Real-time scheduling method for networked discrete control systems

doi:10.1016/j.conengprac.2008.10.006

Control Engineering Practice

Volume 17, Issue 5, May 2009, Pages 564-570

https://doi.org/10.1016/j.conengprac.2008.10.006 Get rights and content

Abstract

This paper proposes a new scheduling method to obtain a maximum allowable delay bound for a scheduling of networked discrete control systems. The proposed method is formulated in terms of linear matrix inequalities (LMI) and can give a much less conservative delay bound than the existing methods. An event based network scheduling method is presented based on the delay bound obtained through the proposed method, and it can adjust the sampling period to allocate identical utilization to each control loop. The presented method can handle sporadic emergency data, periodic data, and non-real-time data.

Introduction

In distributed control systems (DCSs), a feedback control loop is closed through a network. The DCSs with networks are called networked control systems (NCSs). In an NCS, various delays occur due to sharing a common network medium, which are called network-induced delays (Asok and Yoram, 1988, Krtolica et al., 1994). Network-induced delays can vary widely according to the transmission time of messages and the overhead time. The performance of the control system is assumed to be affected by network-induced parameters such as delays, jitters, packet losses and link failures (Vatanski, Georges, Aubrun, Rondeau, & Jamsa-Jounela, 2008). The network in the NCS should handle three types of data: sporadic emergency data, periodic data, and non-real-time message. The transmission time through the media is largely dependent on the network protocols, especially data link layer protocols of networks and data length. Hence, it is necessary to present the methods to make these network-induced delays bounded and smaller, which are called network scheduling methods for the NCS.

In general, a faster sampling rate is said to be desirable in sampled-data systems so the discrete-time control design and performance can approximate that of the continuous-time system. But in NCSs, a faster sampling rate bound can increase network load, which in turn results in longer delay of the signals. Thus finding a sampling rate that can both tolerate the network-induced delay and achieve desired system performance is important in NCS design. This certain bound is called a maximum allowable delay bound (MADB) of the NCS.

Therefore, it is necessary to find the MADB for stability of the NCS, and then to find an appropriate network scheduling method that limits the network-induced delay to less than the MADB. A network scheduling method is required to reduce network-induced delays within the MADBs, while guaranteeing real-time transmission of sporadic, periodic data, and minimizing network utilization for non-real-time message.

The MADB has been obtained from stability conditions of control systems. There have been some results on the stability of NCSs (Lian et al., 2002, Yoram and Asok, 1988). Less conservative results on the MADB in non-NCSs are reported in Li and de Souza, 1997a, Li and de Souza, 1997b and Park (1999). In these papers, the MADB is obtained using the Ricatti equation approach, which yields conservative delay bounds. A scheduling method was presented in the NCS with Fieldbus networks (Beauvais and Deplanche, 1995, Cavalieri et al., 1995). But those papers did not consider the MADB, which were important in control applications.

There have been some studies on scheduling algorithms that can be applied to the NCS (Hong, 1995, Raja et al., 1993, Walsh et al., 1999, Zhang et al., 2001). A dynamic scheduling algorithm modified from the rate monotone scheduling algorithms was presented for periodic and sporadic data in Fieldbus networks (Raja et al., 1993). A heuristic algorithm was presented for periodic tasks only (Beauvais & Deplanche, 1995), but it did not support sporadic data. The several algorithms for dynamically scheduling of NCSs were proposed (Hong and Walsh, 2001, Zuberi and Shin, 1997). It had limitations when applied to the NCS because it did not consider some characteristics of the NCS, such as the MADB and sampling periods. A scheduling algorithm that can allocate the bandwidth of a network and determine sensor data sampling periods was presented by Hong (1995). In Hong (1995), the control system had only single input and single output (SISO), only periodic data were considered, and the MADB was not obtained analytically.

A network scheduling method considering three types of data based on a multi-input and multi-output (MIMO) system was proposed by Park, Kim, Kim, and Kwon (2002). In this paper, the estimation of MADB using the Ricatti equation is too conservative, which means the estimated MADB is too small and the network scheduling method discussed is somewhat heuristic.

In Branicky, Phillips, and Zhang (2000) and Walsh and Hong (2001), calculation methods of MADBs and stability analysis of NCSs were presented. However, these results were conservative to be of practical use and still remains to be improved. Further research is needed with regard to estimation of a less conservative MADB for stability of the NCS and systematic scheduling methods for three types of data.

In Kim, Lee, Kwon, and Park (2003), a calculation method of MADBs of NCS based on continuous-time was presented in terms of linear matrix inequalities (LMI). This method gave a much less conservative delay bound than previous methods. However, a calculation method of MADBs based on continuous model and a scheduling method for three types of data remain to be improved.

This paper proposes a method to obtain the MADB guaranteeing a stability of the discrete-time NCS. Using obtained MADBs, sampling period decision and bandwidth allocation method are presented. A proposed scheduling method can adjust the sampling period to allocate the same utilization to each control loop. It can handle three types of data and guarantees real-time transmission of sporadic emergency and periodic data. It is modified earliest deadline first (EDF) scheduling method which give priority to sporadic emergency data.

This paper is organized as follows. In the following section, an discrete-time NCS model is described. The MADB for the stability of the NCS is derived by LMI formulation. In Section 3, a network scheduling method that allocates the bandwidth and determines the sampling period for the NCS is presented. In Section 4, simulation results are given to show that method is useful. Finally, the conclusions are presented in Section 5.

Section snippets

MADB for stability in a control loop

In general, NCSs can be described as Fig. 1 (Nilson, 1998, Nilson et al., 1998). A networked control loop is composed of a controller, sensors, and actuators through a common communication medium.

In Fig. 2 (Kim et al., 2003), the timing diagram illustrates the process output and sampling instants, the signal into the controller node, the signal into the actuator node and the network-induced delay.

The MADB is defined as the maximum allowable interval from the instant when sensor nodes sample

Event-based scheduling algorithm

This section describes an event-based network scheduling method using the MADB. The modified EDF algorithm is proposed to guarantee real-time transmission of sporadic emergency data. The modified EDF algorithm is that the sporadic data have a high priority than real-time periodic data. In general, a real-time periodic data has a priority higher than non-real-time data. Hence, real-time periodic data is scheduled by EDF algorithm using MADB of each loop as a deadline. After the end of

Simulation

For the simulation, a plant with three DC motors is considered. Each motor has an armature position controller with two sensors and one actuator, which are linked via the network. If the armature inductance $(L_{a})$ and viscous frictional coefficient $(B_{m})$ are negligible, the motor dynamics becomes (Park et al., 2002) $x_{p} (k + 1) = F_{p} x_{p} (k) + G_{p} u_{p} (k) = [\begin{matrix} - K_{i} K_{b} / R_{a} J & 0 \\ 1 & 0 \end{matrix}] x_{p} (k) + [\begin{matrix} K_{i} / R_{a} J \\ 0 \end{matrix}] u_{p} (k),$ $y_{p} (k) = x_{p} (k),$ where $x_{p} (k) = [ω θ]^{T}$ , $u_{p} (k)$ is applied voltage (V), and $ω$ and $θ$ are, respectively, the rotor angular velocity (rad/s) and

Conclusion

In this paper, the MADBs are obtained for the stability of the discrete-NCS using LMI formulation, and are used as the basic parameter for an event-based scheduling method for the NCS. The scheduling method for the NCS can schedule efficiently to guarantee real-time transmission for sporadic data. The presented sampling period decision algorithm is useful, as it provides a fair channel utilization to loops, and calculates sampling period easily. The modified EDF algorithm schedules sporadic

Acknowledgments

This work was supported by the Korea Research Foundation grant funded by the Korean government under Grant No. KRF-2007-D-00150, Korea. The authors thank the editor and anonymous reviewers for their time and efforts.

References (24)

D.S. Kim et al.
Maximum allowable delay bounds of networked control system
Control Engineering Practice
(2003)
X. Li et al.
Criteria for robust stability and stabilization of uncertain linear systems with state delays
Automatica
(1997)
R. Asok et al.
Integrated communication and control systems: Part II—design consideration
Journal of Dynamic Systems, Measurement, and Control
(1988)
Beauvais, J. P., & Deplanche, A.-M. (1995). Heuristics for scheduling periodic complex real-time tasks in a distributed...
Branicky, M. S., Phillips, S. R., & Zhang, W. (2000). Stability of networked control systems: Explicit analysis of...
S. Cavalieri et al.
Pre-run-time scheduling to reduce schedule length in the fieldbus environment
IEEE Transactions on Software Engineering
(1995)
S.H. Hong
Scheduling algorithm of data sampling times in the integrated communication and control systems
IEEE Transactions on Control Systems Technology
(1995)
Y. Hong et al.
Real-time mixed-traffic wireless networks
IEEE Transactions on Industrial Electronics
(2001)
R. Krtolica et al.
Stability of linear feedback systems with random communication delays
International Journal of Control
(1994)
X. Li et al.
Delay-dependent robust stability and stabilization of uncertain linear delay systems: A linear matrix inequality approach
IEEE Transactions on Automatic Control
(1997)

F.-L. Lian et al.

Network design consideration for distributed control systems

IEEE Transactions on Control Systems Technology

(2002)

Lorenz, P., & Mammeri, Z. (1995). Real-time software architecture: Application to FIP fieldbus. In Proceedings of AARTC...

Cited by (47)

Event-triggered active disturbance rejection control for a class of networked systems with unmatched uncertainties: Theoretic and experimental results
2021, Control Engineering Practice
In this work, an event-triggered control problem for a class of networked systems with unmatched uncertainties is investigated based on an active disturbance rejection control approach. To estimate the effect of unmatched uncertainties, a bank of extended state observers with guaranteed convergence is proposed. Based on the obtained estimates, a tracking-differentiator-enabled Zeno-free event-triggering condition is introduced with reduced sampling cost. An event-triggered controller is then designed to guarantee the closed-loop stability of the networked system with unmatched uncertainties, leveraging a backstepping control approach. Implementation issues of the proposed approach are discussed, and the effectiveness of the results is illustrated through experimental results on a DC torque motor platform.
Distributed control system for ship engines using dual fieldbus
2017, Computer Standards and Interfaces
This paper describes a distributed control system (DCS) for ship engines using a dual fieldbus. Communication among DCS entities is provided by considering the redundancy between Modbus and the controller area network (CAN) bus. The dual fieldbus consists of Modbus and an alternative CAN bus. Owing to its short time frame, CAN networks have the advantage of a short time latency. Moreover, Modbus is a simple protocol and is powerful in its support of many types of real-time industrial applications. By considering the benefits of both Modbus and CAN bus, a DCS based on a dual fieldbus for monitoring and controlling the condition of a ship engine has been proposed. In the proposed scheme, Modbus has been used as a primary communication link for engine system. If link errors arise with Modbus, the system automatically switches to CAN in a reliable way. The performance of the proposed DCS has been tested and evaluated by a real implementation in a testbed. The experimental results show that the proposed DCS satisfies the redundancy time required by the International Association of Classification Societies.
Optimal modified tracking performance for networked control systems with QoS constraint
2016, ISA Transactions
This paper investigates the optimal modified tracking performance of networked control systems with a constraint on quality of service (QoS). The QoS is characterized by two parameters of the system, viz. data dropout and the additive white Gaussian noise. The proposed modified tracking performance index prevents the probability of invalid data arising from the variations in the tracking error in the absence of an integrator in the plant. The derived optimal filter eliminates the influence of channel noise in the feedback channel. The optimal modified tracking performance expression is obtained by using the co-prime factorization. Results indicate that the optimal modified tracking performance is influenced by the non-minimum phase zeros, modification factor, packet dropout probability, and the characteristics of the reference signals. The obtained results will give some guidance for the design of networked control systems. The efficiency of the model is verified using some typical examples.
Real-time message scheduling for ISA100.11a networks
2015, Computer Standards and Interfaces
Citation Excerpt :
In addition, ISA100.11a also uses the CSMA-CA mechanism used by the original IEEE 802.15.4 standard for contending transmissions. In ISA100.11a, as well as networked systems in general, real-time scheduling is one of the most important tasks [11,12]. In Ref. [5], the authors described a scheduling method of wireless control networks using IEEE 802.15.4 networks.
This paper proposes two new message scheduling methods on shared timeslots of the ISA100.11a standard to enhance real-time performance, namely, traffic-aware message scheduling (TAMS) and contention window size adjustment (CWSA). In TAMS, instead of competing to transmit sporadic messages in consecutive cycles, end-nodes are divided into groups, which then access the channel in specific cycles when the probability of timeslots getting involved in collisions exceeds a specified threshold. Conversely, in CWSA, the contention window is adjusted when the probability of timeslots getting involved in collisions exceeds the threshold. The results of simulations conducted indicate that these two proposed methods provide performance improvements in terms of success probability and end-to-end delay.
Robust H<inf>∞</inf> control for uncertain networked systems with communication constraints
2013, Journal of the Franklin Institute
This paper considers robust $H_{\infty}$ control for networked control systems (NCSs) with communication constraints, network-induced delay and uncertainties in both system dynamic and access rates. Medium access constraints of both sensor–controller and controller–actuator channels are considered, that is, not all the sensors and actuators are granted access to the network simultaneously to transfer measurements, the access status of sensors or actuators are governed by some stochastic variables. Then new NCSs model is proposed by using these stochastic variables. The purpose of this paper is to design the robust $H_{\infty}$ controller to stabilize the NCSs with communication constraints and random network-induced delay. By using the Lyapunov functional method and the linear matrix inequality technology, sufficient conditions for the robust mean square stable (RMSS) of the NCSs with an $H_{\infty}$ norm bound $γ$ are obtained. A simulation example is given to demonstrate the effectiveness and application of the proposed method.
H<inf>∞</inf> fault detection for nonlinear networked systems with multiple channels data transmission pattern
2013, Information Sciences
Citation Excerpt :
For networked systems, at each sampling time k, due to the bandwidth constraint of the wireless/wire network, only some of these sensors or packets signal can be transmitted successfully. In this note, if we regard every sensors or packets as one information channel, then multi-input and multi-output [9], medium access constraint [5,10,13] and multiple packets transmission [6,16,23] can be described validly by multiple channels transmission framework. On the other hand, modeling is one of the most important issues in networked control systems which has received an ever increasing research attention [4–10,14,16,23,24].
This paper is concerned with fault detection for a class of complex networked control systems. By introducing transmission matrix, nonlinear delayed Markovian jump systems model with partially unknown transition probabilities are established by multiple channels data transmission framework. Based on the obtained model, mode-dependent fault detection filters are used for residual generator, the addressed fault detection problem is converted into nonlinear H_∞ attenuation problem. Then the desired mode-dependent fault detection filters are constructed in terms of linear matrix inequalities such that the fault detection systems are stochastically stable with H_∞ attenuation level. A numerical example is given to demonstrate the effectiveness of the proposed design approach.

View all citing articles on Scopus

View full text

Real-time scheduling method for networked discrete control systems

Abstract

Introduction

Section snippets

MADB for stability in a control loop

Event-based scheduling algorithm

Simulation

Conclusion

Acknowledgments

Control Engineering Practice

Automatica

Integrated communication and control systems: Part II—design consideration

Journal of Dynamic Systems, Measurement, and Control

Pre-run-time scheduling to reduce schedule length in the fieldbus environment

IEEE Transactions on Software Engineering

Scheduling algorithm of data sampling times in the integrated communication and control systems

IEEE Transactions on Control Systems Technology

Real-time mixed-traffic wireless networks

IEEE Transactions on Industrial Electronics

Stability of linear feedback systems with random communication delays

International Journal of Control

Delay-dependent robust stability and stabilization of uncertain linear delay systems: A linear matrix inequality approach

IEEE Transactions on Automatic Control

Network design consideration for distributed control systems

IEEE Transactions on Control Systems Technology