Page 119 - Modern Control of DC-Based Power Systems

CHAPTER THREE

Background

This chapter will provide a short recall of control theory fundamentals,
which will be used in the designed controller throughout Chapter 6,
Simulation. Sections 3.1 3.3 summarize the most important concepts of
classic control theory. Sections 3.4 and 3.5 introduce the basic methods of
modern control theory which focuses on systems represented in the state-
space. In Section 3.6, we introduce the droop control concept which is
necessary for operating parallel converter systems as is shown in
Chapter 6, Simulation.

3.1 FREQUENCY RESPONSE APPROACHES

The frequency response approaches, which are based on the con-
cept of frequency response, provide powerful tools for analysis and design
of linear, time-invariant (LTI) systems. These approaches were developed
by Bode, Nyquist, and Nichols, among other contributors, in the 1930s
and 1940s [1].
Frequency response of a system can be defined as its steady-state
response to a sinusoidal input signal as the frequency of the signal varies
from zero to infinity. For a stable, LTI system, the frequency response can
be described by
jφ
GjωðÞ 5 Me (3.1)
where M is the ratio of the amplitudes of the output and input sinusoids
and φ is the phase shift of the output sinusoid with respect to the input
sinusoid. If GsðÞ is the transfer function of the system, it can be shown
that the frequency response can be obtained by replacing s with jω.
When the transfer function of the system is not known, the frequency
response can be usually obtained using a signal generator and precise mea-
surement equipment.

Modern Control of DC-Based Power Systems. © 2018 Elsevier Ltd.
DOI: https://doi.org/10.1016/B978-0-12-813220-3.00003-X All rights reserved. 83