Analysis of time-delay systems using an alternative technique

The Taylor delayed operational matrix is first developed. With the introduction of the Taylor product matrix, the Taylor series approximation can be extended to the analysis of time-varying systems. The method is better than that using Walsh series, as demonstrated by numerical examples. The result is quite satisfactory.     

Analysis of plates and laminates using the element-free Galerkin method

A meshless method, the element-free Galerkin method (EFGM), is extended and used in the analysis of anisotropic plates and laminates considering a Reissner–Mindlin laminate theory (FSDT). The approximation functions are calculated considering a moving least squares (MLS) approach which is consistent provided the basis is complete in the polynomials up to a desired order. An alternative integration method avoiding the consideration of background cells is considered. Shear locking in plate bending is avoided considering the appropriate polynomials for the displacements and rotations, continuity being insured. Obtained results show the adequacy of the method for the analysis of plates and laminates.     

Analysis and control of time-delay systems using finite dimensional approximations

Analysis and control of time-delay systems governed by differential-difference equations are considered using finite dimensional approximations obtained from truncated Taylor series expansion of the delay terms. Through the use of simple examples a tutorial presentation is given of some of the problems in control and analysis caused by the finite dimensional models.     

Analysis of nonlinear time-delay systems using modules over non-commutative rings

The theory of non-commutative rings is introduced to provide a basis for the study of nonlinear control systems with time delays. The left Ore ring of non-commutative polynomials defined over the field of meromorphic function is suggested as the framework for such a study. This approach is then generalized to a broader class of nonlinear systems with delays that are called generalized Roesser systems. Finally, the theory is applied to analyze nonlinear time-delay systems. A weak observability is defined and characterized, generalizing the well-known linear result. Properties of closed submodules are then developed to obtain a result on the accessibility of such systems.     

New stability criteria for linear time-delay systems using complete LKF method

This paper focuses on the stability test for linear systems with time-varying delay and provides new stability conditions in terms of linear matrix inequalities (LMIs). The basic idea is the use of complete Lyapunov–Krasovskii functional (LKF) method and the derivation employs the discretisation technique and the reciprocally convex combination. The main feature of this work lies in that the present result not only leads to some improvements over existing results in the LMI framework but also is applicable for time-delay systems with unstable delay-free case. Three numerical examples are given to show the effectiveness and merits of the present result.     

An efficient hybrid reduction method for time-delay systems using Hermite expansions

This paper presents an efficient model reduction method for time-delay systems in the time domain. We expand the systems under a Hermite polynomial basis and show that Hermite coefficients of the expansion are determined by a linear equation, thus can be calculated efficiently. Such linear relationship is well taken in the projection methods of model reduction, and reduced models are generated to preserve a desired number of Hermite coefficients in the time domain, in contrast to other existing techniques which aim at approximating the transfer function of time-delay systems in the frequency domain. We also exploit two-sided projections for time-delay systems, leading to a hybrid reduction method which generates reduced models sharing the nice properties both in the time and frequency domains. Two numerical examples illustrate the feasibility and effectiveness of the approach.     

A novel criterion for nonlinear time-delay systems using LMI fuzzy Lyapunov method

This study presents a kind of fuzzy robustness design for nonlinear time-delay systems based on the fuzzy Lyapunov method, which is defined in terms of fuzzy blending quadratic Lyapunov functions. The basic idea of the proposed approach is to construct a fuzzy controller for nonlinear dynamic systems with disturbances in which the delay-independent robust stability criterion is derived in terms of the fuzzy Lyapunov method. Based on the robustness design and parallel distributed compensation (PDC) scheme, the problems of modeling errors between nonlinear dynamic systems and Takagi–Sugeno (T–S) fuzzy models are solved. Furthermore, the presented delay-independent condition is transformed into linear matrix inequalities (LMIs) so that the fuzzy state feedback gain and common solutions are numerically feasible with swarm intelligence algorithms. The proposed method is illustrated on a nonlinear inverted pendulum system and the simulation results show that the robustness controller cannot only stabilize the nonlinear inverted pendulum system, but has the robustness against external disturbance.     

Stabilization of time-delay systems using finite-dimensional compensators

For linear time-invariant systems with one or more noncommensurate time delays, necessary and sufficient conditions are given for the existence of a finite-dimensional stabilizing feedback compensator. In particular, it is shown that a stabilizable time-delay system can always be stabilized using a finite-dimensional compensator. The problem of explicitly constructing finite-dimensional stabilizing compensators is also considered.     

Finite-time estimation for a class of systems with unknown time-delay using modulating functions-based method

Time-delay systems are widely used to model real problems. Most of the works on such systems assume prior knowledge of the delay, which is mostly unknown in real applications. This paper aims to fast and robustly estimate unknown delay, parameters, and output derivatives for a class of linear time-delay systems in noisy environment. First, the classical modulating functions method is combined with the recursive least square algorithm and the Gauss–Newton method to estimate the coefficients and the time-delay, respectively. Second, the generalized modulating functions method is adopted to provide algebraic integral formulas to estimate the output derivatives using the estimated parameters. Finally, numerical simulations are given to demonstrate the efficiency and robustness of the proposed methods.     

Controller design for time-delay systems using genetic algorithms

This paper presents a new approach to design controllers for time-delay systems by using genetic algorithms (GAs) together with the solvability of linear matrix inequalities (LMIs). Both of the state-feedback controller and the static output feedback controller can be designed with this approach. It is confirmed by numerical examples that this approach achieves less conservative results than previously existing methods on the given examples.     

Modeling, control, and stability analysis for time-delay TLP systems using the fuzzy Lyapunov method

In this study, we present a Takagi–Sugeno (T–S) fuzzy model for the modeling and stability analysis of oceanic structures. We design a nonlinear fuzzy controller based on a parallel distributed compensation (PDC) scheme and reformulate the controller design problem as a linear matrix inequalities (LMI) problem as derived from the fuzzy Lyapunov theory. The robustness design technique is adopted so as to overcome the modeling errors for nonlinear time-delay systems subject to external oceanic waves. The vibration of the oceanic structure, i.e., the mechanical motion caused by the force of the waves, is discussed analytically based on fuzzy logic theory and a mathematical framework. The end result is decay in the amplitude of the surge motion affecting the time-delay tension leg platform (TLP) system. The feedback gain of the fuzzy controller needed to stabilize the TLP system can be found using the Matlab LMI toolbox. This proposed method of fuzzy control is applicable to practical TLP systems. The simulation results show that not only can the proposed method stabilize the systems but that the controller design is also simplified. The effects of the amplitude damping of the surge motion on the structural response are obvious and work as expected due to the control force.     

Analysis of absolute stability for time-delay teleoperation systems

In this paper, a new bilateral control algorithm based on absolute stability theory is put forward, which aims at the time-delay teleoperation system with force feedback from the slave directly. In the new control algorithm, the delay-dependent stability, instead of delay-independent stability, is taken as the aim of control design. It improves the transparency of the system at the price of unnecessary stability. With this algorithm, the time-delay teleoperation systems have good transparency and stability. A simulation system is established to verify the effect of this algorithm.     

Finite-time estimation for linear time-delay systems via homogeneous method

This paper presents a finite-time observer for linear time-delay systems with commensurate delay. Unlike the existing observers in the literature which converge asymptotically, the proposed observer provides a finite-time estimation. This is realised by using the well-known homogeneous technique, and the results are also extended to investigate the estimation problem for linear time-delay systems with unknown inputs. Simulation results are presented in order to illustrate the feasibility of the proposed method.     

Delay identification in time-delay systems using variable structure observers

In this paper we discuss delay estimation in time-delay systems. In the introduction section a short overview is given of some existing estimation techniques as well as identifiability studies. In the following sections we propose several algorithms for the delay identification based on variable structure observers.     

Analysis of factors influencing the solution of the consolidation problem by using an element-free Galerkin method

The meshless method is new type numerical method developed in recent years. There are no fewer than 20 variations published to-date, and some of them were successfully applied to solve Biot's consolidation problem. In the present paper, the system equations for the plain-strain consolidation problem using an element-free Galerkin method (EFGM) are presented on the basis of enforcing essential boundary conditions with a penalty method. Next, a large number of calculations and analyses of the displacement and excess pore-water pressure for nodes are carried out. It is shown that the accuracy of the calculations is influenced by many factors including the distribution mode of nodes, the shape and size of the domain of influence of nodes, the numerical integration scheme, and the adopted penalty factor. Some useful conclusions are drawn. The findings can be advantageous to improve the computational capability and accuracy of numerical solutions to the Biot's consolidation problem with EFGM.     

网络控制系统传输时延分析与测试

为了了解时延的变化规律，尽可能减小时延对控制系统性能的影响，对不同协议下的传输时延进行了测试和分析，找出了影响时延大小的因素，并为网络控制系统传输协议的选择提供了参考意见。     

Topology optimization of compliant mechanisms using element-free Galerkin method

This paper will propose a topology optimization approach for the design of large displacement compliant mechanisms with geometrical non-linearity by using the element-free Galerkin (EFG) method. In this method, the Shepard function is applied to construct a physically meaningful density approximant, to account for its non-negative and range-bounded property. Firstly, in terms of the original nodal density field, the Shepard function method functionally similar to a density filter is used to generate a non-local nodal density field with enriched smoothness over the design domain. The density of any node can be evaluated according to the nodal density variables located inside the influence domain of the interested node. Secondly, in the numerical implementation the Shepard function method is again employed to construct a point-wise density interpolant. Gauss quadrature is used to calculate the integration of background cells numerically, and the artificial densities over all Gauss points can be determined by the surrounding nodal densities within the influence domain of the concerned computational point. Finally, the moving least squares (MLS) method is applied to construct the shape functions using the weight functions with compact support for assembling the meshless approximations of state equations. Since MLS shape functions are lack of the Kronecker delta function property, the penalty method is applied to enforce the essential boundary conditions. A typical large-deformation compliant mechanism is used as the numerical example to demonstrate the effectiveness of the proposed method.     

Time discretization of nonlinear time-delay system using matrix exponential method

A time discretization method for nonlinear time-delay systems is proposed in this paper. The proposed method is based on the matrix exponential method and includes the automatic correction of rounding errors. It is robust to ill-conditioned problems and suitable for any nonlinear system. In the proposed algorithm, each sampling time interval is divided into two subintervals to be considered separately according to the time delay and the sampling period. The performance of the proposed discretization procedure is evaluated by two case studies.