Robust control

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Robust control is a branch of control theory that explicitly deals with uncertainty in its approach to controller design. Robust control methods are designed to function properly so long as uncertain parameters or disturbances are within some (typically compact) set. Robust methods aim to achieve robust performance and/or stability in the presence of bounded modeling errors.

The early methods of Bode and others were fairly robust; the state-space methods invented in the 1960s and 1970s were sometimes found to lack robustness,[1] prompting research to improve them. This was the start of the theory of Robust Control, which took shape in the 1980s and 1990s and is still active today.

In contrast with an adaptive control policy, a robust control policy is static; rather than adapting to measurements of variations, the controller is designed to work assuming that certain variables will be unknown but, for example, bounded.[2][3]

When is a control method said to be robust?

Informally, a controller designed for a particular set of parameters is said to be robust if it would also work well under a different set of assumptions. High-gain feedback is a simple example of a robust control method; with sufficiently high gain, the effect of any parameter variations will be negligible. High-gain feedback is the principle that allows simplified models of operational amplifiers and emitter-degenerated bipolar transistors to be used in a variety of different settings. This idea was already well understood by Bode and Black in 1927.

The modern theory of robust control

The theory of robust control began in the late 1970s and early 1980s and soon developed a number of techniques for dealing with bounded system uncertainty.[4][5]

Probably the most important example of a robust control technique is H-infinity loop-shaping, which was developed by Duncan McFarlane and Keith Glover of Cambridge University; this method minimizes the sensitivity of a system over its frequency spectrum, and this guarantees that the system will not greatly deviate from expected trajectories when disturbances enter the system.

An emerging area of robust control from application point of view is Sliding Mode Control (SMC) which is a variation of variable structure control (VSS). Robustness property of SMC towards matched uncertainty as well as the simplicity in design attracted a variety of application.

Another example is loop transfer recovery (LQG/LTR),[6] which was developed to overcome the robustness problems of LQG control.

Other robust techniques includes Quantitative Feedback Theory (QFT), Gain scheduling etc.

References

  1. ↑ M. Athans, Editorial on the LQG problem, IEEE Trans. Autom. Control 16 (1971), no. 6, 528.
  2. ↑ J. Ackermann (1993) (in German), Robuste Regelung, Springer-Verlag (Section 1.5) In German; an english version is also available
  3. ↑ Manfred Morari : Homepage
  4. ↑ Safonov: editorial
  5. ↑ Kemin Zhou: Essentials of Robust Control
  6. ↑ http://www.nt.ntnu.no/users/skoge/book.html

Further reading

  • Dullerud, G.E.; Paganini, F. (2000). A Course in Robust Control Theory: A Convex Approach. Springer Verlag New York. ISBN 0-387-98945-5. 
  • Zhou, Kemin; Doyle C., John (1999). Essentials of Robust Control. Prentice Hall. ISBN 0-13-525833-2. 
  • Morari, Manfred; Zafiriou, Evanghelos (1989). Robust Process Control. Prentice Hall. ISBN 0-13-782153-0. 
  • Mahmoud S., Magdi; Munro, Neil (1989). Robust Control and Filtering for Time-Delay Systems. Marcel Dekker Inc. ISBN 0-8247-0327-8. 
  • Calafiore, G.; Dabbene, F. (ed.) (2006). Probabilistic and Randomized Methods for Design under Uncertainty. Springer Verlag London Ltd. ISBN 978-1-84628-094-8. 

See also

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