Rossi, Mauro2006-07-282006-07-2819991999http://hdl.handle.net/10012/399The application of a digital controller to a continuous-time plant results in a closed loop system that contains both continuous-time and discrete-time signals; such a system is referred to as a sampled-data system. In this thesis, we consider finite-dimensional linear time-invariant plants, and the emphasis is placed on designing low order linear time-varying digital controllers that are straightforward to design and easy to implement. We consider two basic controller structures: statis generalized sampled-data hold function (GSHF) controllers and linear periodic controllers (LPCs) that consist of a sampler, a low order linear discrete-time compensator, and a zero-order-hold function. We consider three control problems. The first problems is the combined gain/phase margin problem, which can be viewed as a robust stabilization problem. We show that it is possible to design a statistic GSHF controller, which can be implemented with a low order LPC, that can provide a gain margin as large as desired and any desired phase margin up to 9 degrees. An analysis of the tolerance of such a controller to unstructured uncertainty in the nominal model is also presented. This controller suffers from poor intersample behaviour, so we also present another low order LPC that has good intersample behaviour while providing a gain margin as large as desired and any desired phase margin up to 90 degrees. The second problem is the model reference control problem (MRCP), where the goal is to track a class of reference signals despite the presence of noise. We show that there exists a static GSHF controller that solves the MRCP when the single-input, single-output plant is minimum phase. Finally, in our third problem we look at an optimal step tracking problem for an arbitrary multi-input, multi-output plant. We show that it is possible to design a low order LPC that not only provides near LQR-optimal step tracking for the nominal plant, but also provides step tracking when there is some uncertainty in the gain of the plant.application/pdf7851516 bytesapplication/pdfenCopyright: 1999, Rossi, Mauro. All rights reserved.Harvested from Collections CanadaDoctoral Thesis