Non-minimal state-space model-based continuous-time model predictive control with constraints

Abstract

This article proposes a model predictive control scheme based on a non-minimal state-space (NMSS) structure. Such a combination yields a continuous-time state-space model predictive control system that permits hard constraints to be imposed on both plant input and output variables, whilst using NMSS output-feedback without the need for an observer. A comparison between the NMSS and observer-based approaches using Monte Carlo uncertainty analysis shows that the former design is considerably less sensitive to plant-model mismatch than the latter. Through simulation studies, the article also investigates the role of the implementation filter in noise attenuation, disturbance rejection and robustness of the closed-loop predictive control system. The results show that the filter poles become a subset of the closed-loop poles and this provides a straightforward method of tuning the closed-loop performance to achieve a reasonable balance between speed of response, disturbance rejection, measurement noise attenuation and robustness.

Keywords:

• predictive control
• continuous-time systems
• non-minimal state-space realisation
• multivariable systems
• Laguerre functions

Acknowledgements

Part of the work reported here was accomplished whilst P.C. Young and P.J. Gawthrop were visiting professors at RMIT University, Melbourne, supported by the RMIT Professorial Fund. Young completed part of the work while visiting the School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney. The research was also partially funded by the Royal Academy of Engineering through international travel grants to P.C. Young and P.J. Gawthrop.

Notes

1. Of course, standard NMSS control, which is equivalent to model predictive control (Taylor et al. 2000), provides a simpler implementation in the case where there are no constraints.

2. This is a toolbox for use in Matlab™ and it can be downloaded from http://www.es.lancs.ac.uk/cres/captain/.