Adaptive control of nonminimum-phase systems using shifted Laurent series

ABSTRACT

We present a direct discrete-time output-feedback adaptive control algorithm for single-input, single-output systems that are possibly unstable and nonminimum phase. The plant modeling information is given by impulse response components, and the plant is modelled within the algorithm by a truncated shifted Laurent series. A shifted Laurent series is a Laurent series at a point different from the origin in the complex plane and about infinity. The shifted Laurent series is analysed, including its convergence and its relationship to other Laurent series. In particular, we provide a technique for constructing a truncated shifted Laurent series using impulse response components. Numerical examples show that retrospective cost adaptive control can achieve asymptotic command following for a class of exponentially unstable, nonminimum-phase systems.

Keywords:

• Adaptive control
• nonminimum-phase zero
• unstable system
• Laurent series
• Markov parameters
• impulse response

Acknowledgments

The authors wish to thank Khaled Aljanaideh for helpful discussions.

Disclosure statement

No potential conflict of interest was reported by the authors.