Reduced-order block techniques for singularly perturbed systems with application to permanent-magnet synchronous motors

The use of so-called block controllers and observers in the presence of stable high frequency parasitics is explored. Block control is based on an input-to-state map, which is derived from a discrete-time representation of the system. The inversion of this map, which theoretically only requires local controllability, provides a prescription for a block control law that achieves deadbeat tracking of arbitrary discrete-time sequences. The block observer problem, the dual of the control problem, is based on the inversion of a state-to-measurement map, and requires only local observability.;Because the block techniques rely on inversion of system derived nonlinear mappings, they lose many of their advantages when applied to singularly perturbed systems. The difficulties of applying the block techniques to singularly perturbed systems include: (i) the stiffness associated with the separation in time-scales makes numerical inversion of the maps difficult or intractable; (ii) the increase in system order resulting from the inclusion of fast parasitics leads to significantly increased computational requirements; (iii) the higher sampling frequencies required by the speed of the parasitics requires more expensive analog-to-digital converters and increases the computational requirements.;In this thesis, new reduced-order block controllers and observers for singularly perturbed systems are developed that overcome the previously mentioned difficulties. A key tool in the development is a new time-scale decomposition that is valid for systems with piecewise-constant inputs. This decomposition leads to an order reduction that eliminates the stiffness associated with the full-order problem, and permits a multirate implementation that reduces the computational requirements. The new designs achieve these benefits at the expense of accuracy. The tradeoff between the reduced-order requirements and the accuracy of a full-order design, however, always favors the new approach as the separation in time-scales increases.;By specializing the reduced-order block techniques to permanent-magnet synchronous motors, new controllers, observers and identifiers for the motor are developed that achieve performance which meets or exceeds the performance obtained using previously reported techniques, and does so with a significant savings in computational requirements. Extensive experimental results using a commercially available motor demonstrate the utility of the reduced-order block techniques.