimal digital observer for the multiple input–output time-delay system, the multiple time-delay state obtained from the multiple time-delay outputs is discretised. Then, the well-known duality concept is employed to design an optimal digital observer using the low-order discretised multiple input time-delay system together with the newly discretised multiple time-delay state. The proposed approach is restricted to multiple time-delay systems where multiple time delays arise only in the input and output, and not in the state.

Digital redesign of analog Smith predictor for systems with input time delays

Abstract This paper presents a new methodology for digitally redesigning an existing analog Smith predictor control system, such that the cascaded analog controller with input delay can be implemented with a digital controller. A traditional analog Smith predictor system is reformulated into an augmented system, which is then digitally redesigned using the predicted intersampling states. The paper extends the prediction-based digital redesign method from a delay free feedback system to an input time-delay cascaded system. A tuning parameter v is optimally determined online such that in any sampling period, the output response error between the original analogously controlled time-delay system and the digitally controlled sampled-data time-delay system is significantly reduced. The proposed method gives very good performance in dealing with systems with delays in excess of several integer sampling periods and shows good robustness to sampling period selection.

Modeling and solution of two-dimensional input time-delay system

The discrete-time model of the two-dimensional continuous-time input time-delay system is newly presented in this paper, and the solution of the continuous-time input time-delay system is then solved based on the newly presented discrete-time model. The presented discrete-time model significantly facilitates analysis and design of a system when it faces the unavoidable inherent time delay and the computation time delay which can be modeled as a part of delay at the system input, in practice.