Delays In Networked Control Systems Research Articles

Dual Event-Triggered Controller Co-Design for Networked Control Systems with Network-Induced Delays

To address the presence of network-induced delays in networked control systems (NCSs), a dual event-triggered mechanism (DETM) is used to investigate the problem of reducing network delays and controller co-design. Firstly, the DETM of the sensor–controller (SC) and the controller–actuator (CA) is adopted. By determining whether the sampled data meet the event-triggered threshold conditions for network transmission, we effectively reduce the sampled data transmitted over the network, which can reduce a network delay by reducing occupation of the network resources. Secondly, a dual event-triggered NCS model with a network-induced delay is developed, and a Lyapunov function including a DETM and network-induced delay is chosen. The functional upper limit of the Lyapunov function is estimated by combining the Wirtinger’s-based integral inequality with the reciprocally convex approach. This results in a stability criterion for systems with low conservativeness and a controller co-design method for a DETM. Finally, the availability of this method was verified through a numerical example and case study.

Measurement of master node delay in networked control systems

Master node delay is an unavoidable factor in a networked control system (NCS), which will lead to performance deterioration of the system, and large delay may even cause instability. In order to measure the master node delay in NCSs, its influence factors are analyzed and a non-perturbative black-box measurement method is proposed. In this method, a FPGA-based (Field-Programmable Gate Array) measurement device is developed, which sends out testing frames to master node periodically and triggers the master node to send out a response frame for every testing frame. Then the measurement device can get the measurement delay value by calculating the time interval between sending the testing frame and receiving the response frame, which consists of master node delay and some other delay that can be calculated precisely. Therefore, the accurate master node delay can be obtained by further processing the measurement delay value. A set of experiments were carried out and the results show that the proposed method can effectively measure the master node delay without a thorough understanding about its hardware and operating system software, and is not constrained by the type of operating system. Besides, as the master node delay can be measured exactly in the actual working condition without perturbing its user program by using this method, the results can reflect the real-time performance of the master node accurately. So that, it can provide a direct reference for choosing an appropriate master node for NCSs.

Fault diagnosis and fault‐tolerant control of uncertain network control systems

SummaryIn this article, the equivalent control strategy based on Laplace transform is proposed for the problem of stochastic delay in networked control systems. The original system is transformed into an equivalent control system without random delay block by Laplace transform. Then, a new augmented variable and equivalent control system is introduced to construct an augmented system. An adaptive fault diagnosis observer is designed based on the augmented system. The adaptive turning rate of the observer is obtained by solving the corresponding linear matrix inequality. Based on the information of online fault diagnosis and state estimation, a fault‐tolerant controller based on PI control strategy is designed to compensate the fault. Finally, a model of the switched reluctance motor system is considered to show the effectiveness of this method.

Modelling and Prediction of Random Delays in NCSs Using Double-Chain HMMs

This paper is concerned with the modelling and prediction of random delays in networked control systems. The stochastic distribution of the random delay in the current sampling period is assumed to be affected by the network state in the current sampling period as well as the random delay in the previous sampling period. Based on this assumption, the double-chain hidden Markov model (DCHMM) is proposed in this paper to model the delays. There are two Markov chains in this model. One is the hidden Markov chain which consists of the network states and the other is the observable Markov chain which consists of the delays. Moreover, the delays are also affected by the hidden network states, which constructs the DCHMM-based delay model. The initialization and optimization problems of the model parameters are solved by using the segmental K-mean clustering algorithm and the expectation maximization algorithm, respectively. Based on the model, the prediction of the controller-to-actuator (CA) delay in the current sampling period is obtained. The prediction can be used to design a controller to compensate the CA delay in the future research. Some comparative experiments are carried out to demonstrate the effectiveness and superiority of the proposed method.

Research of NCS Random Time Delay Prediction Based on FNN-PSO

Networked control systems have been attracting considerable attention during the last decades, not only because of their theoretical value, but also of their widespread practical applications. In practice, networked control systems are inevitably affected by the random time delays. Aiming at the problem of system performance degradation caused by random time delay in networked control systems, a method of combining particle swarm optimization with fuzzy neural network is used to establish a networked control system time delay prediction model and predicts the future time delay. According to the simulation, we verify the effectiveness and feasibility of the proposed method. The results of simulation show that the fuzzy neural network optimized by particle swarm optimization has a high prediction accuracy for random time delay and is suitable for practical applications.

A novel method for time delay prediction in networked control systems

Time delay prediction is a crucial issue of networked control systems. Previous methods mainly use individual model to predict time delay, which causes the limitation that the proposed model can only be suitable applied to either linear or nonlinear data. This paper proposed a novel method to predict time delay in networked control systems which considers several different individual models as the component models to form a combined model and takes full advantages of these component models. By applying Lagrange multiplier method to minimise prediction error, the proposed optimal weight (OW) algorithm is able to calculate the proper weight coefficients of component models in order to improve the prediction performance. Compared with the existing methods, the proposed combined model can improve the prediction accuracy and support robustness, variability and scalability. The simulation experiments verify the effectiveness of the proposed method.

A novel method for time delay prediction in networked control systems

Time delay prediction is a crucial issue of networked control systems. Previous methods mainly use individual model to predict time delay, which causes the limitation that the proposed model can only be suitable applied to either linear or nonlinear data. This paper proposed a novel method to predict time delay in networked control systems which considers several different individual models as the component models to form a combined model and takes full advantages of these component models. By applying Lagrange multiplier method to minimise prediction error, the proposed optimal weight (OW) algorithm is able to calculate the proper weight coefficients of component models in order to improve the prediction performance. Compared with the existing methods, the proposed combined model can improve the prediction accuracy and support robustness, variability and scalability. The simulation experiments verify the effectiveness of the proposed method.

Compensation of Time-Varying Delay in Networked Control System over Wi-Fi Network

In this study, we design a state predictor-based output feedback controller that compensates for unavoidable time-varying network delays in networked control systems (NCSs) over Wi-Fi networks. We model time-varying network delays as timevarying input delays of NCSs over Wi-Fi networks. The designed controller consists of a linear quadratic regulator (LQR), a full-order observer, and a time-varying stepahead state predictor. The state predictor plays a key role in compensating for the time-varying input delay by providing the LQR with an estimation of future states ahead by the current network delay time. The time-varying network delays are acquired in real time by measuring the time differences between sent and received control data packets. We verify the stability and compensation performance of the designed controller by performing extensive experiments for an NCS in which a rotary inverted pendulum is controlled over Wi-Fi networks.

SCHMM-based compensation for the random delays in networked control systems

In order to compensate the network-induced random delays in networked control systems (NCSs), the semi-continuous hidden Markov model (SCHMM) is introduced in this paper to model the controller-to-actuator (CA) delay in the forward network channel. The expectation maximization algorithm is used to obtain the optimal estimation of the model's parameters, and the Viterbi algorithm is used to predict the CA delay in the current sampling period. Thus, the predicted CA delay and the measured sensor-tocontroller (SC) delay in the current sampling period are used to design an optimal controller. Under this controller, the exponentially mean square stability of the NCS is guaranteed, and the SC and CA delays are compensated. Finally, the effectiveness of the method proposed in this paper is demonstrated by a simulation example. Moreover, a comparative example is also given to illustrate the superiority of the SCHMM-based optimal controller over the discrete hidden Markov model (DHMM)-based optimal controller.

Initialization of the HMM-based delay model in networked control systems

When hidden Markov models (HMMs, including discrete HMM and semi-continuous HMM) are used to model and predict the random delays in networked control systems, there are five parameters needed to be estimated. They are the number of different network states, the initial distribution of the network states, the state transition matrix of the hidden Markov chain formed by the network states, the number of different delay observations in the discrete HMM (DHMM) or the number of the Gaussian densities in the semi-continuous HMM (SCHMM), and the delay observation matrix in the DHMM or the combination of the mixture Gaussian distributions in the SCHMM. How to initialize these parameters is very crucial to the precision of the modeling and prediction of random delays. In this paper, the entropy and cluster based initialization methods are proposed to obtain the optimal initialization of these parameters. The effectiveness of the proposed methods is demonstrated by some simulation examples.

SCHMM-based modeling and prediction of random delays in networked control systems

This paper is concerned with the modeling and prediction of random delays in networked control systems. Considering the Gaussian mixture distribution followed by the random delays in real networks, the semi-continuous hidden Markov model (SCHMM) is proposed in this paper to model the random delays. The initialization and optimization problems of the model parameters are solved by using the K-mean clustering algorithm and the expectation maximization algorithm. Based on the model, the prediction of the controller-to-actuator (CA) delay in the current sampling period is obtained. The prediction can be used to design a controller to compensate the CA delay in the future research. Two illustrative examples are given to demonstrate the effectiveness and superiority of the proposed modeling and prediction methods.

Improved stabilization method for Lurie networked control systems.

The problem of stabilization of Lurie networked control systems (NCSs) is investigated in this paper. The network-induced delays in NCSs are assumed to be time-varying and bounded. By utilizing a reciprocally convex technique to consider the relationship between the network-induced delay and its varying interval, a new absolute stability condition is derived in terms of linear matrix inequalities (LMIs). Based on the obtained condition, an improved cone complementary linearisation (CCL) iteration algorithm is presented to design a state feedback controller. The effectiveness of the proposed method is verified by a numerical example.

On the delay effects of different channels in Internet-based networked control systems

The sensor-to-controller and the controller-to-actuator delays in networked control systems (NCSs) are investigated for the first time with respect to their different effects on the system performance. This study starts with identifying the delay-independent and delay-dependent control laws in NCSs, and confirms that only two delay-dependent control laws can cause different delay effects in different channels. The conditions under which the different delays in different channels can cause different effects are then given for both delay-dependent control laws. The results are verified by numerical examples. Potentially, these results can be regarded as important design principles in the practical implementation of NCSs.

Modeling of Random Delays in Networked Control Systems

In networked control systems (NCSs), the presence of communication networks in control loops causes many imperfections such as random delays, packet losses, multipacket transmission, and packet disordering. In fact, random delays are usually the most important problems and challenges in NCSs because, to some extent, other problems are often caused by random delays. In order to compensate for random delays which may lead to performance degradation and instability of NCSs, it is necessary to establish the mathematical model of random delays before compensation. In this paper, four major delay models are surveyed including constant delay model, mutually independent stochastic delay model, Markov chain model, and hidden Markov model. In each delay model, some promising compensation methods of delays are also addressed.

Application of Fuzzy Neural Network PID Controller in Networked Control Systems

Aiming at the performance degradation and system destabilization which are caused by time delay in networked control systems (NCSs), a novel fuzzy neural network PID controller is proposed to alleviate the adverse effect. This approach enjoys the advantage of functional mapping of the fuzzy neural network, and gives better performance in tuning the PID controller parameters online. The simulation of the improved networked controller is carried out through the matlab/truetime, and the DC motor which has higher real-time performance is chosen as a control object. The simulation results illustrate that the controller can effectively improve the control performance and keep the system stable.

H∞ Estimation for Stochastic Time Delays in Networked Control Systems by Partly Unknown Transition Probabilities of Markovian Chains

This paper is concerned with the problem of H∞ estimation for networked control systems. Time delays and packet dropouts are considered simultaneously. The occurrence probability of each time delay is considered. The packet dropouts have the Bernoulli distributions. The system is modeled as Markovian jump linear systems with partly unknown transition probability. State observer is designed to estimate the practical state with H∞ feature. The estimation problem is cast into a set of linear matrix inequalities. An example is provided to illustrate the effectiveness and applicability of the proposed method.

Maximum Allowable Delay Bound Estimation in Networked Control of Bounded Nonlinear Systems

Net worked Control Systems (NCSs) has been recognized as an area where theory is behind the development of technology. The defining feature of NCSs can be considered as the information is exchanged through a network among control system co mponents. So the network induced time delay is inevitable in NCSs. The time delay may degrade the performance of control systems and even destabilize the systems if they are designed without considering the effects of the time delays properly. Once the structure of a NCS is confirmed, it is essential to identify what the maximu m t ime delay is allo wed for maintaining the system stability which, in turn, is also associated with the process of controller design. Th is paper proposes a new method for estimating the maximu m allowab le time delay in networked control systems with norm bounded nonlinearity. The relation between the maximu m nonlinearity and the maximu m allowable delay is studied using the proposed method, and it is found that increasing the maximu m nonlinearity bound reduces the maximu m allo wable delay. Furthermore, increasing the time delay leads to shrink the domain of attraction. The results of the maximu m allo wable delay bound and the maximu m nonlinearity are co mpared with some of the published results.

Nonlinear Stabilization Under Sampled and Delayed Measurements, and With Inputs Subject to Delay and Zero-Order Hold

Sampling arises simultaneously with input and output delays in networked control systems. When the delay is left uncompensated, the sampling period is generally required to be sufficiently small, the delay sufficiently short, and, for nonlinear systems, only semiglobal practical stability is generally achieved. For example, global stabilization of strict-feedforward systems under sampled measurements, sampled-data stabilization of the nonholonomic unicycle with arbitrarily sparse sampling, and sampled-data stabilization of LTI systems over networks with long delays, are open problems. In this paper, we present two general results that address these example problems as special cases. First, we present global asymptotic stabilizers for forward complete systems under arbitrarily long input and output delays, with arbitrarily long sampling periods, and with continuous application of the control input. Second, we consider systems with sampled measurements and with control applied through a zero-order hold, under the assumption that the system is stabilizable under sampled-data feedback for some sampling period, and then construct sampled-data feedback laws that achieve global asymptotic stabilization under arbitrarily long input and measurement delays. All the results employ “nominal” feedback laws designed for the continuous-time systems in the absence of delays, combined with “predictor-based” compensation of delays and the effect of sampling.

Smoothing delay jitter in networked control systems

Delay jitter is a critical factor that must be considered in many real-time applications that require accurate prediction of packet delivery times. Delay jitter can be smoothed by holding packets in a play-back buffer for a certain time called a play-back delay. In this paper, we extensively examine the new scheme that we have proposed in [1] to enhance the prediction of the play-back delay in Networked Control Systems (NCSs). Our newly proposed scheme differs from previous schemes by using the one way delay variation that we have studied its behavior by conducting extensive measurements between fifty strategically located wired and wireless connected hosts. The advantages of our scheme are that it predicts sudden delay spikes, provides a closer approximation to the round trip time (RTT), and exhibits less frequent outliers.

Fault diagnosis for networked control systems with delayed measurements and inputs

This study researches the fault diagnosis approach for networked control systems (NCSs) with delayed measurements and inputs. Different from current fault diagnosis approaches that regard all delays in NCSs as an input delay, this paper presents a new fault diagnosis approach for NCSs that considers delayed measurements and inputs simultaneously and presents a discrete delay-free transformation approach for delayed measurements. By constructing an augmented system that comprises the states of faults and by delay-free transformations of delayed measurements and inputs for the augmented system, the problem of fault diagnosis for NCSs with delayed measurements and inputs is transformed into the problem of state observation of a delay-free augmented system. A new design approach to the fault diagnoser is presented for NCSs by constructing a novel reduced-order state observer of the augmented system, which can real-time diagnose faults without using residual to embody faults. Finally, the feasibility and effectiveness of the proposed approaches are validated by a numerical example.