Discrete-time observers for singularly perturbed continuous-time systems

The use of discrete-time observers for nonlinear singularly perturbed continuous-time systems is explored. The observer design approach is based on inversion of state-to-measurement maps. The two-time-scale nature of the system is exploited by constructing separate reduced-order observers for the approximate slow and fast subsystems, using multirate measurements and computation. The reduced-order observers are compared to a full-order observer designed for the same system. The comparison shows that although the reduced-order observers exhibit some approximation error, they also result in reduced computational requirements if the inversion is performed on-line, reduced memory requirements if the inversion is implemented by look-up table and reduced stiffness. The trade-off between accuracy and implementation requirements always favors the reduced-order approach for systems with significant separation of time scales. Numerical examples are provided, including a case-study of an observer-based control system for permanent-magnet synchronous motors