New Designs of Reduced-Order Observer-Based Controllers for Singularly Perturbed Linear Systems

Abstract EN

The slow and fast reduced-order observers and reduced-order observer-based controllers are designed by using the two-stage feedback design technique for slow and fast subsystems.

The new designs produce an arbitrary order of accuracy, while the previously known designs produce the accuracy of O(ϵ) only where ϵ is a small singular perturbation parameter.

Several cases of reduced-order observer designs are considered depending on the measured state space variables: only all slow variables are measured, only all fast variables are measured, and some combinations of the slow and fast variables are measured.

Since the two-stage methods have been used to overcome the numerical ill-conditioning problem for Cases (III)–(V), they have similar procedures.

The numerical ill-conditioning problem is avoided so that independent feedback controllers can be applied to each subsystem.

The design allows complete time-scale separation for both the reduced-order observer and controller through the complete and exact decomposition into slow and fast time scales.

This method reduces both offline and online computations.