Zero-order Hold Research Articles

Residence time density (RTd) identification through deconvolution of finite time horizon input output data and its Application to a novel analytical dispersion process RTd model

This work presents first an approach to the identification of Residence Time density (RTd) and Residence Time Distribution (RTD) functions, through deconvolution of finite time horizon, input/output data generated by a zero-order hold input, using the novel concept of zero-order hold, average, impulse response coefficients. Subsequently, a novel RTd analytical expression is derived for an open-open axial dispersion process with a finite experimental section in a tube of infinite length, and an explanation is provided for this RTd model’s differences from the literature. This new RTd expression is then employed in two case studies to demonstrate the effectiveness of the proposed identification through a deconvolution conceptual framework in identifying RTd model parameters, and in assisting in the selection of RTd models which are compatible with experimental data.

Adaptive gain design for Zero-Order Hold discrete-time implementation of explicit reference governor

Explicit reference governor (ERG) is an add-on unit that provides constraint handling capability to pre-stabilized systems. The main idea behind ERG is to manipulate the derivative of the applied reference in continuous time such that the satisfaction of state and input constraints is guaranteed at all times. However, ERG should be practically implemented in discrete-time. This paper studies the discrete-time implementation of ERG, and provides conditions under which the feasibility and convergence properties of the ERG framework are maintained when the updates of the applied reference are performed in discrete time. Specifically, using Zero-Order Hold (ZOH) discretization method, we develop an adaptive algorithm to adjust the gain of the discretized term based on actual measurements to maintain all properties of ERG when implemented in discrete-time. The proposed approach is validated via extensive simulation and experimental studies.

Impact load identification method based on frequency response pattern recognition and dynamic sensor filter strategy

Identification of impact loads plays important role in marine structures health monitoring but is difficult to be measured directly most time. This study investigates a two-stage framework for impact load localization and reconstruction, consisting of load region identification and local refined nodal search. For the region identification, a novel frequency response feature preprocessing method based on FFT is proposed and incorporated into a multi-layer perceptron (MLP) neural network as the embedding function of the Matching Network (MN), the core model adopted for pattern recognition. Based on the region probabilities predicted by MN, a local refined nodal search strategy is provided, which is initialized by a region correction method for amending the possible region misclassification and further guided by error metrics with iteration search strategy. Moreover, the inverse problem in this study is formulated in the discretized state space expression with the reduced modal coordinates. For improving the load inverse accuracy affected by Zero Order Hold (ZOH) simplification in this formulation, a dynamic sensor filter strategy is provided. Eventually, a numerical experiment of impact load identification on a steel plate is performed and discussed, whose results indicate the validity and robustness of the proposed method.

VSG Sequence Impedance Modeling and Stability Analysis of Dead-Beat Control

Virtual Synchronous Generator uses dead-beat predictive control in the voltage and current loop to improve the dynamic response speed of the system, but the presence of zero-order hold and computation time can lead to system instability. To address this issue, this paper adopts an improved dead-beat predictive control strategy for VSG. This is achieved by linear interpolation to forward predict voltage-current reference values to reduce the impact of delay, while introducing error compensation coefficients to enhance the stability of the voltage-current inner loop of VSG. The selection of error compensation coefficients is based on closed-loop impulse response functions. A harmonic linearization method is used to construct a complete sequence impedance model of VSG, and it's stability is analyzed. The results indicate that VSG's negative sequence impedance exhibits instability in the low-frequency range. To address this, a method of introducing a virtual resistor into VSG is proposed to improve stability. By constructing a sequence impedance model of VSG that includes virtual resistance, the variations in system stability under different virtual resistances and grid impedances are analyzed. The effectiveness of the proposed method is verified by building a VSG model.

Non‐fragile observer‐based security control for networked systems via event‐triggered WTOD protocol

AbstractThis paper investigates the security control issue for fuzzy networked systems with uncertainty under false data injection (FDI) and aperiodic denial‐of‐service (ADoS) attacks via sliding mode approach. To mitigate the communication burden, a novel mechanism compromising the advantages of the adaptive event‐triggered (AET) scheme and weighted try‐once‐discard (WTOD) protocol is proposed. In particular, the triggered threshold with real‐time characteristics varies with the measurement outputs. To be specific, the shared insecure communication network can be subjected to hybrid attacks including the stochastic FDI attacks and ADoS attacks limited by duration and frequency. Moreover, the token‐dependent fuzzy non‐fragile observer (NFO) with norm‐bounded uncertainty and corresponding fuzzy control law are constructed by virtue of the Zero‐Order‐Hold (ZOH) strategy. Then, several sufficient criteria that guarantee the exponential stability of the system and the reachability of the specified sliding surface are given. Eventually, a numerical example is presented to verify the applicability of the proposed security control strategy.

On derivative-free sample-and-hold control with prescribed performance

A feedback controller is proposed to perform output reference tracking with prescribed performance for nonlinear continuous-time systems of relative degree two. The controller is of sampled-data type, i.e., measurements are available only at sampling times – a typical situation in real systems when sensors are involved. Furthermore, only output information is available, i.e., neither the full state nor derivatives can be used for feedback. A sufficient uniform sampling rate is derived and the control consists of piecewise constant signals on the sampling intervals, i.e., zero-order hold. Feasibility of the controller and satisfaction of the control objective are rigorously proven. The controller is illustrated by a numerical example.

Discrete-time Negative Imaginary Systems from ZOH Sampling

A new definition of discrete-time negative imaginary (NI) systems is provided. This definition characterizes the dissipative property of a zero-order hold sampled continuous-time NI system. Under some assumptions, asymptotic stability can be guaranteed for the closed-loop interconnection of an NI system and an output strictly negative imaginary system, with one of them having a one step advance. In the case of linear systems, we also provide necessary and sufficient frequency-domain and LMI conditions under which the definition is satisfied. Also provided is a simple DC gain condition for the stability results in the linear case.

Performance analysis of digitally controlled nonlinear systems considering time delay issues

In this paper, a comprehensive investigation into discretization, effective sample time selection considering delays in the system, and time and frequency domain analysis of a DC-DC buck converter, which plays a vital role in photovoltaic (PV) systems, is conducted to enhance the understanding of their dynamic behavior, optimize control algorithms, improve system efficiency, and ensure reliable power conversion in photovoltaic applications. To effectively address the non-linear behavior and enhance digital control of a buck converter by selecting the best sample time, several approaches can be employed. These include accurate modeling and identification of non-linear elements, development of advanced control algorithms that account for non-linearities, implementation of adaptive control techniques, and utilization of feedback mechanisms to compensate for deviations from linearity. By considering and mitigating the non-linear behavior, digital control systems can achieve improved accuracy, stability, and transient behavior in regulating the buck converter's output waveforms (voltage or current). The results of the study demonstrated that the trapezoidal integration method which is also known as bilinear approximation, or Tustin's approach outperformed other commonly used discretization methods, such as first-order hold (FOH), zero-order hold (ZOH), impulse response matching (impulse invariant), and matched pole-zero (MPZ) technique, in dual-domain (both time and frequency) analysis. The key finding highlighting the superiority of the bilinear approximation was its ability to achieve the closest match in the frequency domain bridging the continuous-time and discrete systems. This finding emphasizes the significance of the bilinear approach in preserving the frequency characteristics of the original continuous-time system during discretization. By employing this method, the discrete system closely approximated the behavior of its continuous-time counterpart, ensuring accurate frequency-domain representation.

Event-Triggered Control for a Second Order ODE-Heat System Coupling at Intermediate Point

Motivated by the thermoelastic coupling effect arising in microelectromechanical systems (MEMS), event-triggered control of second-order ODE-heat systems coupled at intermediate point is investigated. The event-triggered control includes two parts, one is the feedback control signal, and the other is the event-triggered mechanism that decides when to update the control input. First, we design an event-triggered controller by using Zero-Order Hold to a continuous-time controller. Then, a dynamic triggering condition is established. Next, we derive that the existence of a minimal dwell-time, which avoids the occurrence of Zeno behavior. By utilizing Lyapunov-Krasovskii functional method, the global exponential stability of the closed-loop system is demonstrated. Finally, the simulation data based on the thermoelastic coupling system is displayed to demonstrate the availability of the theoretical results.

Autonomous Spacecraft Attitude Reorientation Using Robust Sampled-Data Control Barrier Functions

This paper presents a provably safe method for constrained reorientation of a spacecraft in the presence of input constraints, bounded disturbances, and fixed frequency zero-order-hold (ZOH) control inputs. The set of states satisfying all pointing and rate constraints, herein called the safe set, is expressed as the intersection of the sublevel sets of several constraint functions, which are subsequently converted into control barrier functions (CBFs). The method then extends prior results on utilizing CBFs with ZOH controllers to the case of relative-degree-2 constraint functions, as occurs in the constrained attitude reorientation problem. The developed sampled-data controller is also shown to remain provably safe in the presence of input constraints and bounded disturbances. Finally, the method is validated and compared to three prior approaches via both low-fidelity and mid-fidelity simulations.

Latency vs precision: Stability preserving perception scheduling

In robotic systems, perception latency is a term that refers to the computing time measured from the data acquisition to the moment in which perception output is ready to be used to compute control commands. There is a compromise between perception latency, precision for the overall robotic system, and computational resource usage referred to here as the latency-precision trade-off. In this work, we analyze a robot model given by a linear system, a zero-order hold controller, and measurements taken by several perception mode possibilities with different noise levels. We show that the analysis of this system is reduced to studying an equivalent switching system. Our goal is to schedule perception modes such that stability is attained while optimizing a cost function that models the latency-precision trade-off. Our solution framework comprises three main tools: the construction of perception scheduling policy candidates, admissibility verification for policy candidates, and optimal strategies based on admissible policies.

Analysis of the influence of the discrete period of the zero-order hold of the digital automatic control system on dynamic indicators of control quality

The issue of increasing the accuracy of reproduction of the master signal in a digital system for automatic control of an electric drive in the presence of a zero-order extrapolator in the block diagram is considered. The formation of discreteness in a control system with a zero-order extrapolator is considered. The analysis of the influence of the extrapolator discreteness on the dynamic indicators of the system control quality is carried out. As indicators of the quality of control direct indicators: overshoot and time of the transition process. The necessary relationship between the zero-order extrapolator quantization frequency and the bandwidth frequency of the linear part of the system is shown, which ensures the approximation of the above indicators of the quality of control of a discrete system to those of an analog prototype. The bandwidth of the analog part of the system is determined from the logarithmic frequency response. The article provides a recommendation for choosing the quantization frequency of digital controllers with zero-order extrapolators for multi-loop control systems, for example, built on the principle of slave control systems.

Continuous-time approach of sampled-data systems

This paper studies the continuous-time behavior of sampled-data control systems. In these systems, a discrete-time control law is applied to a continuous-time system model using sampling and zero-order hold. Traditionally, sampled-data systems are modeled in discrete-time, and thus, the intersample dynamics cannot be examined. This paper shows that the classical methods (such as the d2c function of MATLAB) for obtaining continuous-time models can be inaccurate between the sampling instants, even when Shannon’s sampling theorem is satisfied. In this paper, a new method is also presented which can be used to characterize the continuous-time dynamics of sampled-data control systems. The new continuous-time system model including the intersample behavior is derived analytically from the discrete-time model, and the results are verified by simulations.

Observer-Based Consensus for Multi-Agent Systems With Semi-Markovian Jumping Via Adaptive Event-Triggered SMC

This paper investigates the observer-based event-triggered adaptive sliding mode control (SMC) problem of the semi-Markovian jumping multi-agent systems (S-MJMASs) with completely unknown and uncertain bounded transfer probabilities (TPs). As impacted by the limited bandwidth of the communication network between individual agents and the unmeasurable state information of the systems, an innovative observer based distributed event-triggered adaptive mechanism (ETAM) is proposed, in which the global information of the network is not used and the triggering threshold is dynamically regulated by the adaptive law to reduce excessive network communication. Additionally, since delays exist between the event trigger and the zero-order holder (ZOH) during data transmission in network communication systems, as well as the semi-Markovian jumping parameters, the uncertainty of systems is increased. In this paper, a novel integral sliding surface is constructed and its reachability and continuity in stochastic senses are guaranteed to withstand interferences. With the help of a stochastic semi-Markovian Lyapunov functional and numerous linear matrix inequalities (LMIs) approaches, certain adequate conditions are achieved to ensure that all agents in S-MJMASs can track the leader. Finally, certain numerical simulations are used to demonstrate the efficiency of the suggested theoretical conclusions.

Prefilter Design for Improved Spectral Flatness of Physical Pseudorandom Perturbations

System identification techniques have been applied to model human sensorimotor systems for research and diagnostic purposes. Accurate human modeling via system identification requires informative experimental data, which further require informative perturbations applied to the human. Previously, designing ideal perturbations for system identification has been extensively studied. On the other hand, the physical realization of perturbations often produces distorted perturbations, resulting in less accurate system identification and incorrect conclusions about the target dynamic system. However, such issues associated with an uncompensated physical realization process have not been fully resolved in the literature. A notable application is the design and use of the pseudorandom sequence (PRS). This article considers the physical realization of PRS perturbations. The impact of zero-order-hold (ZOH) on perturbation quality in terms of the previously proposed band-limited spectral flatness measure (SFM) is identified. To compensate for the spectral flatness degradation due to ZOH, a reference prefilter designed by the Parks–McClellan algorithm is incorporated into the motion control design. A relationship between the prefilter performance and band-limited SFM is established, based on which a prefilter design procedure that guarantees an SFM lower bound of the physically realized perturbations is proposed. Experimental results demonstrated that the proposed prefilter design method effectively improves the SFM of the physical perturbations.

Stability and Robustness Analysis of Finite-Time Consensus Algorithm for Second-Order Multiagent Systems Under Sampled-Data Control

The consensus problem for second-order multiagent systems based on nonsmooth sampled-data control is considered. First, a continuous-time nonsmooth consensus protocol is proposed, which can realize the consensus of systems in a finite time when the external disturbance is absent. Next, based on the sampled data and the zero-order holder, a new discrete-time nonsmooth protocol is proposed. Considering external disturbances, the explicit relationship between the ultimate boundary of errors of any two agents and the sampling period and external disturbance is given with the Lyapunov method and graph theory, which theoretically shows that the nonsmooth control algorithm has a stronger ability to resist external disturbance than the smooth control algorithm. Finally, a simulation example shows the superiority of the nonsmooth consensus algorithm over a smooth consensus algorithm.

Performance Improvement of an NMP Mini Segway Using Sample and Hold Inputs

Early analytical work showed that it is possible to discretize a continuous-time non-minimum phase (NMP) system using special sample and hold inputs (SHIs) and obtain a discrete-time minimum phase (MP) system with a higher sampling rate than that of conventional zero-order sample and hold. As a result, high-gain discrete-time control law can be used to further improve closed-loop system performance since the resulting discrete-time system is MP. In this paper, this technique is adopted for performance improvement on a mini-Segway (MS), a developed robot equipped with an extremely low-cost microcontroller (Arduino). A dual-loop control tuning method was developed to optimize the overall closed-loop system performance. The system performance improvement is demonstrated by the reduction of the mini-Segway oscillation magnitude under idle conditions. The experimental results show that the low-cost microcontroller can be used for the dual-loop SHI control scheme, and the MS cart displacement oscillation magnitude is significantly reduced by more than 65% over the baseline controller. The main contribution of this paper is implementing the proposed sample and hold input (SHI) scheme into an extremely low-cost micro-controller (Arduino) and demonstrating that low-cost microcontrollers can effectively utilize the proposed SHI.

Adaptive Secure Practical Fault-tolerant Output Regulation of Multiagent Systems With DoS Attacks by Asynchronous Communications

The secure practical fault-tolerant output regulation of multiagent systems (MASs) with denial-of-service (DoS) attacks is considered in this paper. Different from most existing output regulation problems: 1) The leader matrix is only known to a part of followers; 2) The communication networks are unreliable and there exist DoS attacks; 3) Actuator faults exist in the MASs. Firstly, to overcome the impact of DoS attacks, the adaptive edge-event-triggered observer is designed to estimate the leader's matrix and state. The novel edge-event-triggered mechanism enables asynchronous intermittent communication between agents, and the adaptive learning rate makes the observer design independent of the global information for the communication topology. Secondly, in order to compensate for the impact of actuator faults on system stability, a novel resilient adaptive event-triggered fault-tolerant controller is designed, and it has zero-order holder (ZOH) characteristics and avoids chattering phenomenon. Finally, two simulation examples well show the effectiveness of our developed methods.

On the Synthesis of Discrete-time Energy-based Regulators for Port-Hamiltonian Systems

This paper aims at describing a synthesis procedure of discrete-time, energy-based regulators for continuous-time port-Hamiltonian systems. The methodology consists of three steps. The first twos deal with the definition of a discrete-time approximation of the plant to be successively employed in the development of the control law. Here, the focus is mainly on the last step, i.e. on how to interconnect digital controller and plant. The coupling is implemented via a zero-order hold and relies on the solution of an optimisation problem that determines the “best” and “minimal” correction to be applied to the nominal action to achieve the same performances obtained when the regulator is in closed-loop with the discrete-time model of the plant. This is the reference scenario used by the designer to develop and tune the control law. The procedure (time-discretisation, control design and coupling implementation) is illustrated in an example.

Sampled-Data Output Feedback Control of Nonlinear ODE-PDE Systems

The aim of this paper is to propose an extension of the high-gain observed-based control design obtained in Ahmed-Ali et al. (2023) to the case of sampled-data systems by considering a Zero-Order-Hold (ZOH) device at the input. Moreover the class of nonlinear PDE is also enlarged by adding a nonlinear term in the heat equation. The stability of the overall closed systems is analyzed by using a suitable Lyapunov function.