Zero-order Hold Research Articles

An H∞ Output Tracking Control Approach to Sampled-Data Control for Nonlinear Networked Control Systems

In this article, we study the problem of H ∞ output tracking control and analyze the stability of nonlinear networked control systems with dynamic quantization, variable sampling intervals and communication delays. To improve the bandwidth utilization, an event-triggered mechanism is introduced in network control systems. Different from traditional periodic sampling control, the event trigger control adopted in this study is only controlled when the current sampling signal meets the triggering conditions, which can effectively reduce resource waste in network control systems by ensuring system control performance. By adopting input-delay and parallel distributed compensation (PDC) techniques, we establish an augment tracking model based on the Takagi-Sugeno (T-S) fuzzy model, in which the sampling interval of the sampler and the signal transmission delay are transformed into the refreshing interval of a zero-order holder (ZOH). Furthermore, we use the applicable lyapunov-krasovski-based approach to derive conditions expressed in linear matrix inequalities (LMIs), helping the problem to be accurately solved using the LMI toolbox in Matlab. Examples are given to illustrate the effectiveness of our results, especially the good tracking effect of the designed fuzzy controller.

Observer-based sliding mode control for discrete nonlinear systems with packet losses: an event-triggered method

In this paper, the observer-based output feedback sliding mode control (SMC) problem is investigated for discrete delayed nonlinear systems subject to packet losses under the event-triggered strategy. It is assumed that the packet losses may occur in the control channel from the sensor to the observer. A suitable compensation strategy via the Bernoulli distributed random variable is used to reduce the effects of packet losses. In order to avoid the phenomenon of network congestion during the networked transmission, an event-triggered mechanism is introduced to determine if the last released measurement needs to be updated. Based on the zero-order-hold (ZOH) measurement, an output feedback observer is designed to reconstruct the system state. This method can facilitate the design of the discrete-time sliding surface. A sufficient condition is proposed to guarantee the stochastic stability of sliding mode dynamics systems by using linear matrix inequality (LMI) method, and a novel observer-based sliding mode controller is synthesized to force the trajectories of the error systems onto the pre-designed sliding mode surface within finite time. Finally, an example is given to illustrate the validity of the proposed theoretical result.

Robust Regulator Design of General Linear Systems with Sampled Measurements

This paper studies the robust output regulation problem of general linear continuous-time systems with periodically sampled measurements, consisting of both the regulation errors and the extra measurements. With some standard conditions, we propose a novel robust implementable regulator design paradigm, that is comprised of a generalized zero-order hold device, a discrete-time compensator, a discrete-time washout filter and a discrete-time stabilizer.

Stabilization of systems with sector bounded nonlinearity by a sawtooth sampled-data feedback

The paper considers a nonlinear Lur’e type system with a sector bounded nonlinearity. The zero equilibrium of the system may be unstable, so it is stabilized by a periodically sampled feedback signal. Such stabilization problems were previously explored by a number of researches with the help of the zero-order hold (ZOH) control that is kept constant between successive sampling times. The main disadvantage of this method is that the time delay introduced by ZOH has a destabilizing impact on the closed feedback system, especially in the case when the sampling frequency is sufficiently low and the feedback gain is high. To reduce this effect it is proposed to modify the form of the stabilizing signal. In this paper the reverse sawtooth control is introduced instead of ZOH. The stability criterion is obtained in the form of a feasibility problem for some linear matrix inequalities (LMI). A numerical example demonstrates how the new stabilization method allows to reduce the sampling frequency required for stabilization.

Nuclear Norm Subspace System Identification and Its Application on a Stochastic Model of Plague

The discrete-time model of plague is deduced by zero-order holder based on the continuous-time model. Due to the existence of stochastic disturbances, the stochastic model is given corresponding to the discrete-time model. The state estimation and noise reduction of the stochastic model are achieved by designing Kalman filter. Nuclear norm minimization is to structure the low-rank matrix approximation instead of the singular value decomposition in the process of subspace system identification. According to the plague data from the World Health Organization, the system matrices and noise intensity of the model are identified. Simulations are carried out to show the higher approximation capability of the proposed method.

Neutralizing zero dynamics attack on sampled-data systems via generalized holds

Zero dynamics attacks can be lethal to cyber–physical systems because they can be harmful to physical plants and impossible to detect. Fortunately, if the given continuous-time physical system is minimum phase, the attack is not so effective even if it cannot be detected. However, the situation can become unfavorable if one uses digital control by sampling the sensor measurement and using a zero-order hold for actuation because of the ‘sampling zeros.’ When the continuous-time system has a relative degree greater than two and the sampling period is small, the sampled-data system must have unstable zeros (even if the continuous-time system is minimum phase), so that the cyber–physical system becomes vulnerable to ‘sampling zero dynamics attack.’ In this paper, we present an idea to neutralize the zero dynamics attack for single-input and single-output sampled-data systems by shifting the unstable discrete-time zeros into stable ones. This idea is realized by employing the so-called ‘generalized hold’ which replaces a standard zero-order hold. It is shown that, under mild assumptions, a generalized hold exists which places the discrete-time zeros at desired positions. Furthermore, we formulate the design problem as an optimization problem whose performance index is related to the inter-sample behavior of the physical plant, and propose an optimal gain which alleviates the performance degradation caused by generalized hold as much as possible.

Stabilizing transmission intervals and delays in nonlinear networked control systems through hybrid-system-with-memory modeling and Lyapunov–Krasovskii arguments

This article employs the hybrid-system-with-memory formalism to attain transmission intervals and delays that provably stabilize Networked Control Systems (NCSs). Nonlinear time-varying plants and controllers with variable discrete and distributed input, output and state delays along with nonconstant discrete and distributed network delays are considered. We bring together nominal system L2-stability, Uniformly Globally Exponentially Stable (UGES) scheduling protocols and linear upper bounds of network-induced output error dynamics to infer Uniform Global pre-Asymptotic Stability (UGpAS) of the closed-loop system via Lyapunov–Krasovskii arguments. Namely, we replace the Lyapunov–Razumikhin conditions and trajectory-based small-gain theorem with linear L2-gains arguments, featured in our previous works, with Lyapunov–Krasovskii functionals to prove UGpAS of interconnected hybrid systems with memory. The present methodology allows for more general delays (e.g., multiple input/output/state discrete and distributed delays) and output error dynamics (e.g., multiple discrete and distributed delays) as well as less conservative estimates of Maximally Allowable Transfer Intervals (MATIs). Our results are applicable to control problems with output feedback and the so-called large delays, that is, delays larger than the transmission intervals. In addition, model-based estimators between two consecutive updates, rather than merely the Zero-Order Hold (ZOH) strategy, are allowed for in order to prolong MATIs. Lastly, a nonlinear numerical example involving a single-link robot arm and observer–predictor-based control law is provided to illustrate our theoretical findings.

The research of the influence of digital exchange in the stabilization system of the unmanned aerial vehicle on the dynamic characteristics of the steering actuator

When designing a stabilization system for highly maneuverable unmanned aerial vehicles (UAVs), one of the relevant tasks is to impose requirements on the dynamic characteristics and control methods of the steering actuators, which will ensure the required stability margins of the stabilization system as part of the UAV control system. Currently, there is an increasing preference for microcontroller method of electric actuator control and digital exchange between the control system and the steering actuators. One of the reasons for the reduction of stability margins of the stabilization system is the delay introduced by the digital exchange between the elements of the stabilization system. In the process of solving the problem of transition to digital exchange between the elements of the stabilization system, a research was conducted of the influence of amplitude and phase distortions arising in the path "data transmission interface steering actuator" on the dynamic characteristics of the steering actuator. As an actuator of the stabilization system, the real electric drive used on highly maneuverable UAVs is considered. For this drive, extremely stringent requirements for bandwidth and phase delays are introduced, which complicates the problem of ensuring the stability of the stabilization system, taking into account the delays in the digital exchange. As a result of the research, a frequency model has been proposed that allows to estimate the minimum possible exchange rate in the path "data interface steering actuator", taking into account ensuring the required dynamic characteristics of the actuator. In the proposed model, the data transfer interface is represented as a zero-order hold, the transfer function of which is replaced by Pade approximations of the second order. In the course of the research, a comparison was made of the results obtained on the proposed model with the results of experiments on a real electric actuator and its complete nonlinear time model. The main advantage of the proposed frequency model is the simplicity of obtaining the transfer function of the path "data interface steering actuator". This allows at the initial stage of the research to quickly and accurately determine the minimum possible rate of exchange, which will ensure the fulfillment of the requirements imposed on the drive dynamics.

Event-triggered sliding mode control of Markovian jump systems against input saturation

In this work, we pay attention to investigating event-triggered sliding mode control (SMC) strategy with input saturation for a class of Markovian jump systems (MJSs). The state vectors of MJSs are to be sufficiently sampled by a performed event trigger mechanism in a periodic computation way. However, there are some inevitable delays, on the channel from sensor to controller, occurring on the sampling process. For the demand of updates of control input, it is necessary to keep receiving and sending delayed state signals, thus we employ a zero-order-hold (ZOH) in the proposed framework to make the event-triggered SMC strategy come true. Then, by designing an integral-type sliding surface function, combining with the prior knowledge of event trigger scheme, the sliding mode dynamics is derived and the criterion of stochastic stability with H∞ attenuation performance are established. After that, an event-triggered SMC law, which aims at impelling the system trajectories to arrive on the sliding surface, is designed. Furthermore, we take input saturation into account, and specially, in this situation, we propose an adaptive control law of the integral-type sliding surface for the first time. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed results.

Discretisation performance analysis of sliding mode controlled DC–DC buck converter via zero‐order holder

This study investigates the discretisation effects of the zero-order holder (ZOH) on DC–DC buck converters under the direct ON/OFF control of sliding mode (SM), and the two core issues of stability and periodicity for the discrete system are focused on. The optimal parameter for the SM controller is first given on the basis of stability and response speed in the continuous-time domain, following its ZOH discretisation. Restricted by the existence condition of discrete SM, the guaranteed stability is investigated and compared with that of the continuous system in the phase plane, proving that the sampling time of ZOH affects its stability region. Meanwhile, the periodic dynamics, including the system state and the symbolic sequence of switching control law, is further studied via analysing the steady limit cycle of state in phase plane; and the existence condition of multi-periodicity is also deduced. Innovatively this study establishes the influence relationship of the periodic dynamics with the performances of the steady-state error of output voltage and switching frequency. Simulation and experiment results are presented to validate the theoretical and practical value of the proposed research.

Stability Analysis of Nonlinear Networked Control System with Integral Quadratic Constraints Performance in Takagi-Sugeno Fuzzy Model

This paper focuses on the stability analysis of nonlinear networked control system with integral quadratic constraints (IQC) performance, dynamic quantization, variable sampling intervals, and communication delays. By using input-delay and parallel distributed compensation (PDC) techniques, we establish the Takagi-Sugeno (T-S) fuzzy model for the system, in which the sampling period of the sampler and signal transmission delay are transformed to the refreshing interval of a zero-order holder (ZOH). By the appropriate Lyapunov-Krasovskii-based methods, a delay-dependent criterion is derived to ensure the asymptotic stability for the system with IQC performance via the H∞ state feedback control. The efficiency of the method is illustrated on a simulation exampler.

Spectral Analysis of UPWM Signals for Filterless Digital Class D Power Amplifiers

Filterless digital class D power amplifiers usually utilize three-level uniform sampling pulse width modulation (UPWM) technique to convert the digital input signal into a UPWM signal which is used to drive the power stage. Therefore, the spectral estimation expressions for different three-level UPWM signals obtained by modulating the digital signal can be an evaluation tool for signal distortion and electromagnetic interference when filterless digital class D power amplifiers are designed. Based on the time-domain characteristics of three-level UPWM signals, the spectral estimation expressions for six types of three-level UPWM signals are proposed in this paper by using the discrete Fourier transform technique and the frequency response of the zero-order holder. According to these expressions, the relationships among the total harmonic distortion, the pulse repetition frequency and the pulse width resolution of the UPWM signal are studied. A UPWM generator test system based on field-programmable gate array is designed and implemented to measure the spectra of different UPWM signals. The measured results are compared with the calculated results obtained by the proposed expressions to verify the correctness of the proposed expressions.

The Generation Mechanism of Tracking Error During Acceleration or Deceleration Phase in Ultraprecision Motion Systems

In this paper, the generation mechanism of the tracking error during the acceleration or deceleration phase in ultraprecision motion systems is studied. For the first time, the analytical relationship among the tracking error, a feedforward controller, a feedback controller, and a reference trajectory is presented. Quantitative analysis shows that the tracking error is approximately proportional to a specific derivative of trajectory with given feedback and feedforward controllers. Moreover, the tracking error in ultraprecision motion systems is also greatly influenced by the effect of zero-order hold and time delay, which necessitates jerk feedforward. The analysis not only explains the generation mechanism of the tracking error, but also provides a criterion to judge the accuracy of feedforward coefficients by the shape of a residual tracking error. Based on this criterion, a feedforward tuning algorithm using dichotomy is proposed. The simulation and experiment both well-validate the generation mechanism of the tracking error and the proposed feedforward tuning algorithm.

Protocol-Based Unscented Kalman Filtering in the Presence of Stochastic Uncertainties

In this paper, the unscented Kalman filtering (UKF) problem is investigated for a class of general nonlinear systems with stochastic uncertainties under communication protocols. A modified unscented transformation is put forward to account for stochastic uncertainties caused by modeling errors. For preventing data collisions and mitigating communication burden, the round-robin protocol and the weighted try-once-discard protocol are, respectively, introduced to regulate the data transmission order from sensors to the filter. Then, by employing two kinds of data-holding strategies (i.e., zero-order holder and zero input) for those nodes without transmission privilege, two novel protocol-based measurement models are formulated. Subsequently, by resorting to the sigma point approximation method, two resource-saving UKF algorithms are developed, where the impact from the underlying protocols on the filter design is explicitly quantified. Finally, compared with the protocol-based extended Kalman filtering algorithms, a simulation example is presented to demonstrate the effectiveness of the proposed protocol-based UKF algorithms.

Synchronization of Network Systems via Aperiodic Sampled-Data Control With Constant Delay and Application to Unmanned Ground Vehicles

In this paper, the synchronization issue for network systems with nonlinear dynamics is considered. Together with zero-order holder, the aperiodic sampled-data control law is utilized. Compared with the traditional periodic sampled-data control method, this approach demonstrates more greater flexibility. Adopting input delay approach, the initial sampled-data system is remodeled by continuous time system involving time-varying delays in the control signals. For the purpose of designing the sampling controllers suffering constant delays, an updated Lyapunov functional is developed from the augmentation of Wirtinger's inequality. Such a Lyapunov functional results in efficient and simplified synchronization conditions. A sufficient condition for synchronizability of network systems is set up. Then, for the case of unstable systems with some constant delays, a fresh discretized Lyapunov functional is introduced. Finally, we utilize the numerical simulation outcomes to prove the efficacy and advantage of our algorithm. Moreover, based on the network unmanned ground vehicle systems, the experiment results in a real scenario are provided to illustrate the effectiveness of the designed synchronization scheme.

A comparative study of phase margin based digital and analog controlled synchronous buck with optimum LC filter

PurposeTraditionally, industrial power supplies have been exclusively controlled through analog control to sustain high reliability with low cost. However, with the perpetual decrement in cost of digital controllers, the feasibility of a digitally controlled switch mode power supply has elevated significantly. This paper aims to outline the challenges related to the design of digital proportional-integral (PI) controlled synchronous rectifier (SR) buck converter by comparing controller performance in continuous and discrete time. The trapezoidal approximation-based digital PI control is designed for low voltage and high-frequency SR buck converter operating under continuous conduction mode.Design/methodology/approachThe analog and digital controller are designed using a SISO tool of MATLAB. Here, zero-order hold transform is used to convert the transfer function from continuous to discrete time. Frequency and time domain analysis of continuous plant, discrete plant and close loop system is performed. The designed digital PI control is simulated in MATLAB Simulink. The simulated results is also verified on hardware designed around digital signal processing control.FindingsThe continuous and discrete control loops are validated with multiple tests in the time and frequency domain. The detailed steady state theoretical analysis and performance of the SR buck converter is presented and verified by simulation. It is found that the delay in digital control loop results in a low phase margin. This phase margin decreases with higher bandwidth. The hardware experiments with the digital control loop are carried out on a 10 W prototype. The chosen parameters for the SR buck converter are found to be optimum for steady and transient state response.Originality/valueThis paper compares the digital and analog control approach of compensator design. It focuses on the implications created at the time of transforming the control design from continuous to discrete time. Further, it also focuses on the selection of parameters such as phase margin, bandwidth and low pass filter.

The Small-Signal Stability Analysis of the Droop-Controlled Converter in Electromagnetic Timescale

Recently, the converters controlled by droop controller with phase-locked loop were observed in islanded ac microgrids. However, only the state-space-based approach was applied to investigate the stability of this converter in the previous works. Compared with the state-space-based approach, the characteristic equation approach has plenty of advantages, such as convenient stability margin analysis (phase margin, gain margin, etc.) and simple stability criterion (Routh criterion). Thus, a novel small-signal modeling approach based on characteristic equation for converter-dominated ac microgrids is proposed to assess the system low-frequency stability in this paper. First, considering zero-order holder and time delay, the small-signal characteristic equation of this converter is presented by Pade approximation and dynamic phasor model. Furthermore, the implementation and parameter design of the converters are studied under the practical considerations. Compared with the existing characteristic equation methods, the proposed approach can verify that the performance is significantly improved. Eventually, simulations and experimental results are presented, indicating that the proposed approach can assess the system low-frequency stability conveniently and accurately.

Multirate control of nonlinear robotic manipulators with network structure under bounded disturbances

This paper investigates a novel nonlinear multirate controller for robotic manipulators exposed to communication constraints and external disturbances. An improved tracking control methodology using an estimated discrete-time model of the robot is presented in this paper. The input-to-state stability of the sampled-data dynamics of the robot is preserved for both single-rate and multirate samplings. The obtained outcomes demonstrate that the sampled-data structure can stabilize the robotic manipulator when the continuous-time controller is not valid in the presence of communication networks. The output sampled measures of the robot provide piecewise signals for the controller, and the input to the plant results from a time-driven zero order hold device. In this paper, the discontinuous Lyapunov-based method is proposed to reject time variant and bounded disturbances. This is a novel controller design that can lead to the exact trajectory following without having details of the nonlinear dynamics of the robot. The main target is improving the accuracy of tracking ability of the robot manipulator to follow a reference input affected by constant bounded disturbances. Simulation results performed on a two degrees of freedom manipulator indicate that under proper assumptions, accurate trajectory tracking, and disturbance rejection at the input can be obtained by using the proposed structure. The example also demonstrates that the proposed multirate controller can successfully stabilize the robotic system.

High-precision tracking differentiator via generalized discrete-time optimal control

An enhanced discrete-time tracking differentiator (TD) with high precision based on discrete-time optimal control (DTOC) law is proposed. This law takes the form of state feedback for a double-integral system that adopts the Isochronic Region approach. There, the control signal sequence is determined by a linearized criterion based on the position of the initial state point on the phase plane. The proposed control law can be easily extended to the TD design problem by combining the first-state variable of the double-integral system with the desired trajectory. To improve the precision of the discretization model, we introduced a zero-order hold on the control signal. We also discuss the general form of DTOC law by analysing the relationship between boundary transformations and boundary characteristic points. After comparing the simulation results from three different TDs, we determined that this new TD achieves better performance and higher precision in signal-tracking filtering and differentiation acquisition than do existing TDs. Also the comparisons of the computational complexities between the proposed DTOC law and normal one are demonstrated. For confirmation of its utility, we processed raw phasor measurement units data via the proposed TD. In the absence of complex power system modelling and historical data, it was verified that the proposed TD is suitable for applications of real-time synchrophasor estimations, especially when the states are corrupted by noise.

Stability of Limiting Zeros of Sampled-data Systems with Backward Triangle Sample and Hold

The backward triangle sample and hold (BTSH) is a novel sample and hold function. This paper concentrated on the stability of zeros in the sampled-data system that arising from the case of a BTSH and a continuous-time system in cascade. The properties and stable conditions of the limiting zeros for sufficiently small or large sampling period in BTSH case are displayed. The framework of the limiting zeros is derived in the two different sampling rates. It is demonstrated that one can choose a suitable parameter value of BTSH, where the limiting zeros of the resulting sampled-data system can be located inside the stable region while the zero order hold (ZOH) fails to do. Finally, numerical examples are provided to better show proposed theories in this paper.