Sharif Digital Repository

This study presents a new approach to decompose singular time-delay systems (STDSs) in a way that they can be transformable to normal time-delay systems (TDSs) with a lower order. Necessary and sufficient conditions are provided to determine which STDSs can be transformed to TDSs. Also, a stabilisation method is provided to stabilise the system, while the time delay in the system can belong to several distinct intervals or even everywhere. The proposed method is non-fragile towards controller parameters. This method also reveals one of the many applicable situations of the proposed decomposition. The effectiveness of the proposed method is illustrated through some examples. © 2018 The... 

One of the most important problems in teleoperation systems is time delay and packet loss in the communication channel, which can affect transparency and stability. One way to overcome the time delay effects in a teleoperation system is to predict the master-side motion. In this way, when data is received in the slave side, it will be considered as the current position of the master robot and, thus, complete transparency could be achieved. The majority of the previous works regarding operator position prediction have considered known and constant time delay in the system; however, in the real applications, time delay is unknown and variable. In this paper, an adaptive online prediction... 

Brain-machines - also termed neural prostheses, could potentially increase substantially the quality of life for people suffering from motor disorders or even brain palsy. In this paper we investigate the non-stationary continuous decoding problem associated to the rat's hand position. To this aim, intracortical data (also named ECoG for electrocorticogram) are processed in successive stages: spike detection, spike sorting, and intention extraction from the firing rate signal. The two important questions to answer in our experiment are (i) is it realistic to link time events from the primary motor cortex with some time-delay mapping tool and are some inputs more suitable for this mapping... 

The time delay equations are frequently used to model real systems since they can describe the after-effect phenomenon. It is usually difficult to analyze the properties of time delay systems. Thus it would be beneficial to make the systems as simple as possible. For this purpose, the decomposition of the systems into some separate or cascaded sub-systems with smaller dimension is introduced as the solution of the mentioned complex task. The decomposition of the time delay systems with one delay is directly related to simultaneous similarity of two matrices. In this regard, necessary and sufficient conditions are derived for the existence of a common similar block diagonal or triangular form... 

One of the most important problems in teleoperation systems is time delay and packet loss in the communication channel, which can affect transparency and stability. One way to overcome the time delay effects in a teleoperation system is to predict the master-side motion. In this way, when data is received in the slave side, it will be considered as the current position of the master robot and, thus, complete transparency could be achieved. The majority of the previous works regarding operator position prediction have considered known and constant time delay in the system; however, in the real applications, time delay is unknown and variable. In this paper, an adaptive online prediction... 

The bounded-input bounded-output stability of fractional delay systems of neutral type is investigated in this study. The proposed method calculates the number of unstable poles of the system for each delay value. All time-delay intervals in time-delay space where system is stable are precisely determined. The stability of systems with not only indefinitely large values of time-delay, but also with multiple poles on the imaginary axis has been studied. The proposed method is employed for investigating the stability of a fractional delay system when its fractional orders approach to the integer numbers or zero. It is proved that simple case of neutral types and time-delay systems have the... 

In [1] three theorems are presented which relate to the problem of stabilizing PID controller design for interval time-delay plants. We present a counterexample for these results  

The problem of time delay estimation (TDE) in the presence of zero mean white Gaussian noise is addressed. A novel and efficient algorithm for obtaining Conditional Maximum Likelihood (CML) estimates of delays, attenuation factors and the number of paths from a transmitter to a receiver is introduced. This approach is quite suitable for the cases in which time delay difference is less than the duration of signal autocorrelation  

This paper deals with defining the concept of agent-based time delay margin and computing its value in multi-agent systems controlled by event-triggered based controllers. The agent-based time delay margin specifying the time delay tolerance of each agent for ensuring consensus in event-triggered controlled multi-agent systems can be considered as complementary for the concept of (network) time delay margin, which has been previously introduced in some literature. In this paper, an event-triggered control method for achieving consensus in multi-agent systems with time delay is considered. It is shown that the Zeno behavior is excluded by applying this method. Then, in a multi-agent system... 

This paper presents a new method for assessing the bounded input bounded output stability of a class of fractional delay systems with commensurate orders and multiple commensurate delays of retarded type. In the proposed method, first, by mapping the principal sheet of the Riemann surface and a pseudo-delay transformation, an auxiliary polynomial is generated. Then, this auxiliary polynomial is employed to find roots of the characteristic equation on the imaginary axis. The properties of the root path close to these roots are used to identify intervals of delay values, in which the system is stable. The obtained results are illustrated via some numerical examples  

This study deals with proposing a Lyapunov-based technique for stability analysis of fractional order time-delay systems. The proposed technique is constructed on the basis of modifying the convex part of a class of Lyapunov-Krasovskii functionals commonly used in stability analysis of integer order time-delay systems. As a consequence for this achievement, it is revealed that the Lyapunov-Krasovskii-based stability conditions in integer order time-delay systems can result in stability of their fractional order counterparts defined based on Caputo/Riemann-Liouville derivative operators with orders in the range (0,1). The applicability of the study results is shown through three different... 

This paper studies fractional-order systems of retarded type with two independent delays, and determines the stability regions in spaces of delays. In this approach, an auxiliary polynomial is employed to calculate all purely imaginary roots of the characteristic equation of the system on the imaginary axis. Since roots of the characteristic equation are continuous with respect to delays, these purely imaginary roots determine the stability regions in delay space. Also, the necessary and sufficient condition for stability independent of delays is developed for the systems. Furthermore, a simple inequality constraint is established to obtain pure imaginary poles of the scalar systems.... 

This paper investigates the dynamical behaviour of the fractional delayed damped Mathieu equation. This system includes three different phenomena (fractional order, time delay, parametric resonance). The method of harmonic balance is employed to achieve approximate expressions for the transition curves in the parameter plane. The n = 0 and n = 1 transition curves (both lower and higher order approximations) are obtained. The dependencies of these curves on the system parameters and fractional orders are determined. Previous results for the transition curves reported for the damped Mathieu equation, delayed second-order oscillator, and fractional Mathieu equation are confirmed as special... 

In Ref. [1], it has been claimed that the value set of a fractional order interval plant, having one uncertain time delay is a polygon. This note illustrates that this claim is not true, and in fact the value set has a nonconvex shape. Therefore, Theorem 3.1 and the stabilization algorithm presented in the reference to design a PIλDμ controller, are not true. © 2018 Elsevier B.V  

A new method is proposed to analyze stability of descriptor systems with multiple commensurate time-delays. In this method, purely imaginary roots of the system are calculated, asymptotic behavior of root path at these roots is studied, and unstable regions of the system in the space of delays are determined. Moreover, the number of roots in each unstable region is calculated. Also necessary and sufficient conditions for τ-stabilizability of these systems are presented. Examples are provided to illustrate the effectiveness and validity of the proposed method. © 2019 The Franklin Institute  

During the milling process, one of the most important factors in reducing tool life expectancy and quality of workpiece is the chattering phenomenon due to self-excitation. The milling process is considered as a MIMO strongly coupled nonlinear plant with time delay terms in cutting forces. We stabilize the plant using two independent Emotional Learning-based Intelligent Controller (ELIC) in parallel. Control inputs are considered as forces Ux and Uy in two directions x and y, which are applied by the piezoelectrics. The ELIC consists of three elements; Critic, TSK controller and the learning element. The results of the ELIC have been compared with a Sliding Mode Controller (SMC). The... 

This paper presents a new model to short-term prediction of air pollution using a new structure is based on the intelligent neural networks. A new structure known as Time Delay Cerebellar Model Arithmetic Computer (TD-CMAC), an extension to the CMAC, it requires fewer memory sizes. The new model is demonstrated and validated with three primary air pollutants known as carbon monoxide (CO), sulfur dioxide (SO2), and nitrogen dioxide (NO 2). The simulation results for the half an hour ahead-prediction of the air pollutant data set show that the suggested new model is suitable for our purpose