Stability Analysis of Linear Time-Delay Systems and Its Application to the Synthesis of Digital Quasi-PD Controller
Date Issued
2014
Date
2014
Author(s)
Lin, Chun-Pi
Abstract
This dissertation studies a general class of linear systems with multiple successive delay components. First of all, the delays are assumed to vary in intervals, and delay-dependent exponential stability conditions are derived in terms of linear matrix inequalities. To reduce conservativeness, a new Lyapunov-Krasovskii functional is designed to contain more complete state information, so that a derivation procedure with time-varying delays treated as uncertain parameters can be adopted. Secondly, when the lower bound of time-varying delay’s rate of change is greater than or equal to zero, a delay-parameter-dependent Lyapunov functional is built to analyze the stability of linear systems with a non-decreasing time-varying delay. Pure numerical examples as well as an example with a DC motor model are provided to demonstrate the effectiveness of the proposed stability criteria.
Finally, a digital quasi-PD controller is proposed to achieve exponential stabilization for linear continuous-time systems. As a variation of the traditional position and delayed position (PDP) control, the proposed controller uses samples of the output signals, which is easier to implement and more practical. A second-order negatively damped system and a double inverted pendulum system are tested to show the control method is effective.
Subjects
時延系統
時變時滯
多時滯系統
穩定性
線性矩陣不等式
比例微分控制器
Type
thesis
File(s)![Thumbnail Image]()
Loading...
Name
ntu-103-D94921008-1.pdf
Size
23.32 KB
Format
Adobe PDF
Checksum
(MD5):06a9cc364b7ee23cf4289fac84fdc9f1