‘Periodically-active phenomenon’ of DIS-NCS with scattering transformation. (English) Zbl 1230.93016
Summary: When Networked Control Systems (NCSs) are stable with any constant time delays, they are called Delay-Independently Stable (DIS). For Delay-Independently Stable Networked Control Systems (DIS-NCSs), ‘staircase phenomenon’ in its dynamic response has been discovered and proven to be an intrinsic problem, which can only be eliminated by changing the system’s traditional feedback structure. Recent research proves that the introduction of scattering transformation into DIS-NCS can effectively eliminate the ‘staircase phenomenon’. But new problems appear, as the DIS-NCS with scattering transformation displays another undesired ‘periodically-active phenomenon’ in its dynamic response, which literally means that the system’s dynamic response is active periodically. In this article, the definition and certain examples of ‘periodically-active phenomenon’ are given at the beginning, which show that the phenomenon is indeed a problem and may bring unexpected results. Then, the analysis of the reason for its appearance is provided. To eliminate it, this article proceeds to propose a simple but effective method: inserting certain filters into the system. The needed theoretical proof of this method is given. A simulation is provided in the end.
Keywords:
periodically-active phenomenon; staircase phenomenon; scattering transformation; networked control systems; delay-independent stabilityReferences:
| [1] | DOI: 10.1109/9.24201 · doi:10.1109/9.24201 |
| [2] | DOI: 10.1109/9.983374 · Zbl 1364.34101 · doi:10.1109/9.983374 |
| [3] | DOI: 10.1109/9.412637 · Zbl 0834.93044 · doi:10.1109/9.412637 |
| [4] | DOI: 10.1109/9.412644 · Zbl 0834.93045 · doi:10.1109/9.412644 |
| [5] | Chopra, N. (2008), ’Passivity Results for Interconnected Systems with Time Delay’, inIEEE Conference on Decision and Control, pp. 4620–4625 |
| [6] | Chopra N, Advances in Robot Control, From Everyday Physics to Human-Like Movements, pp 107–, 1. ed. (2006) |
| [7] | Chopra, N and Spong, MW. (2007), ’Delay-independent Stability for Interconnected Nonlinear Systems with Finite L2 Gain’, inIEEE Conference on Decision and Control, pp. 3847–3852 |
| [8] | DOI: 10.1049/iet-cta.2009.0614 · doi:10.1049/iet-cta.2009.0614 |
| [9] | Fang, S. Li, N., Li, S. (2011), ’Staircase Phenomenon’ in Delay-independently Stable Networked Control System’s Dynamic Response: Discrete-time Case’, inThe 8th Asian Control Conference, Taiwan |
| [10] | DOI: 10.1007/978-1-4612-0039-0 · doi:10.1007/978-1-4612-0039-0 |
| [11] | DOI: 10.1016/j.automatica.2009.04.016 · Zbl 1185.93120 · doi:10.1016/j.automatica.2009.04.016 |
| [12] | DOI: 10.1109/TAC.1980.1102482 · Zbl 0458.93046 · doi:10.1109/TAC.1980.1102482 |
| [13] | Matiakis, T. Hirche, S., and Buss, M.A. (2005), ’The Scattering Transformation for Networked Control Systems,’ inProceedings of 2005 IEEE Conference on Control Applications, pp. 705–710 |
| [14] | Matiakis, T. Hirche, S., and Buss, M.A. (2006a), ’A Novel Input–Output Transformation Method to Stabilize Networked Control Systems Independent of Delay’, inProceedings of 17th International Symposium Mathematical Theory of Networks and Systems, pp. 2891–2897 |
| [15] | Matiakis, T. Hirche, S., and Buss, M.A. (2006b), ’Memoryless Input-output Encoding for Networked Systems with Unknown Constant Time Delay’, inProceedings of 2006 IEEE Conference on Control Applications, pp. 1707–1712 |
| [16] | Matiakis, T. Hirche, S., and Buss, M.A. (2008), ’Local and Remote Control Measures for Networked Control Systems’, inProceedings of 47th IEEE Conference on Decision and Control, pp. 4626–4631 |
| [17] | DOI: 10.1109/TCST.2008.922570 · doi:10.1109/TCST.2008.922570 |
| [18] | DOI: 10.1093/imamci/14.3.299 · Zbl 0886.93056 · doi:10.1093/imamci/14.3.299 |
| [19] | DOI: 10.1109/48.64895 · doi:10.1109/48.64895 |
| [20] | Niemeyer, G. and Slotine, J.J.E. (1997), ’Using Wave Variables for System Analysis and Robot Control’, inProceedings of the 1997 IEEE International Conference on Robotics and Automation, pp. 1619–1625 |
| [21] | DOI: 10.1177/0278364904045563 · doi:10.1177/0278364904045563 |
| [22] | O’Dwyer, A. (2003), ’PID Compensation of Time Delayed Processes 1998–2002: A Survey’, inProceedings of the American Control Conference, pp. 1494–499 |
| [23] | DOI: 10.1016/S0005-1098(03)00167-5 · Zbl 1145.93302 · doi:10.1016/S0005-1098(03)00167-5 |
| [24] | Smith OJ, Chemical Engineering Progress 53 pp 217– (1957) |
| [25] | DOI: 10.1016/j.automatica.2009.05.012 · Zbl 1175.93195 · doi:10.1016/j.automatica.2009.05.012 |
| [26] | Tsypkin YaZ, Automation and Remote Control 7 pp 107– (1946) |
| [27] | Verriest, EI. Fan, M.K.H., and Kullstam, J. (1993), ’Frequency Domain Robust Stability Criteria for Linear Delay Systems’, inProceedings of the 32nd IEEE Conference on Decision and Control, pp. 3473–3478 |
| [28] | DOI: 10.1109/37.898794 · doi:10.1109/37.898794 |
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