Discrete-Time Observers for Singularly Perturbed Continuous-Time Systems: Part II, Nonautonomous Systems

A new technique for designing discrete-time observers for nonlinear singularly perturbed continuous-time nonautonomous systems is presented. Our design approach is based on inversion of state-to-measurement maps. In order to exploit the two-time-scale nature of the system, separate slow and fast reduced-order observers are constructed using multirate measurements and computation. The underlying approximations, on which the reduced-order observers are based, are introduced here in the form of a Tikhonov-like approximation theorem for systems with piecewise-constant inputs. The paper concludes with a practical application of the theory, namely, velocity regulation of permanent-magnet synchronous motors using only stator current measurements. Numerical simulations demonstrate for this application the strengths and weaknesses of our reduced-order observers.