Model Reduction for LPV systems

A primer on model reduction in the LPV framework.

Contents

Introduction

LPVTools provides tools for LPV model reduction. LPV model reduction is different from Linear Time-Invariant (LTI) model reduction techniques which act on a single point, because they perform the model reduction for all values of the scheduling parameter simultaneously. The resulting reduced order model is still a LPV model with consistent state, input and output vectors. If LTI model reduction techniques (e.g. balreal) are applied to a LPV model, the resulting model may lose state consistency and the resulting reduced order model is no longer a LPV system. LPVTools provides two functions for LPV model reduction. lpvbalancmr performs balanced trunctation, and provides the option of weighting different frequency bands in the model reduction to emphasize accuracy for some dynamics while de-emphasizing others.. However it is restricted to stable LPV systems. lpvncfmr performs a contractive coprime factorization of a LPV system, and can handle unstable LPV systems.

Further Reading

  1. G. D. Wood, "Control of parameter-dependent mechanical systems," Ph.D. Dissertation, University of Cambridge, 1995.
  2. G. D. Wood, P. J. Goddard, and K. Glover, "Approximation of linear parameter-varying systems," IEEE Conference on Decision and Control, Vol. 1, pp 406-411, 1996.
  3. R. Widowati, R. Bambang, R. Sagari, S. M. and Nababan, “Model reduction for unstable LPV system based on coprime factorizations and singular perturbation,” 5th Asian Control Conference, Vol. 2, pp. 963-970, Melbourne, Australia, 2004.

LPV Model Reduction Commands

LPVGRAM Compute Gramians for PSS objects.
LPVBALREAL Perform Gramian-based balancing for PSS objects.
LPVBALANCMR Balanced truncation model reduction.
LPVNCFMR Balanced truncation model reduction through contractive coprime factorization.

Examples and How To

Concepts