Power-constrained intermittent control

Abstract

In this article, input power, as opposed to the usual input amplitude, constraints are introduced in the context of intermittent control. They are shown to result in a combination of quadratic optimisation and quadratic constraints. The main motivation for considering input power constraints is its similarity with semi-active control. Such methods are commonly used to provide damping in mechanical systems and structures. It is shown that semi-active control can be re-expressed and generalised as control with power constraints and can thus be implemented as power-constrained intermittent control. The method is illustrated using simulations of resonant mechanical systems and the constrained nature of the power flow is represented using power-phase-plane plots. We believe the approach we present will be useful for the control design of both semi-active and low-power vibration suppression systems.

Keywords:

• intermittent control
• hybrid control
• vibration control
• semi-active damping
• power phase-plane

Acknowledgements

Peter Gawthrop is a Visiting Research Fellow at the University of Bristol. He is also partially supported by the linked EPSRC Grants EP/F068514/1, EP/F069022/1 and EP/F06974X/1 ‘Intermittent control of man and machine’ and gratefully acknowledges the many discussions about intermittent control with Henrik Gollee, Ian Loram and Martin Lakie. The authors wish to thank Irina Lazar, University of Bristol, for her constructive comments on the draft of this article. The authors gratefully acknowledge the many insightful comments of the referees which have led to an improved article.