Zero-order Hold Research Articles

Membership-Function-Dependent Control Design and Stability Analysis of Interval Type-2 Sampled-Data Fuzzy-Model-Based Control System

This article investigates the design and stability analysis of the interval type-2 (IT2) sampled-data (SD) fuzzy-model-based (FMB) control system with the optimal guaranteed cost performance. An IT2 Takagi–Sugeno (T-S) fuzzy model is applied to describe the dynamics of the nonlinear systems where the parameter uncertainties are captured by the lower and upper membership functions. To conduct the stability analysis for the SD FMB control system, a looped-functional approach taking the advantage of the information about the sampling periods is employed. Because of the SD control strategy, the state will be sampled at each sampling instant and the control signal generated by the IT2SD fuzzy controller will be kept by the zero-order holder during the sampling period, which will result in mismatched membership grades between IT2 T-S fuzzy model and IT2SD fuzzy controller that leads to the complexity in carrying out stability analysis. Thanks to the imperfect premise matching concept, which allows the difference on the number of rules and the premise membership functions between model and controller, the design of the IT2SD fuzzy controller can be more flexible. To further relax the stability conditions and minimize the upper bound of the guaranteed cost index, the membership-function-dependent stability analysis approach which can make use of the features of the IT2 membership functions is adopted. The performance of the control system can also be adjusted through the choice of the weighting matrices in the cost function. The stability conditions building on the Lyapunov stability theory and the performance conditions building on the concept of the guaranteed cost control in the shape of linear matrix inequalities are established to assure the system stability and acquire the optimal guaranteed cost performance. The proposed IT2SDFMB control design is tested on the inverted pendulum system and the simulation results verify the effectiveness of the proposed approach.

Towards implementation of PDE control for Stefan system: Input-to-state stability and sampled-data design

The Stefan system is a representative model for a liquid–solid phase change which describes the dynamics of a material’s temperature profile and the liquid–solid interface position. Our previous work designed a boundary feedback control to stabilize the phase interface position modeled by the Stefan system. This paper resolves two issues our previous work did not study, that are, the robustness analysis under the unknown heat loss and the digital control action. First, we introduce the one-phase Stefan problem with a heat loss by modeling a 1-D diffusion Partial Differential Equation (PDE) dynamics of the liquid temperature and the interface position governed by an Ordinary Differential Equation (ODE) with a time-varying disturbance. We focus on the closed-loop system under the control law proposed in our previous work, and show an estimate of L2 norm in a sense of Input-to-State Stability (ISS) with respect to the unknown heat loss. Second, we consider the sampled-data control of the one-phase Stefan problem without the heat loss, by applying Zero-Order-Hold (ZOH) to the control law in our previous work. We prove that the closed-loop system under the sampled-data control law satisfies the global exponential stability in the spatial L2 norm. Analogous ISS result for the two-phase Stefan problem which incorporates the dynamics of the solid phase is also obtained. Numerical simulation verifies our theoretical results for showing the robust performance under the heat loss and the digital control implemented to vary at each sampling time.

Event-triggered Consensus Control of Nonlinear Multi-agent Systems based on First-order Hold

In this paper, consensus problem is studied for the first-order nonlinear multi-agent systems under directed topology, and a novel event-triggered consensus protocol is proposed. Different from the existing results with general zero-order hold, the first-order hold is adopted to construct the event-triggered control signal so as to reduce the triggering rate. By using Lyapunov stability method and matrix theory, a sufficient consensus condition is derived for the agents to reach the asymptotic consensus, and Zeno-behavior can be avoided. Finally, a numerical example is presented to demonstrate the effectiveness of our proposed protocol.

Determining the Quantization Frequency of a Zero-Order Hold in a Digital Positioning System

The quantization period of a zero-order hold (extrapolator) may be determined so as to ensure that the precision with which the setting signal is reproduced in a digital control system matches the precision of the analog prototype. The determination of the lowest possible quantization frequency of a zero-order hold corresponding to specified accuracy of signal reproduction is considered. The solution obtained by the frequency method is confirmed by simulation, with geometric verification of the approximation of the part’s actual curvature.

Modified repetitive periodic event-triggered control with equivalent-input-disturbance for linear systems subject to unknown disturbance

ABSTRACT This paper studies the disturbance rejection and the periodic signal tracking problems for linear systems with unknown exogenous disturbances under limited communication resources. The developed scheme achieves periodic reference tracking and improves the performance of periodic and aperiodic unknown disturbances rejection by incorporating the equivalent-input-disturbance (EID) estimator with the modified repetitive controller (MRC). Furthermore, a periodic event-triggered feedback observer (PETFO) is proposed to reduce the computational burden and energy consumption, and saving communication resources. The PETFO observes the occurrence of a predetermined event or not, where the current data are transmitted only when the event occurs otherwise, there is a zero-order hold keeps the data unchanged. The stability of the overall systems is guaranteed using the Lyapunov Krasovskii functional theory and linear matrix inequalities (LMIs). The observer and the controller gains are designed using the LMI and matrix decomposition approaches. Simulation results illustrate the effectiveness and feasibility of the proposed scheme.

Simplified Realization of Zero Phase Error Tracking

Abstract Zero phase error tracking (ZPET) control has gained popularity as a simple yet effective feedforward control method for tracking time varying desired trajectories by the plant output of a continuous time transfer function of relative order greater than or equal to two. In this paper, we will note that the sampling zeros of the zero-order hold equivalent of chain of integrators, 1/sn, are configured for natural realization of zero phase error tracking. This property is exploited to realize a simplified realization of zero phase error tracking control for chain of integrators. The property can also be utilized for general transfer functions when the sampling period for digital control is small. The effectiveness of the proposed approach for general transfer functions is demonstrated by simulations.

Sampled-Data Resilient Control for Hybrid Nonlinear Stochastic Systems Under Periodic DoS Attacks

This paper concerns the sampled-data resilient control for hybrid nonlinear stochastic systems under periodic denial of service (P-DoS) attacks. First of all, considering that the system is attacked by P-DoS and using the zero-order holder (ZOH) technique to further analyze the impact of such attacks on the control input. Secondly, via using the time-delay transform method, the attacked sampled-data resilient control system is modeled as a switched stochastic nonlinear time-delay closed-loop system. Thirdly, by using the piecewise Lyapunov functional method, the sufficient conditions to guarantee the mean square exponential stability of the attacked system are given. Then, according to these sufficient conditions, the controller parameters are solved when specific Lyapunov functional and controller design are given. Finally, an example is given to illustrate the efficiency of our results.

Observer-Based Predictive Control of Nonlinear Clutchless Automated Manual Transmission for Pure Electric Vehicles: An LPV Approach

This study develops a novel robust control approach for a nonlinear clutchless automated manual transmission (CAMT) in pure electric vehicles. The developed approach comprises model predictive control (MPC), observer, and polytopic linear parameter varying (LPV) model with inexactly measured scheduling parameters. The stability of the online-designed MPC and the offline-designed observer, as well as the overall closed-loop system, is guaranteed by presenting the quadratic Lyapunov function stability conditions in terms of linear matrix inequalities (LMIs). Moreover, by the means of sampler and zero-order-hold (ZOH), the discrete-time LPV-MPC is merged with continuous-time LPV-observer to construct the overall observer-based controller. The first contribution of the presented approach is that the issue of inexactly measured scheduling parameters is considered, which avoids the simplifying separation principal technique. The second contribution is assuring the stability of the closed-loop system with hybrid continuous- and discrete-time systems. Also, the LPV-observer design procedure utilizes the singular value decomposition (SVD) method to reduce the conservativeness; and, a constrained one-step-ahead PV-MPC is suggested. Finally, to illustrate the performance improvement and optimality of the developed controller, it is applied to a nonlinear CAMT system and comparison numerical results are given.

Adaptive Event-Triggered SMC for Stochastic Switching Systems With Semi-Markov Process and Application to Boost Converter Circuit Model

In this article, the sliding mode control (SMC) design is studied for a class of stochastic switching systems subject to semi-Markov process via an adaptive event-triggered mechanism. Network-induced communication constraints, semi-Markov switching parameters, and uncertain parameters are considered in a unified framework for the SMC design. Due to the constraint of measuring transducers, the system states always appear with unmeasurable characteristic. Compared with the traditional event-triggered mechanism, the adaptive event-triggered mechanism can effectively reduce the number of triggering than the static event-triggered mechanism. During the data transmission of network communication systems, network-induced delays are characterized from the event trigger to the zero-order holder. The aim of this work is to design an appropriate SMC law based on an adaptive event-triggered communication scheme such that the resulting closed-loop system could realize stochastic stability and reduce communication burden. By introducing the stochastic semi-Markov Lyapunov functional, sojourn-time-dependent sufficient conditions are established for stochastic stability. Then, a suitable SMC law is designed such that the system state can be driven onto the specified sliding surface in a finite-time region. Finally, the simulation study on boost converter circuit model (BCCM) illustrates the effectiveness of the theoretical findings.

Sampled-data based structural controllability of multi-agent systems with switching topology

This paper investigates the structural controllability problem for multi-agent systems with switching topology in a sampled-data setting, where each agent can obtain its neighbors’ state information at sampling instants. Based on the zero-order hold circuit, we show that the sampled-data general linear switched multi-agent system is structurally controllable if the union graph has a spanning tree. For sampled-data switched multi-agent systems, we prove that controllability property is preserved if an unsampled subsystem is controllable and the sampling time is not pathological. Our results show that the sampled-data based multi-agent systems with switching topology can be structurally controllable even if each of its subsystems is not controllable. A numerical example is presented to demonstrate the effectiveness of the proposed results.

Power Efficiency Comparison of Event-Driven and Fixed-Rate Signal Conversion and Compression forBiomedical Applications.

Energy-constrained biomedical recording systems need power-efficient data converters and good signal compression in order to meet the stringent power consumption requirements of many applications. In literature today, typically a SAR ADC in combination with digital compression is used. Recently, alternative event-driven sampling techniques have been proposed that incorporate compression in the ADC, such as level-crossing A/D conversion. This paper describes the power efficiency analysis of such level-crossing ADC (LCADC) and the traditional fixed-rate SAR ADC with simple compression. A model for the power consumption of the LCADC is derived, which is then compared to the power consumption of the SAR ADC with zero-order hold (ZOH) compression for multiple biosignals (ECG, EMG, EEG, and EAP). The LCADC is more power efficient than the SAR ADC up to a cross-over point in quantizer resolution (for example 8 bits for an EEG signal). This cross-over point decreases with the ratio of the maximum to average slope in the signal of the application. It also changes with the technology and design techniques used. The LCADC is thus suited for low to medium resolution applications. In addition, the event-driven operation of an LCADC results in fewer data to be transmitted in a system application. The event-driven LCADC without timer and with single-bit quantizer achieves a reduction in power consumption at system level of two orders of magnitude, an order of magnitude better than the SAR ADC with ZOH compression. At system level, the LCADC thus offers a big advantage over the SAR ADC.

On construction of sampling patterns for preserving observability/controllability of linear sampled-data systems

ABSTRACT In this paper, we design a new nonequidistant sampling pattern such that the property of controllability and observability of the linear continuous time systems is preserved during the procedure of the sample and zero-order hold operation. The idea behind the strategy comes from Kronecker's theorem and it is proven that new construction is more effective by requiring less number of sampling times which guarantees controllability and observability of sampled-data system in two dimensional space. Moreover, we provide one application in the concept of controllability of the pendulum in two dimensional space and obtain corresponding digital controls which make the corresponding sampled-data system controllable. Finally, the research is extended to different type of sampling patterns which are compared with the constructed sampling pattern separately.

Optimized non-uniform sampling of blood pressure time series from the operating room.

We investigate an optimized non-uniform sampling strategy for blood pressure time series from the operating room (OR). Our aim is to obtain an approximate bound on the achievable reconstruction fidelity given an average sampling rate constraint. Our data set consists of 117 hours of recordings of continuous invasive blood pressure from 28 surgery patients. We evaluate the root mean squared error (RMSE) of the zero-order hold sampling reconstruction of the blood pressure time series. We quantitatively compare the errors achieved by uniform versus optimized non-uniform sample placements for several average sample rates, ranging from 2 to 24 measurements per hour. An optimized non-uniform measurement schedule can lead to approximately 50% reduction of reconstruction RMSE for systolic, mean, and diastolic blood pressure time series with respect to uniform sampling, while maintaining the same average sampling rate.

Course-keeping control for ships with nonlinear feedback and zero-order holder component

Course keeping control is the core of automatic navigation for ships in marine transportation. To optimize the steering conditions of course-keeping controller and enhance its robustness in heavy sea states, a new nonlinear course-keeping control algorithm is designed with power function nonlinear feedback and ZOH model controller. Take the new generation of teaching-training vessel Yupeng from Dalian Maritime University as the research plant, and the nonlinear Nomoto ship model with a zero-order holder component is constructed to design the ZOH model controller. Then the deviation signal from the closed-loop system is modified by a power function nonlinear feedback component to reduce the control output. The stability of the closed-loop system is analyzed by the describing function method and Nyquist criterion. The simulation experiments in normal sea states and heavy sea states are respectively carried out to verify the control performance. The simulation experiments show that the performance of this nonlinear course-keeping control algorithm is satisfactory, which can still be effective in heavy sea states. The steering frequency is reduced significantly, and the steering condition of the controller meets the requirements of navigation practice. The nonlinear course-keeping control algorithm is more suitable for the navigation practice and engineering application.

Interval Type-2 Fuzzy Sampled-Data $H_{\infty }$ Control for Nonlinear Unreliable Networked Control Systems

This paper is concerned with the problem of interval type-2 (IT2) fuzzy sampled-data $H_{\infty }$ control for nonlinear networked control systems with parameter uncertainties, data dropout, and transmission delay. The IT2 fuzzy system used to describe the networked control systems and the IT2 networked sampled-data controller implemented by a zero-order holder is connected in the closed-loop system. By means of the input delay approach, the resulting closed-loop system is converted into a continuous-time delayed system. Subsequently, the continuous-time Lyapunov–Krasovskii functional theory is used to carry out the stability analysis. Some slack matrices and the bound information in membership functions are introduced to obtain the relaxed sufficient conditions formed by the linear matrix inequalities, which guarantee the anticipant $H_{\infty }$ performance. Finally, the efficiency and merits of the proposed design method are verified by four practical systems.

THE STABILIZATION ACCURACY OF THE PHASE POSITION OF THE WORKING BODY OF THE ROBOTICS COMPLEX

To stabilize the phase position of the working body of the robotics complex a single-circuit precision electric drive system was developed based on the principle of phase-locked loop. The direct-driven electric drive is made on the basis of brushless direct current motor, which is switched to synchronous mode with minimal discrepancy between the phases of the reference signals and the pulse speed sensor. The phase error signal is fed to the input of the PID controller, which controls the pulse width modulation of the impulses controlling the operation of the power transistors of the autonomous voltage inverter. In a static mode, the control system of the autonomous voltage inverter implements a sinusoidal law of the pulse width modulation of the output pulses. The PID controller and the control system of the autonomous voltage inverter are programmatically implemented on the basis of the controller.
 In the process of analysing of the stabilization accuracy, the synchronous motor is represented by a second-order linear link, which establishes a relation between the phase deviations of the motor rotor and the stator magnetic field. The autonomous voltage inverter is represented by a zero-order hold whose coefficient of amplification on amplitude is found by the results of the approximation of its output voltage using the Walsh-Fourier series.
 The analysis of the phase stabilization process is performed on the basis of the state variables method taking into account the perturbations at the moment of load using the program which implements the recurrent procedure.
 The settings of the PID controller are determined by the variation results when the moment of load changes. Their initial values ​​are determined as a result of optimizing the system in terms of operation speed considering the condition of finite duration processes. It is assumed that there is no moment of load perturbation.
 The procedure for setting the PID controller parameters to the optimal operation speed mode can also be performed on the basis of neural networks.
 As a result of the calculations, it was found that with an increase of the load moment by 5%, the maximum deviation of the rotor phase was 0.22 us and 0.03 us of minimum deviation respectively.

Reduced-Order Transfer Function Model of the Droop-Controlled Inverter via Jordan Continued-Fraction Expansion

This article proposes a reduced-order small-signal closed-loop transfer function model based on Jordan continued-fraction expansion to assess the dynamic characteristics of the droop-controlled inverter and provide the preprocessing method for the real-time simulation of power systems. Firstly, dynamic phasors, time delay and zero-order hold are embedded into the small-signal model at the same time, then the closed-loop transfer function of the droop-controlled inverter is built. Compared with the existing closed-loop transfer function approaches, the accuracy of the built transfer function model is dramatically enhanced. Meanwhile, the inner cascaded voltage/current controller parameters are also designed. In order to directly obtain and preserve the maximum overshoot and settling time, which are main features to evaluate the system input-output dynamic response characteristics, the reduced second order closed-loop transfer function is proposed through the continued-fraction expansion regarding arbitrary points on the real frequency axis. Therein, this second order closed-loop transfer function with dynamic response of the original inverter is reduced to the lowest order. Furthermore, combined with the impedance-based approach, the proposed stability assessment approach is utilized to analyze the stability of the microgrid with multiple converters. Finally, simulations and experimental results demonstrate the convenience and accuracy of the proposed approach.

Control strategy for networked control systems with time delay and packet dropout using linear matrix inequalities

A control strategy using linear matrix inequalities towards time delay and stochastic packet dropout of networked control system is proposed in this paper. First, a reconfigured target plant of networked control system is built based on a linear time-invariant target. Before discretization of target plant, a Pade approximation is employed towards the time delay segment of reconfigured target plant, while zero-order holder compensator and an estimator are employed for packet dropout of control input and measured output, respectively. Then the control target is reformed as a programming problem of an uncertain time-variant multi-parametric state space. In order to deal with such problem, herein the time-variant state space is rewritten as a linear parametric-varying prediction model by enumerating all possible occasions. Afterwards, a novel robust model predictive controller is proposed as a constrained minimax optimization of the predictive cost function. Finally, we present two simulations based on an aircraft model and a second-order numeric model, by which step responses and explicit solutions are derived, performed and analysed. Simulation results demonstrate both the stability and robustness of the proposed control strategy.

A novel method for evaluating the validity of dynamic accuracy test pieces for five-axis machine tools

The detection method for direct machining the standard test pieces, which is commonly employed to exhibit the machining precision of five-axis machine tools, can truly reflect the dynamic accuracy of five-axis machine tools in the actual machining process. Existing theories on explaining the phenomenon that the ability of S-shaped test pieces to detect dynamic accuracy for five-axis machine tools are stronger than those of NAS979 test pieces mostly used the qualitative research methods, and they cannot be quantitatively used to reveal the mathematical relationship between machine tools and test pieces. Therefore, this article makes the first attempt to investigate the quantitative evaluation method for the validity of dynamic accuracy test pieces. The dynamic error function of the servo feed system in the frequency domain was derived first by establishing the mechanical system model and control system model. The method of dipole cancellation was used to acquire a simplified transfer function for the dynamic error affected by the input. Based on the zero-order hold property of the discrete input signals, the expression of dynamic error affected by input in the time domain, which intuitively shows the mathematical relationship among the machine tool performances, the test piece characteristics and the dynamic error of the servo feed system, was obtained. Then, the novel evaluation methods of the linear combinatorial value and the combinatorial linear combinatorial value were proposed. A series of comparative analyses between an S-shaped test piece and an NAS979 test piece were carried out based on the proposed new evaluation methods. A machining experiment conducted on a five-axis machine tool is used to verify the evaluation results.

Stability analysis for time delay control of nonlinear systems in discrete-time domain with a standard discretisation method

This paper provides stability analysis results for discretised time delay control (TDC) as implemented in a sampled data system with the standard form of zero-order hold. We first substantiate stability issues in discrete-time TDC using an example and propose sufficient stability criteria in the sense of Lyapunov. Important parameters significantly affecting the overall system stability are the sampling period, the desired trajectory and the selection of the reference model dynamics.