×

Frequency conditions for stable networked controllers with time-delay. (English) Zbl 1416.93180

Summary: The paper analyses a networked control system consisting of a linear time-invariant system with a static feedback nonlinearity, subject to large delays in the feedback loop. This model is valid for example in wireless data flow control, where a saturation occurs since the flow is one-directional. The present paper extends previous results by proving necessity, in case the loop gain is uniformly less than one. The results are validated and illustrated in a simulation study.

MSC:

93D25 Input-output approaches in control theory
93B52 Feedback control
93C10 Nonlinear systems in control theory
Full Text: DOI

References:

[1] Baillieul, J., Feedback coding for information based control: Operating near the data-rate limit, Proceedings of the 41st IEEE Conference on Decision and Control, 3229-3236 (2002), Las Vegas, NV
[2] Björklund, S.; Ljung, L., A review of time delay estimation, Proceedings of the 42nd IEEE Conference on Decision and Control, 2502-2507 (2003), Maui, HI
[3] Callier, F. M.; Desoer, C. H., A graphical test for checking the stability of a linear time-invariant feedback system, IEEE Transactions on Automatic Control,, 17, 6, 773-780 (1972) · Zbl 0261.93023
[4] Ericsson, A. B., 5G Radio access - Research and vision (Ericsson White Paper No. 284 23-3204 Uen) (2013)
[5] Fridman, E.; Dambrine, M., Control under quantization, saturation and delay: An LMI approach, Automatica,, 45, 2258-2264 (2009) · Zbl 1179.93089
[6] Goodwin, G. C.; Quevedo, D.; Silva, E. I., Architectures and coder design for networked control systems, Automatica,, 44, 1, 248-257 (2008) · Zbl 1138.93302
[7] Goodwin, G. C.; Seron, M. M.; Dedona, J. A., Constrained control and estimation - An optimization approach. (2005), London: Springer, London · Zbl 1078.93003
[8] Ho, F.-S.; Ioannou, P., Traffic flow modeling and control using artificial neural networks, IEEE Control Systems,, 16, 5, 16-26 (1996)
[9] Jankovic, M., Control Lyapunov-Razumikhin functions and robust stabilization of time delay systems, IEEE Transactions on Automatic Control,, 46, 7, 1048-1060 (2001) · Zbl 1023.93056
[10] Lee, B.-K.; Chen, H.-W.; Chen, B.-S., Power control of cellular radio systems via robust Smith prediction filter, IEEE Transactions on Wireless Communications,, 3, 1822-1831 (2004)
[11] Liu, G.-P.; Xia, Y.; Rees, D.; Hu, W., Design and stability criteria of networked predictive control systems with random network delay in the feedback channel, IEEE Transactions on Systems, Man, and Cybernetics, Part C Applications and Reviews,, 37, 2, 173-184 (2007)
[12] Megretski, A.; Rantzer, A., System analysis vis integral quadratic constraints, IEEE Transactions on Automatic Control,, 42, 6, 819-830 (1997) · Zbl 0881.93062
[13] Nair, G. N.; Evans, R. J., Stabilization with data-rate-limited feedback: Tightest attainable bound, Systems & Control Letters,, 41, 1, 49-56 (2000) · Zbl 0985.93059
[14] Quevedo, D. E.; Wigren, T., Design of embedded filters for inner-loop power control in wireless CDMA communication systems, Asian Journal of Control,, 14, 4, 891-900 (2012) · Zbl 1286.93177
[15] Rappaport, T. S.; Heath, R. W. Jr.; Daniels, R. C.; Murdock, J. N., Millimeter wave wireless communications. (2014), Westford, MA: Prencice Hall, Westford, MA
[16] Samad, T., Control systems and the internet of things, IEEE Control Systems Magazine,, 36, 1, 13-16 (2016)
[17] Sandberg, I. W., A frequency-domain condition for the stability of feedback systems containing a single time-varying element, The Bell System Technical Journal,, 43, 1601-1608 (1964) · Zbl 0131.31704
[18] Silva, E. I.; Quevedo, D.; Goodwin, G. C., Optimal controller design for networked control systems, IFAC Proceedings Volumes, 41, 2, 5167-5172 (2008)
[19] Verriest, E.; Fan, M. K. H.; Kullström, J., Frequency domain robust stability criteria for linear delay systems, Proceedings of the 32nd IEEE conference on decision and control, 3473-3478 (1993), San Antonio, TX
[20] Vidyasagar, M., Nonlinear systems analysis (1978), Englewood Cliffs, NJ: Prentice-Hall, Englewood Cliffs, NJ · Zbl 0407.93037
[21] Wigren, T., Low-frequency limitations in saturated and delayed networked control, Proceedings of the 2015 IEEE Conference on Control Applications, 564-571 (2015), Sydney
[22] Wigren, T., Robust \(####\)-stable networked control of wireless packet queues in delayed internet connections, IEEE Transactions on Control Systems Technology,, 24, 2, 502-513 (2016)
[23] Wigren, T.; Brus, L., Time horizon in feedforward MPC for non-linear systems with time delays, Proceedings of the 7th IFAC symposium on nonlinear control systems, NOLCOS 2007, 978-983 (2007), Pretoria
[24] Yang, H.; Xia, Y.; Shi, P.; Fu, M., Stability analysis for high frequency networked control systems, IEEE Transactions on Automatic Control,, 57, 10, 2694-2700 (2012) · Zbl 1369.93543
[25] Zames, G., On the input-output stability of time-varying nonlinear feedback systems, Part1: Conditions derived using concepts of loop-gain, conicity and positivity, IEEE Transactions on Automatic Control,, 11, 2, 228-238 (1966)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.