Multirate control with incomplete information over Profibus-DP network

Abstract

When a process field bus-decentralized peripherals (Profibus-DP) network is used in an industrial environment, a deterministic behaviour is usually claimed. However, due to some concerns such as bandwidth limitations, lack of synchronisation among different clocks and existence of time-varying delays, a more complex problem must be faced. This problem implies the transmission of irregular and, even, random sequences of incomplete information. The main consequence of this issue is the appearance of different sampling periods at different network devices. In this paper, this aspect is checked by means of a detailed Profibus-DP timescale study. In addition, in order to deal with the different periods, a delay-dependent dual-rate proportional-integral-derivative control is introduced. Stability for the proposed control system is analysed in terms of linear matrix inequalities.

Keywords:

• multirate control systems
• network delay
• networked control system
• PID controller
• stability analysis
• Profibus-DP

Acknowledgements

We would like to express as well our gratitude to both P. Tormos and A. Lova with the Department of Statistics of the Universitat Politecnica de Valencia for their support and help in this work.

Notes

1. Actually, an irregular sequence with random delays is found.

2. Although an NCS with sensor and actuator usually share one side, in general they will be separated.

3. This slave could be the same one previously used, or another one.

4. This period will be denoted later simply as T.

5. Actually, this is a usual configuration in this kind of installations.

6. Actually, a small difference is obtained when the window of data is shifted.

7. The next restriction is assumed: the round trip delay cannot be greater than the following NT. If this case appears, the best option is to perform another execution with a different bus time-scale offset.

8. In this work N^* = 1 was selected.

9. Note, α_N is the decay rate α for the considered N.

10. In this case, the total number of transitions coincide with , but the network behaviour could involve a lower number of them.

11. Denoting E[·] as the statistical expectation, E[V(x)] will tend to zero hence the state will converge to zero with probability one.

12. Details on the crane characteristics can be obtained at http://www.inteco.com.pl (3D crane apparatus).

Additional information

Funding

The authors are grateful to the financial support of the Spanish Ministry of Economy and Competitivity [Research Grant TEC2012-31506].

Notes on contributors

J. Salt

Julián Salt received his MSc degree in Industrial Engineering in 1986 and his PhD degree in Control Engineering in 1992, from the Technical University of Valencia. His current position is as a full professor at the Technical University of Valencia. Recently, he was appointed the head of the Department of Systems Engineering and Control at the Technical University of Valencia. He has been director of nine PhD theses and co-author of about 70 papers in journals and technical meetings. His research interests include non-conventionally sampled control and networked control systems (NCSs).

V. Casanova

Vicente Casanova received the MSc degree in Computer Science in 1994, in Telecommunication Engineering in 2000 and his PhD degree in Automatics and Industrial Informatics in 2005 from Technical University of Valencia. His research interests include NCSs, multirate control, control with time-varying delays and analysis and modelling of Profibus-DP.

A. Cuenca

Ángel Cuenca received his MSc degree in Computer Science in 1998 and his PhD degree in Control Engineering in 2004 from the Technical University of Valencia. He has taken part in research projects funded by government and European community. His research interests include multirate control systems, network-based control systems and event-based control systems.

R. Pizá

Ricardo Pizá received his BEng degree in 1997 and his PhD degree in Control Engineering in 2003 from Technical University of Valencia. He has taken part in research projects funded by local industries and government. His research interests include network-based control systems, computer-aided manufacturing and robotics.