Probabilistic Modeling of Network-induced Delays in Networked Control Systems

Authors: Manoj Kumar, A.K. Verma, A. Srividya

Abstract:

Time varying network induced delays in networked control systems (NCS) are known for degrading control system-s quality of performance (QoP) and causing stability problems. In literature, a control method employing modeling of communication delays as probability distribution, proves to be a better method. This paper focuses on modeling of network induced delays as probability distribution. CAN and MIL-STD-1553B are extensively used to carry periodic control and monitoring data in networked control systems. In literature, methods to estimate only the worst-case delays for these networks are available. In this paper probabilistic network delay model for CAN and MIL-STD-1553B networks are given. A systematic method to estimate values to model parameters from network parameters is given. A method to predict network delay in next cycle based on the present network delay is presented. Effect of active network redundancy and redundancy at node level on network delay and system response-time is also analyzed.

Keywords: NCS (networked control system), delay analysis, response-time distribution, worst-case delay, CAN, MIL-STD-1553B, redundancy

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1330537

References:

[1] J. Yepez, P. Marti, and J. M. Fuertes, "Control loop performance analysis over networked control systems," in Proceedings of IECON2002, 2002.
[2] T. Yang, "Networked control systems: a brief survey," IEE Proc.-Control Theory Applications, vol. 153, pp. 403-412, July 2006.
[3] W. Zhang, M. S. Branicky, and S. M. Phillips, "Stability of networked control systems," IEEE Control System Magazine, pp. 84-99, Feburary 2001.
[4] J.-P. Richard, "Time-delay systems: an overview of some recent advances and open problems," Automatica, vol. 39, pp. 1667-1694, 2003.
[5] H. Yang and B. Sikdar, "Control loop performance analysis over networked control systems," in Proceedings of ICC 2007, pp. 241-246, 2007.
[6] B. Lu, "Probabilistic design of networked control systems with uncertain time delay," in ASME International Mechanical Engineering Congress and Exposition, Proceedings, 9 Part A, pp. 355-362, 2008.
[7] D. Huang and S. Nguang, "State feedback control of uncertain networked control systems with random time-delays," in ASME International Mechanical Engineering Congress and Exposition, Proceedings, 9 Part A, pp. 3-362, 2008.
[8] J. Nilsson, B. Bernhardsson, and B. Wittenmark, "Stochastic analysis and control of real-time systems with random time delays," Automatica, vol. 34, pp. 57-64, 1998.
[9] L. Zhang, Y. Shi, T. Chen, and B. Huang, "A new method for stabilization of networked control systems with random delays," IEEE Transaction on Automatic Control, vol. 50, no. 8, pp. 1177-1181, 2005.
[10] G. C. Walsh, H. Ye, and L. Bushnell, "Stability analysis of networked control systems," IEEE Transaction on Control System Technology, vol. 10, pp. 438-446, 2002.
[11] J. Nilsson, Real-Time Control Systems with Delays. PhD thesis, Lund Institute of Technology, Sweden, 1998.
[12] F.-L. Lian, Analysis, Design, Modeling, and Control of Networked Control Systems. PhD thesis, University of Michigan, 2001.
[13] F.-L. Lian, J. Moyne, and D. Tilbury, "Performance evaluation of control networks: Ethernet, controlnet, and devicenet," IEEE Control System Magazine, vol. 21, pp. 66-83, 2001.
[14] Y. Tipsuwan and M.-Y. Chow, "Control methodologies in networked control systems," Control Engineering Practice, vol. 11, no. 10, pp. 1099-1111, 2003.
[15] K. W. Tindell, H. Hansson, and A. J. Wellings, "Analyzing real-time communications: Controller area network (CAN)," in Proceeding of Real-time Symposium, pp. 259-263, Dec. 1994.
[16] K. Tindell, A. Burns, and A. Wellings, "Calculating controller area network (can) message response times," Control Engineering Practice, vol. 3, no. 2, pp. 1163-1169, 1995.
[17] M. Farsi, K. Ratcliff, and M. Barbosa, "An overview of controller area network," Computing & Control Engineering Journal, pp. 113-120, June 1999.
[18] "CAN specification 2.0. part A and B, can in automation (cia)."
[19] T. Nolte, H. Hansson, and C. Norstrom, "Minimizing can response-time jitter by message manipulation," in Proceedings of the 8th Real-time and Embedded Technology and Application Symposium (RTAS-02), 2002.
[20] "MIL-STD-1553B: Aircraft internal time division command/response multiplex data bus," 30 April 1975.
[21] "MIL-STD-1553 tutorial."
[22] M. Kumar, A. K. Verma, and A. Srividya, "Response-time modeling of controller area network (can)," in Communicated to Int. Conf. on Distributed Computing and Networking (ICDCN09).
[23] J. K. Muppala, V. Mainkar, K. S. Trivedi, and V. G. Kulkarni, "Numerical computation of response-time distributions using stochastic reward nets," Annals of Operations Research, vol. 48, pp. 155-184, 1994.
[24] K. S. Trivedi, Probability & Statistics with Reliability, Queueing, and Computer Science Applications. Englewood Cliffs, New Jersey: Prentice-Hall, 1982.
[25] T. Nolte, H. Hansson, and C. Norstrom, "Probabilistic worst-case response-time analysis for the controller area network," in Proceedings of the 9th Real-time and Embedded Technology and Application Symposium (RTAS-03), 2003.