Pure Delay Research Articles

Representation of solutions of discrete linear delay systems with non permutable matrices

We introduce a discrete delayed exponential depending on sequence of matrices. This discrete matrix gives a representation of a solution to the Cauchy problem for a discrete linear system with pure delay with sequence of matrices. We discard the commutativity condition used in recent works related to the representation of solutions for discrete delay linear systems.

Hybrid Smith predictor and phase lead based divergence compensation for hardware-in-the-loop contact simulation with measurement delay

On the ground the hardware-in-the-loop (HIL) simulation is a good approach to test the contact dynamics of spacecraft docking process in space. Unfortunately, due to the time delay in the system the HIL contact simulation becomes divergent. However, the traditional first-order phase lead compensation approach still result in a small divergence for the pure time delay. The serial Smith predictor and phase lead compensation approach proposed by the authors recently will lead to an over-compensation and an obvious convergence. In this study, a hybrid Smith predictor and phase lead compensation approach is proposed. The hybrid Smith predictor and phase lead compensation can achieve a higher simulation fidelity with a little convergence. The phase angle of the compensator is analyzed and the stability condition of the HIL simulation system is given. The effectiveness of the proposed compensation approach is tested by simulations on an undamped elastic contact process.

Decentralized adaptive tracking quantized control for interconnected pure feedback time delay nonlinear systems

This paper focuses on the problem of adaptive tracking quantized control for a class of interconnected pure feedback time delay nonlinear systems. To satisfy the requirement of prescribed performance on the output tracking error, a novel asymmetric tangent barrier Lyapunov function is developed. The decentralized adaptive controller is designed via backstepping method. To deal with the uncertain interconnected nonlinear functions, we design a new virtual control input in the first step. Instead of estimating the bound of each unknown function, we use the adaptive method to estimate the bound of the composite function which is composed of the unknown functions. Thus the over parameterization problem is avoided. It is proved that the output of each subsystem satisfies the prescribed performance requirement and other state variables are bounded. Finally, the simulations are performed and the results verify the effectiveness of the proposed method.

Global attractivity of n-species competition systems with pure distributed delays

Global attractivity of n-species competition systems with pure distributed delays

Active Perturbation in Modifier Adaptation for Real Time Optimization to Cope with Measurement Delays

Iterative optimization is a technique where the model-based optimization problem is iteratively updated to drive the plant to its optimal operating point in the presence of plant-model mismatch. Modifier adaptation (MA) is a state-of-the-art iterative optimization approach which can be used in the presence of both structural and parametric plant-model mismatch. Availability of plant measurements is key for the successful application of MA. In the process industries, analytical sensors cannot always be installed directly at the location of interest. A remote positioning of a measurement device leads to a significant delay in receiving the measurements, since the transportation of the sample to the sensor requires additional time. This leads to a waiting time between two successive iterations during which the standard iterative optimization techniques remain idle. In this contribution, the issue of a pure time delay caused by the remote positioning of a sensor is addressed. We propose an active perturbation strategy to obtain more information by perturbing the plant during the waiting time to improve the estimation of the plant gradient, which reduces the time to reach the plant-optimum. The performance of the proposed strategy is analyzed based on the simulation results from a chemical engineering case study.

Should we forget the Smith Predictor?

The PI/PID controller is the most used controller in industry. However, for processes with large time delays, the common belief is that PI and PID controllers have sluggish performance, and that a Smith predictor or similar dead-time compensator can give much improved performance. We claim in this paper that this is a myth. For a given robustness level in terms of the peak sensitivity (Ms), we find that the performance improvement with the Smith predictor is small even for a pure time delay process. For other first-order processes a PID controller is generally better for a given robustness level. In addition, the Smith Predictor is much more sensitive to time delay errors than pi and pid controllers.

Analysis of Modified Repetitive Control Schemes: the Port-Hamiltonian Approach

Repetitive Control (RC) schemes are described by systems of coupled PDEs and ODEs and, in this paper, their stability analysis relies on the modularity of the port-Hamiltonian framework to characterise a family of linear plants for which this control technique can be successfully applied. To achieve this, the regulator, that is in fact an infinite dimensional system, is treated as a boundary control system in port-Hamiltonian form, and novel results dealing with the exponential stabilisation of this class of infinite dimensional systems are exploited. The focus here is on plants that are strictly proper and, as a consequence, on Modified Repetitive Control (MRC) schemes, i.e. RC schemes in which a low-pass filter is in series with the pure delay block. The result is a characterisation of a class of linear systems for which MRC schemes converge.

A New Design Method for Stable IIR Filters With Nearly Linear-Phase Response Based on Fractional Derivative and Swarm Intelligence

In this paper, a new design method based on fractional derivative (FD) is proposed for designing digital stable infinite impulse response (IIR) filters with nearly linear-phase response. In this method, the design problem is formulated as a phase error optimization of an all-pass filter connected in parallel with a pure delay function. FD is employed to improve the frequency response of the filter at some reference point $(\omega _{{0}})$ in the passband. Optimal values of FD constraints and reference points in passband are determined by minimizing the sum of error in passband $(E_{p})$ and stopband $(E_{s})$ of an IIR filter, using different evolutionary techniques such as particle swarm optimization (PSO), constraint factor inertia PSO (CFI-PSO), quantum PSO, artificial bee colony algorithm, and cuckoo search technique. Comparative study provides evidence that the proposed method, based on CFI-PSO, gives the best performance amongst the employed swarm-based techniques. Experimental results show the impact of the proposed method as compared to earlier reported techniques in terms of improved response in passband and sharper transition width. However, small reduction in stopband attenuation $(A_{s})$ is observed within the allowable limit when compared to nonfractional design approaches.

Relative controllability in fractional differential equations with pure delay

In this paper, we study relative controllability of fractional differential equations with pure delay. Delayed Gram‐type matrix criterion and rank criterion for relative controllability are established with the help of the explicit solution formula. An example is given to illustrate our theoretical results.

Representation of a solution for a fractional linear system with pure delay

This paper gives a representation of a solution to the Cauchy problem for a fractional linear system with pure delay. We introduce the fractional delayed matrices cosine and sine of a polynomial of degree and establish some properties. Then, we use the variation of constants method to obtain the solution and our results extend those for second order linear system with pure delay. As an application, the representation of a solution is used to obtain a finite time stability result.

Classification of Diesel Fuel Using Two-Dimensional Fluorescence Spectroscopy

Air pollution is a serious problem, and to decrease the emission of pollutants, governments have established environmental rules to limit the concentration of sulfur in diesel fuel. Control of sulfur content in diesel streams demands online measurement of this component, with low pure time delay and easy operation. In this regard, two-dimensional (2D) fluorescence spectroscopy becomes a promising choice for soft-sensor development. Despite fluorescence qualities, translation of fluorescence spectroscopic data into process knowledge is not a simple task, demanding multivariate analysis. This work aims to evaluate the applicability of 2D fluorescence spectroscopy for monitoring ultralow sulfur diesel streams (Diesel S10) and the capability of differentiation between ULSD and diesel streams with a higher sulfur concentration (Diesel S100). The evaluation of the different sample groups’ fluorescence spectra made clear the ability of the technique to capture changes in the composition between Diesel S10 and Di...

Identification of perceptually relevant methods of inter-aural time difference estimation.

The inter-aural time difference (ITD) is a fundamental cue for human sound localization. Over the past decades several methods have been proposed for its estimation from measured head-related impulse response (HRIR) data. Nevertheless, inter-method variations in ITD calculation have been found to exceed the known just noticeable differences (JNDs), leading to possible perceptible artifacts in virtual binaural auditory scenes, when personalized HRIRs are being used. In the absence of an objective means for validating ITD estimations, this paper examines which methods lead to the most perceptually relevant results. A subjective lateralization study compared objective ITDs to perceptually evaluated inter-aural pure delay offsets. Results clearly indicate the first-onset threshold detection method, using a low relative threshold of -30 dB, applied on 3 kHz low-pass filtered HRIRs as consistently the most perceptually relevant procedure across various metrics. Several alternative threshold values and methods based on the maximum or centroid of the inter-aural cross correlation of similarly filtered HRIR or HRIR envelopes also provided reasonable results. On the contrary, phase-based methods employing the integrated relative group delay or auditory model were not found to perform as well.

Nonlinear substructuring control for parameter changes in multi-degree-of-freedom systems

Nonlinear substructuring control (NLSC) was developed to render linear substructuring control (LSC), particularly used in dynamically substructured system (DSS), more robust against nonlinearities. This NLSC was examined both numerically and experimentally via substructure tests of nonlinear single-degree-of-freedom (SDOF) systems demonstrating a base-isolated structure. This study examines the application of NLSC to nonlinear multi-degree-of-freedom (MDOF) systems. To begin, NLSC for nonlinear MDOF systems is discussed, and its stability with respect to a pure time delay, which is a critical element in many substructure tests, is analysed by applying the Nyquist criterion. Next, its controller design and stability analysis are numerically and experimentally examined via substructure tests. In the examination, a nonlinear 4DOF system subjected to a ground motion is selected as an emulated system for substructure tests. Based on this emulated system, three types of substructure tests are numerically simulated; the first simulation examines the ground floor as the physical substructure, the second one examines the ground and first floors, and the third one examines only the first floor. Finally, by using a test rig consisting of an actuator and a rubber bearing, a series of substructure experiments targeting the ground floor as the physical substructure was implemented. In both examinations, the design of the NLSC controller has established its efficiency in substructure tests of nonlinear MDOF systems. A stability analysis with respect to pure time delays has been also found useful for predicting instability conditions of substructure tests with nonlinear MDOF systems.

Control Theoretic Modeling and Simulation of Supply Chain Management System

AbstractControl theoretic modelling approaches are very effective in developing a dynamical model of a system. A supply chain system is a dynamical system which contains a number of lead times among supply nodes and is susceptible to demand variation. Control theoretic modelling approaches are proved to be very effective in developing ordering policies for such systems. In this work, we developed a linear discrete time model of a supply chain with multiple supply nodes and pure delays. The model presented here can be used to develop an optimal ordering and distribution policy so that the entire system remains stable. In addition to the mathematical model of the supply chain, a simulation model is also developed using Simulink® toolbox SimEvents®. The simulation model can be used to test various ordering policies to determine system stability. In this work the simulation model is used to test system stability and can be further used to find optimum ordering and optimum routing policies under uncertainty by running a Monte Carlo type simulation using the developed simulation model.

Delay-dependent data rate bounds for containability of scalar systems

This paper considers the problem of containability for a scalar linear unstable system where the communication from the sensor to the actuator is performed over a network with finite capacity The possibilities of event-based sampling concepts in a setup with memoryless coding and decoding components acting together with a static controller are investigated. A robust controller is designed such that the finite communication control system employs an arbitrary possibly vanishing, average data rate in a delay free setup while guaranteeing containability The controller can be applied in the presence of delays as well, whereas the sampling mechanism needs to be adjusted. This leads to an increasing data rate and this increase is precisely quantified. Indications why the uncertainty in time rather than the pure delay causes the increasing data rate are given as well as considerations regarding the relation of transmitted bits and delay.

Stability Analysis of Neutral Type Time-Delay Positive Systems with Commensurate Delays

Recently, the author derived a necessary and sufficient condition for the asymptotic stability of neutral type time-delay positive systems (TDPSs), where the neutral type TDPS of interest is given by a feedback connection between a finite-dimensional LTI positive system and the pure delay The goal of this paper is to extend this result to neutral type TDPSs with multiple commensurate delays. To this end, we first represent a neutral type TDPS with multiple commensurate delays as a neutral type TDPS with a single delay, by augmenting input and output signals in the feedback connection. By this conversion, we can readily apply the latest result already established for single delay neutral type TDPSs. As the main result, we show that a neutral type TDPS with commensurate delays is stable if and only if its delay-free counterpart is stable and an additional "admissibility" condition is satisfied. This result in particular implies that the stability is irrelevant of the length of delays.

Control of large model mismatch systems using multiple models

H ∞ control is an effective approach to handle model uncertainties. However, when modeling mismatch is large, it tends to be challenging to meet the desired requirements of both stability and performance by only using a single H ∞ controller. This study presents a switching method to enhance the robust stability and performance of H ∞ control by dividing the range of dynamics into multiple uncertain models. The candidate robust controllers are designed by solving a set of linear matrix inequalities for each uncertain model. A structural scheduling logic that selects the most proper controller into closed-loop is proposed. The selected controller can ensure bounded exponentially weighted H ∞ norm of the closed-loop switching systems. This work analyses their robust stability and disturbance attenuation performance via a linear fractional transformation by using the small gain theorem. The effectiveness of this method is validated with a fist-order inertial system with pure time delay.

Identifying a perceptually relevant estimation method of the inter-aural time delay

The Inter-aural Time Difference (ITD) is a fundamental cue for human sound localization. Over the past decades, several methods have been proposed for its estimation from measured Head-Related Impulse Response (HRIR) data. Nevertheless, inter-method variations in ITD calculation have been found to exceed the known Just Noticeable Differences (JNDs), hence leading to possible perceptible artifacts in virtual binaural auditory scenes, even for cases when personalized HRIRs are being used. In the absence of an objective means for validating ITD estimations, this paper evaluates which methods lead to the most perceptually relevant results. A subjective lateralization study compared objective ITDs to perceptually driven inter-aural pure delay offsets. Results clearly indicate the first-onset Threshold detection method, using a low relative threshold of -30 dB, applied on 3 kHz low-pass filtered HRIRs as the most perceptually relevant procedure across various metrics. Alternative threshold values and methods based on the maximum or centroid of the Inter-Aural Cross Correlation of similarly filtered HRIRs or HRIR envelopes also provided reasonable results. On the contrary, phase-based methods employing the Integrated Relative Group Delay were not found to perform as well.

Dynamic matrix control and generalized predictive control, comparison study with IMC-PID

Two of control techniques of the Model Predictive Control (MPC) methodology, which are Dynamic Matrix Control (DMC) and Generalized Predictive Control (GPC), with IMC-PID are disputed in this paper. The main characteristics of these important control techniques, widely used in industry, are presented. The optimum solution of the predicted control inputs and outputs are obtained by minimizing a cost function that contains the squared errors between the reference trajectory and predictions output on the prediction horizon. These controllers are applied on a Process Control Module (PCM), a system with pure time delay, and tested in the light of disturbance rejection and tracking performance for the constant and variable trajectory.

Logic circuits dynamic parameters analysis methodology

This paper presents a compact and simple procedure applicable to combinational logic circuits for timing analysis. We follow established guidelines but shall define new variables (time-dependent logic variables—TDLVs) that will improve the efficiency of the previously mentioned procedures. By using the methodology suggested we shall substitute a very laborious technique (pure delay circuit $$+$$ time constant method) with a simpler procedure that will pinpoint the specific conditions for the logic circuit’s anomalous behaviour, within a few steps. The conclusion can be drawn that only a strictly limited number of situations should be considered—in conjunction with the function that is being implemented by the circuit analysed.