2-PERIODIC/2-RATE COMPENSATION OF DISCRETE-TIME PLANTS
Thesis submitted to
Indian Institute of Technology, Kharagpur For award of the degree
of
Doctor of Philosophy
by
Sayantan Chakraborty
Under the guidance of
Prof. Sarit K. Das
DEPARTMENT OF ELECTRICAL ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY KHARAGPUR
JUNE 2015
c
2015 Sayantan Chakraborty. All rights reserved.
Abstract
It is difficult to stabilize a single-input-single-output (SISO), linear-time-invariant (LTI) plant having unstable poles and non-minimum phase (NMP) zeros (in close proximity) with sufficient robustness using LTI controllers. This is so because LTI controllers cannot shift plant zeros. For continuous-time systems, however, it can be done using high-frequency periodic controllers (which yield satisfactory response and are physically implementable as well). As far as discrete-time plants are concerned, zero placement using periodic discrete-time controllers has also been attempted and improvement in robustness has been reported. The controller synthesis problem cor- responding to the same, however, has not been satisfactorily addressed. Moreover, the control objective of achieving satisfactory, ripple-free response has not been consid- ered. The first objective of this thesis is to develop a methodology for the analysis and synthesis of 2-periodic controllers to achieve zero as well as pole placement leading to robust compensation and a satisfactory response as well. In this context, more- over, it is important to note that some attempts have also been made in literature to achieve zero placement using multi-rate control. These attempts, however, used only the fast-input mode of operation which, unfortunately, yields high oscillations in the output and so is unacceptable. The fast-output type of multi-rate control does not have this problem inherently but its zero placement capability or otherwise has not so far been investigated. The second objective of this thesis is to understand the working of 2-rate controllers using a 2-periodic perspective leading to the revelation that the fast-output 2-rate controllers can also effect zero placement and hence robust control
ii
with satisfactory response. In fact a generalized version of 2-rate controllers used so far has also been proposed and the same is shown to be capable of handling third and higher order plants as well. The controller used so far for 2-periodic control has a one-degree-of-freedom structure. The possibility of using a two-degree-of-freedom controller is investigated as well.
