Discrete-time Domain Research Articles

A Review of the Basic Principles and Methods of Signal Sampling Technology

In modern life, communication is an essential human activity. In the process of communication, various information spreads around the world in the form of signals. In order to optimize the communication, the reasonable processing of the signal becomes an important research problem. Signal processing is an important step during signal processing. It is one of two processes that convert an analog signal into a digital equivalent signal. It can be considered that signal sampling transforms the time axis of the signal into a set of discrete time moments, that is, the process of converting a signal in a continuous time domain to a discrete time domain through a series of methods. It is used to convert continuous time signals into digital signals for relevant processing and storage of digital signals in subsequent operations. This paper will summarize the basic principles and methods of signal sampling technology, introduce the sampling theorem, sampling frequency, sampling depth, sampling method and sampling error, and finally discuss the future development of signal adoption technology.

Wide-sense stationary discrete-time random processes: Analyses in the discrete-Fresnel and discrete-frequency domains

This article investigates the expectation and autocorrelation functions of random processes in the discrete-Fresnel and the discrete-frequency domains, originating from wide-sense stationary (WSS) random processes in the discrete-time domain. Through mathematical deduction, it is demonstrated that WSS random processes in the discrete-time domain exhibit the same expectation and autocorrelation functions as transformed to the discrete-Fresnel domain. In contrast, this property is not observed in the discrete-frequency domain. White, pink, and brown random processes are considered to illustrate these behaviors in the discrete-Fresnel and discrete-frequency domains. Furthermore, this study numerically compares data communication systems based on single-carrier with cyclic prefix, orthogonal chirp-division multiplexing, and orthogonal frequency-division multiplexing schemes, which are respectively designed in the discrete-time, discrete-Fresnel, and discrete-frequency domains. The numerical results show that orthogonal chirp-division multiplexing and single-carrier with cyclic prefix schemes achieve comparable communication performance under any additive noise modeled by a wide-sense stationary random process, regardless of the chosen linear equalization or the absence of it.

A low-complexity solution for LMIs of hardly constrained nonlinear MIMO tracking control systems

This research is dedicated to the discrete-time tracking control of nonlinear multi-input multi-output (MIMO) Newtonian mechanics systems with an equal number of inputs and outputs, in the presence of input saturation and high-order dynamics of the actuation system. Firstly, the continuous-time model of the plant and actuation system has been transformed into the discrete-time domain using Adams–Bashforth and Adams–Moulton discretization techniques. In the next step, considering saturation boundaries, the modified position and velocity references are derived using the discrete-time reaching law-based control approach. These modified references are obtained through an optimization algorithm that calculates the closest achievable position and velocity trajectories with respect to the desired reference trajectory. Modifying desired trajectories in MIMO systems results in the formation of a system of linear matrix inequalities (LMIs). Solving such systems of inequalities requires the use of complex methods, and this difficulty increases with the increase in the system’s degrees of freedom (DOFs). The proposed strategy offers a more straightforward approach to solving these inequalities. Once the modified references are calculated, the corresponding position and velocity control signals can be obtained using the mentioned reaching law strategies. The final step of the proposed algorithm is to combine the resulting position and velocity control signals using a Gaussian-weighted averaging method to form the main control signal. A desirable performance for the control system can be achieved by appropriately adjusting the standard deviations of the Gaussian weighing functions. To evaluate the performance characteristics of the proposed method, it has been applied in the tracking control procedure of a nonlinear 3-DOF mechanical system. The numerical simulation results demonstrate the effectiveness of the method.

Online Monitoring System of Electromechanical Transient Simulation Data of Distribution Network Based on Edge Computing

The current distribution network is developing toward the direction of information and intelligent distribution Internet of Things (IoT). In order to explore the online monitoring system for transient electromechanical simulation of distribution networks, this paper is based on the equivalent model of generator sets. Firstly, it describes the relevant theoretical knowledge of edge computing, designs the distribution IoT based on edge computing, and briefly introduces its network architecture. Secondly, based on the discrete-time domain equivalent model of generators, the electromechanical transient simulation distribution network is constructed by introducing the machine network division of the power network. Finally, the Western System Coordinating Council (WSCC)-3 units and 9 nodes are taken as an example, and simulation experiments are conducted under two fault simulation conditions to verify the effectiveness of the simulation model. The results show that under the two fault simulation conditions, the results of equivalent model simulation of generator terminal voltage and relative power angle change are like those of the Power System Analysis Software Package (PSASP). The changing trend of the two is similar and stable. After the PSASP results are stabilized at a value, the simulation results fluctuate extremely up and down the value. For example, under fault condition 1, the changing trend of the relative power angle of the No. 2 generator is first fluctuating and then becomes stable. After violent fluctuation, the relative power angle tends to be stable from about 20s to -12.35°. The result of PSASP software is stable at -12.35°. The transient electromechanical simulation of the generator equivalent model can provide some ideas for the online monitoring system of the distribution network.

A Finite-Time Control Design for the Discrete-Time Chaotic Logistic Equations

Finite-time control theory has been widely used as a mathematical tool to design robust controllers. By manipulating the finite-time convergence proof of this theory, we developed a new control design appropriately tuned for the finite-time control of the chaotic logistics system. In this experimental setup, the logistic equation is programmed into a PIC microcontroller, and a part of the controller was conceived using analog electronics. Because the system to be controlled is in the discrete-time domain, and the finite-time stability proof is stated in the continuous-time representation, our finite-time control approach is a good example for designing control algorithms in both time domain schemes. Hence, our experimental results support our main contribution. Pulse width modulation (PWM) is the format used to translate digital signals into the continuous-time field. Therefore, the main contribution of this article is the theoretical foundations for creating a recent controller that satisfies the convergence criterion in finite time and its construction using an 8-bit microcontroller. All this contributes to the chaotic logistical map.

Chaotic Dynamics of the Fractional Order Predator-Prey Model Incorporating Gompertz Growth on Prey with Ivlev Functional Response

This paper examines dynamic behaviours of a two-species discrete fractional order predator-prey system with functional response form of Ivlev along with Gompertz growth of prey population. A discretization scheme is first applied to get Caputo fractional differential system for the prey-predator model. This study identifies certain conditions for the local asymptotic stability at the fixed points of the proposed prey-predator model. The existence and direction of the period-doubling bifurcation, Neimark-Sacker bifurcation, and Control Chaos are examined for the discrete-time domain. As the bifurcation parameter increases, the system displays chaotic behaviour. For various model parameters, bifurcation diagrams, phase portraits, and time graphs are obtained. Theoretical predictions and long-term chaotic behaviour are supported by numerical simulations across a wide variety of parameters. This article aims to offer an OGY and state feedback strategy that can stabilize chaotic orbits at a precarious equilibrium point.

Anti-creep pretension determination of a mesh reflector antenna for long term surface accuracy retention

During the in-orbit service, mesh reflector antennas inevitably withstand the long-term creep behavior, resulting in changes in material properties and loss of cable tensions, thus decreasing the structural stiffness and surface accuracy. Pretension design plays an important role for mesh reflector antennas in achieving high surface accuracy, and different levels of pretension also affect the antenna’s creep behavior in the time dimension, which can be actively utilized to improve stability of the antenna surface accuracy. In this paper, we present an anti-creep pretension determination method for mesh reflector antennas to improve the surface accuracy stability. The creep model in the discretized time domain is adopted to describe the cable creep behavior. The time-related nonlinear equilibrium equation of the mesh reflector antenna is established with the force density method. The time-related tangent stiffness matrix is derived and adopted to solve the nonlinear equilibrium equation by the Newton-Raphson method, providing an effective way to analyze the antenna creep phenomenon in the discretized time domain. Aiming to minimize the long-term peak value of the time-variant surface error, the pretension schemes are generated and optimized. Finally, this approach is effectively applied to a thirty-unit mesh reflector antenna and its feasibility and effectiveness are verified.

Generalized periodicity and applications to logistic growth

Classically, a continuous function f:R→R is periodic if there exists an ω>0 such that f(t+ω)=f(t) for all t∈R. The extension of this precise definition to functions f:Z→R is straightforward. However, in the so-called quantum case, where f:qN0→R (q>1), or more general isolated time scales, a different definition of periodicity is needed. A recently introduced definition of periodicity for such general isolated time scales, including the quantum calculus, not only addressed this gap but also inspired this work. We now return to the continuous case and present the concept of ν-periodicity that connects these different formulations of periodicity for general discrete time domains with the continuous domain. Our definition of ν-periodicity preserves crucial translation invariant properties of integrals over ν-periodic functions and, for ν(t)=t+ω, ν-periodicity is equivalent to the classical periodicity condition with period ω. We use the classification of ν-periodic functions to discuss the existence and uniqueness of ν-periodic solutions to linear homogeneous and nonhomogeneous differential equations. If ν(t)=t+ω, our results coincide with the results known for periodic differential equations. By using our concept of ν-periodicity, we gain new insights into the classes of solutions to linear nonautonomous differential equations. We also investigate the existence, uniqueness, and global stability of ν-periodic solutions to the nonlinear logistic model and apply it to generalize the Cushing–Henson conjectures, originally formulated for the discrete Beverton–Holt model.

Intermittent event-triggered control for exponential synchronization of delayed neural networks on time Scales

This paper studies the exponential synchronization of delayed neural networks (DNNs) on time scales using the intermittent event-triggered control (IETC) method. Initially, considering the time scale situation, an IETC that merges intermittent control and event-triggered control is introduced, and a new differential inequality is developed. Subsequently, an exponential synchronization criterion is established based on the Lyapunov function, the proposed differential inequality and the time scale theory, applicable to continuous, discrete and hybrid time domains. Furthermore, under the event-triggered condition, it is demonstrated that the lower bound of each event-triggered interval exceeds a positive constant, thereby preventing the occurrence of Zeno’s behavior. Finally, the approach efficacy is validated through numerical examples.

Chatter Stability of Orthogonal Turn-Milling Process in Frequency and Discrete-Time Domains

Abstract As the industry seeks better quality and efficiency, multitasking machine tools are becoming increasingly popular owing to their ability to create complex parts in one setup. Turn-milling, a type of multi-axis machining, combines milling and turning processes to remove material through simultaneous rotations of the cutter and workpiece with the translational feed of the tool. While turn-milling can be advantageous for large parts made of hard-to-cut materials, it also offers challenges in terms of surface form errors and process stability. Because tool eccentricity and workpiece rotation lead to more complexity in process mechanics and dynamics, traditional milling stability models cannot predict the stability of turn-milling processes. This study presents a mathematical model based on process mechanics and dynamics by incorporating the unique characteristics of the orthogonal turn-milling process to avoid self-excited chatter vibrations. A novel approach was employed to model time-varying delays considering the simultaneous rotation of the tool and workpiece. Stability analysis of the system was performed in both the discrete-time and frequency domains. The effects of eccentricity and workpiece speed on stability diagrams were demonstrated and validated through experiments. The results show that the tool eccentricity and workpiece speed alter the engagement geometry and delay in the regeneration mechanism, respectively, leading to significant stability diagram alterations. The proposed approach offers a comprehensive framework for the stability of orthogonal turn-milling and guidance for the selection of process conditions to achieve stable cuts with enhanced productivity.

Linear, Nonlinear, and Distributed-Parameter Observers Used for (Renewable) Energy Processes and Systems—An Overview

Full- and reduced-order observers have been used in many engineering applications, particularly for energy systems. Applications of observers to energy systems are twofold: (1) the use of observed variables of dynamic systems for the purpose of feedback control and (2) the use of observers in their own right to observe (estimate) state variables of particular energy processes and systems. In addition to the classical Luenberger-type observers, we will review some papers on functional, fractional, and disturbance observers, as well as sliding-mode observers used for energy systems. Observers have been applied to energy systems in both continuous and discrete time domains and in both deterministic and stochastic problem formulations to observe (estimate) state variables over either finite or infinite time (steady-state) intervals. This overview paper will provide a detailed overview of observers used for linear and linearized mathematical models of energy systems and review the most important and most recent papers on the use of observers for nonlinear lumped (concentrated)-parameter systems. The emphasis will be on applications of observers to renewable energy systems, such as fuel cells, batteries, solar cells, and wind turbines. In addition, we will present recent research results on the use of observers for distributed-parameter systems and comment on their actual and potential applications in energy processes and systems. Due to the large number of papers that have been published on this topic, we will concentrate our attention mostly on papers published in high-quality journals in recent years, mostly in the past decade.

Empirical study of robust/developed PID control for nonlinear time-delayed dynamical system in discrete time domain

In addition to the high nonlinearity of liquid dynamics inside a tank, a study was conducted to overcome loading/unloading liquid storage tank control problems. In this study, the author developed a nonlinear control system to conquer both nonlinearity and the significant time delay arising from using a pressure-difference-based level sensor. To this end, this study proposes the implementation of nonlinear state dependent (SDP-PID+) control using the SDP transfer function model as a class of nonlinear descriptions of dynamical systems. By incorporating additional robust (plus) compensators alongside the traditional P-, I-, and D-compensators, the robust SDP-PID controller utilizes the complete state feedback to create a time-varying state variable feedback (SDP-SVF) control law. This approach effectively mitigates the effects of the discrete-time SDP-TF. It introduces the pole placement tuning approach, which renders significant performance using the laboratory test rig TPS8.2.2.4, for automatic liquid level control.

Adaptive output-feedback event-triggered formation control for underactuated ships with obstacle avoidance mechanism

This paper focuses on the adaptive output-feedback event-triggered control strategy for the formation tracking and obstacle avoidance activity of unmanned surface vessels (USVs) with unmeasurable velocity, constrained communication and actuator fault. By using the neural networks and minimal learning parameter, a novel output-feedback event-triggered controller is deigned, effectively alleviates constraints related to continuous feedback signal acquisition in dynamic systems. Subsequently, by incorporating an adjustable threshold, the event-triggered condition is established, thus facilitating updates to the state and adaptive law solely within the discrete-time domain. Then, only two aperiodic adaptive laws are derived to mitigate actuator faults and system uncertainties. As for the path planning, benefiting from the artificial potential field method, a novel obstacle avoidance mechanism is developed for obstacle avoidance and waypoint-based path navigation. Considerable effort has been made to guarantee the semi-globally uniformly ultimately bounded stability. Finally, two numerical simulations are illustrated to demonstrate the remarkable performance of the proposed control strategy.

H∞ mean square finite-time control for Markov jump linear system with multiple equilibria

In this article, the mean square finite-time [Formula: see text] control problems of two types of Markov jump linear system with multiple equilibria are investigated. To be specific, Markov jump linear system with multiple equilibria in discrete-time domain and continuous-time domain are considered, respectively, in which the equilibria of subsystems are different. First, an average equilibrium is introduced to equivalently reformulate the initial system expressions. Following this method, some sufficient conditions guaranteeing that Markov jump linear system with multiple equilibria subjected to norm bounded disturbance is mean square finite-time boundedness are proposed, and the results are extended to [Formula: see text] mean square finite-time boundedness. Then, mean square finite-time [Formula: see text] controllers are designed separately to stabilize the two types of Markov jump linear system with multiple equilibria and also achieve the prescribed [Formula: see text] performance index. The proposed methods in this article are a natural generalization of typical results in Markov jump linear system sharing common equilibrium. Finally, two numerical examples are exploited to demonstrate the effectiveness of the methods proposed in this article.

Design of a model‐free controller based on predictive functional control

AbstractIntelligent‐PID (i‐PID) control proposed by Fliess is a simple control algorithm. The controller is designed based on ultra‐local model, and consisted of PID type controller and derivatives of reference signal and controlled variables. Authors have considered discrete i‐PID controller and its properties, and one of the result was that PD controller was sufficient in discrete time domain. In discrete i‐PID controller, PD type controller is still required to ensure convergence of controlled error to zero, and PD type parameters affects convergence property, fast‐response property and stability. In this paper, predictive functional control (PFC) based on an ultra‐local model is proposed. By introducing of PFC, controlled variable converge to reference value without PD type controller. User‐specified parameters of the proposed controller is smaller than the conventional i‐PID controller. Characteristics of the proposed controller are compared with discrete i‐PID controller by numerical examples.

Application of the Z-transform on the deconvolution of lightning electric field waveforms obtained from single-station measurements

Fast electric field measurement systems used in the field of atmospheric electricity often have decay time constants of the order of 1 ms, which means that slower processes – such as long continuing currents – are not visible in the raw electric field records. This paper presents a practical approach to compensate for the time decay caused by the system response and regain the original lightning electric field waveforms. To accomplish this task, the transfer function of the measurement system is modeled in the Z-domain. Then, from the inverse Z-transform of the transfer function, the compensated electric field is obtained in discrete time domain. Based on data obtained at Nova Gameleira campus of CEFET-MG (Belo Horizonte, Brazil), we present and discuss results of typical electric field waveforms that include some slower lightning processes, which are not readily observable in the raw data.

Adaptive Predictive Deadbeat Current Control of Single-Phase Multi-Tuned Shunt Hybrid Active Power Filters

This paper suggests an adaptive predictive deadbeat current control method for single-phase multi-tuned shunt hybrid active power filters (HAPFs) to improve the power quality of single-phase and three-phase four-wire utility grids. The HAPF structure eliminates the resonance between the passive power filter and the grid impedance. Furthermore, it can be integrated into passive filters to enhance their filtering performance. In this paper, a digital algorithm is proposed for managing the performance of each converter leg accurately. To do so, an exact model of the high-order system is developed, and the transfer function of the plant is calculated in continuous and discrete time domains. Then, a predictive deadbeat technique for HAPF current control is presented, which benefits from high accuracy, fast dynamics, and low sensitivity to system parameter mismatches. Extensive simulation and experimental tests are conducted and the results match well to confirm the success and appropriate performance of the overall system. Also, performance comparison with conventional solutions demonstrates the superiority of the suggested filtering technique.

Model-Matching Control for Low Switching Frequency Converters Unifying Different Performance Requirements

This paper presents an active damping control for LCL-filtered grid-connected converters to meet strict grid codes and power quality standards. The control strategy allows unifying into a single design procedure different requirements demanded by system operators. A model-matching approach is used to set the reference tracking and disturbance rejection transfer functions separately, which provides an additional degree of freedom to the converter control design. On the other hand, the measurement stage and digital implementation effects are considered in the control design to maximize the control bandwidth. The proposed control strategy uses a reduced number of sensors and is able to compensate unbalanced and distorted grid voltage conditions; it presents a systematic design and is formulated in the discrete-time domain, enabling a direct digital implementation. Performance assessment and comparison of different control strategies are performed using eigenvalue and transient response analyses. The effectiveness and advantages of the proposed strategy are validated through an experimental setup.

Frequency analysis of a discrete-time fast nonlinear tracking differentiator algorithm based on isochronic region method

<p>In fault detection, feedback control, and other fields, real-time differential estimation of a given signal in a complex noise environment is an important but challenging task. In this paper, a discrete-time fast nonlinear tracking differentiator (FNTD) based on hyperbolic tangent functions was proposed. To start, the differential signal acquisition problem was equated to the time-optimal control (TOC) law for constructing a double-integral system using a state feedback approach. Next, the FNTD algorithm based on the hyperbolic tangent function was presented by utilizing the isochronic region (IR) method in the discrete time domain. Then, the frequency-domain characteristics of the FNTD were analyzed and the rule for tuning the parameters was provided by the frequency scan test method. Finally, the simulation results demonstrated that the proposed FNTD had fast and accurate tracking performance, as well as excellent filtering and differential extraction capability compared with other differentiators.</p>

Finite-time prescribed performance tracking control of seeker stabilized platform in the discrete-time domain

Current prescribed performance control (PPC) focuses on continuous-time systems, while this article proposes a novel discrete-time version of PPC for finite-time tracking of seeker stabilized platform in the discrete-time domain. Firstly, the newly developed performance functions are employed to impose finite-time prescribed performance on tracking errors. After that, a type of stabilization functions with respect to transformed errors are constructed for back-stepping controllers designing. On this basis, transformed errors are indirectly stabilized, and thus the pursued prescribed transient and steady-state behaviors are ensured for tracking errors via Lyapunov synthesis. Different from existing sliding-mode-control based discrete-time PPC, the addressed approach eliminates the sliding-mode structure and hence avoids high frequency chattering caused by such framework. Finally, compared simulations validate the superiority over existing methods.