Non-linear control by input–output state variable feedback pole assignment

Abstract

This article considers pole assignment control of non-linear dynamic systems described by state-dependent parameter (SDP) models. The approach follows from earlier research into linear proportional-integral-plus methods but, in SDP system control, the control coefficients are updated at each sampling instant on the basis of the latest SDP relationships. Alternatively, algebraic solutions can be derived off-line to yield a practically useful control algorithm that is relatively straightforward to implement on a digital computer, requiring only the storage of delayed system variables, coupled with straightforward arithmetic expressions in the control software. Although the analysis is limited to the case when the open-loop system has no zeros, time delays are handled automatically. This article shows that the closed-loop system reduces to a linear transfer function with the specified (design) poles. Hence, assuming pole assignability at each sample, global stability of the non-linear system is guaranteed at the design stage.

Keywords:

• non-linear control
• non-minimal state space
• proportional-integral-plus
• state-dependent parameter model
• inverted pendulum

Acknowledgements

The statistical tools for SDP system identification have been assembled as the CAPTAIN toolbox (Taylor et al. 2007b) within the Matlab® software environment and may be downloaded from: www.es.lancs.ac.uk/cres/captain. Video footage of robot arm experiments may be downloaded from: www.lancs.ac.uk/staff/taylorcj/nonlinear.