Delay Analysis of Sampled-Data Systems in Hard RTOS

In this paper, we have presented the effect of varying time-delays on performance and stability in the single-channel multirate sampled-data system in hard real-time (RT-Linux) environment. The sampling task require response time that might exceed the capacity of RT-Linux. So a straight implementation with RT-Linux is not feasible, because of the latency of the systems and hence, sampling period should be less to handle this task. The best sampling rate is chosen for the sampled-data system, which is the slowest rate meets all performance requirements. RT-Linux is consistent with its specifications and the resolution of the real-time is considered 0.01 seconds to achieve an efficient result. The test results of our laboratory experiment shows that the multi-rate control technique in hard real-time operating system (RTOS) can improve the stability problem caused by the random access delays and asynchronization.

Authors:

• A. M. Azad
• M. Alam
• C. M. Hussain

Keywords:

• Multi-rate
• PID
• RT-Linux
• Sampled-data
• Servo.

References:

[1] V. Casanova & J. Salt, Multirate control for an ICCS environment. Part
I: the random access delays, Proceedings of the 2nd IFAC workshop on
Linear Time Delay Systems, 2000, Ancona (Italy).
[2] J. Salt & P. Albertos, Multirate controllers design by rate decomposition,
Proceedings of the 39th Conference on Decision and Control, 2000,
Sydney, Australia.
[3] C. S. Alan, Real-Time Systems and Software, (Wiley, 2001).
[4] B. Wittenmark, B. Bastian & J. Nilsson, Analysis of Time Delays in
Synchronous and Asynchronous Control Loops, Proceedings of the 37th
Conference on Decision and Control, Tampa, Florida, USA, 1998, pp.
283-288.
[5] K. J. Astrom & B. Wittenmark, Computer-Controlled Systems, (Third
edition, Prentice Hall, 1997).
[6] C. K. Chak, G. Feng & T. Hesketh, Multirate adaptive optimal control
with application to dc motor, Computers Elect. Engng, Vol. 23, No. 2,
1997, pp. 65-79.
[7] A. M. Azad & T. Hesketh, H -Optimal Control Of Multi-rate Sampleddata
Systems, Proceedings of American control Conference, Anchorage,
Alaska, USA, 2002, pp.459-464.
[8] D. S. Bernstein, L. D. Davis & S. W. Greeley (1986), The Optimal
Projection Equations for Fixed-Order Sampled-Data Dynamic
Compensation with Computational Delay, IEEE Transactions on
Automatic Control, Vol. AC-31, 1986, pp. 859-862.
[9] A. M. Azad, T. Hesketh & R. Eaton, Real-time Implementation Multirate
Sampling Systems in RT-Linux Environment, Proceedings of The
fourth International Conference on Control and Automation, Montreal,
Canada, 2003, pp.605-609.
[10] F. S. Robert, (1994), Optimal Control and Estimation, (Dover
Publication, Inc. New York, 1994).