Linear Discrete Time Delay Research Articles

Second-order iterative learning control for a class of switched discrete-time systems with model uncertainties, external noises and time-delay

ABSTRACT The second-order ILC algorithm is studied for a class of linear discrete-time switched systems with model uncertainties, external noises and the time-delay for tracking reference trajectory by taking advantage of super-vector representation. This study is based on the assumption that the systems operate under finite intervals. A sufficient condition for convergence of the algorithms is deduced when the model uncertainties and external noises are absent. Then the convergence is analysed, when the model uncertainties are present but the external noises are absent and the robustness against the bounded external noises is discussed. The analysis manifests that the second-order ILC algorithm is feasible and effective when it is imposed on the linear switched systems specified by the arbitrarily present switching rules when they are imposed on the system. We have presented a simulation example to illustrate effectiveness of the proposed second-order ILC algorithm in the study of robustness of the considered SISO linear discrete time-invariant time delay switched system.

Frequency‐domain‐based iterative learning control utilizing n‐best adaptive Fourier decomposition for nonrepetitive unknown iteration‐independent and iteration‐varying discrete time‐delay systems

AbstractThe bulk of well‐known control techniques for time‐delay systems are sensitive to the system's uncertainty. For unknown nonrepetitive iteration‐independent and iteration‐varying linear discrete time‐delay (LDTD) systems, an iterative learning control (ILC) design with a frequency domain identification technique is devised. The proposed ILC method is based on a novel n‐best adaptive Fourier decomposition (n‐BAFD) approach for approximating the unknown time‐delay transfer function. An extended anticipatory ILC law is developed that uses anticipatory time to compensate for both iteration‐independent and iteration‐varying time delays in the frequency domain for unknown nonrepetitive LDTD systems. Three examples are used to validate the proposed frequency‐domain‐based ILC method.

Online Identification of Multivariable Discrete Time Delay Systems Using a Recursive Least Square Algorithm

This paper addresses the problem of simultaneous identification of linear discrete time delay multivariable systems. This problem involves both the estimation of the time delays and the dynamic parameters matrices. In fact, we suggest a new formulation of this problem allowing defining the time delay and the dynamic parameters in the same estimated vector and building the corresponding observation vector. Then, we use this formulation to propose a new method to identify the time delays and the parameters of these systems using the least square approach. Convergence conditions and statistics properties of the proposed method are also developed. Simulation results are presented to illustrate the performance of the proposed method. An application of the developed approach to compact disc player arm is also suggested in order to validate simulation results.

Necessary and Sufficient Conditions for Delay-Dependent Asymptotic Stability of Linear Discrete Time Delay Autonomous Systems

This paper offers new, necessary and sufficient conditions for delay-dependent asymptotic stability of systems of the form x(k +1) = A0x(k) + A1x(k – h). The time-dependent criteria are derived by Lyapunov's direct method. Two matrix equations have been derived: matrix polynomial equation and discrete Lyapunov matrix equation. Also, modifications of the existing sufficient conditions of convergence of Traub and Bernoulli algorithms for computing the dominant solvent of the matrix polynomial equation are derived. Numerical computations are performed to illustrate the results obtained.

Stabilization of Linear Discrete Time Delay Systems with Additive Disturbance and Saturating Actuators

The stabilization of linear discrete-time systems with additive bounded disturbance subject both to time-delay in the state and to limited actuators is addressed. A saturating state feedback control law and a region, in which the stability of the closed-loop saturated system is ensured, are derived from a Lyapunov-Krasovskii approach. A local approach is chosen in the sense that no open-loop stability assumption is a priori needed. The results can be extended to cope with convex bounded uncertain parameters in the system model. The stability of the closed-loop system is delay-independent.

Application of a discrete optimal tracking controller to an industrial electric heater with pure delays

Abstract This paper discusses the optimal tracking control of linear discrete time delay systems and its application to an industrial electric heater with pure delays. The system with control time delay and a direct path between input and output variables is discussed first, and then a general form of time delay systems is analysed. An extended state vector involving all time delay variables of the original system is constructed to obtain an extended new system without time delays. Using the optimal feedback control theory of LQI, the paper gives an optimal control tracking algorithm and the conditions for stability and exact tracking of closed-loop systems. Finally, a simulation study on an industrial electric heater is carried out. The result shows that, in the case of temperature setpoint changes, the optimal tracking control can result in fast exact tracking with small deviation.