Boundary Controller Design and Robust Stability Analysis of a Class of Distributed Parameter Systems

• Main Authors: Shin-Hao Lu, 盧信豪
• Other Authors: I-Kong Fong
• Format: Others
• Language: en_US
• Published: 2002
• Online Access: http://ndltd.ncl.edu.tw/handle/24129580252614649341

博士 === 國立臺灣大學 === 電機工程學研究所 === 90 === This dissertation presents the study of robust stability analysis and boundary feedback controller design problems for a class of distributed parameter systems. The basis of the study is a theory of how to integrate nonzero boundary conditions into the system equation of the distributed parameter systems in discussion. For the robust stability analysis problems, we consider the nominally normal distributed parameter systems which contain known perturbation operators multiplied by uncertain parameters. The perturbation operators may appear in the system equation itself as well as in the boundary conditions, but are assumed to have the relative boundedness property. The boundary perturbations are first integrated into the system equation, and then by using the Lyapunov stability criterion, simple bounds on uncertain parameters are derived to ensure the stability of the perturbed systems. For the boundary controller design problems, we first consider a class of distributed parameter systems defined on the one-dimensional domains. The systems are described by linear partial differential equations with mixed boundary conditions. Then we consider distributed parameter systems defined on two-dimensional domains with the Neumann boundary conditions. All systems are assumed to be the so-called general boundary input systems. For such systems, the boundary operators may be integrated into the system equation in certain interpolation spaces, and new state-space descriptions without boundary operators may be established. Based on the state-space descriptions without boundary operators, we propose two methods for the boundary feedback controller design. The first method is called the spectrum shift boundary controller design, which produces controllers that shift part of the spectrum of the distributed parameter systems to the desired direction. The second method is called the sub-optimal finite-dimensional observer-based boundary controller design. This method produces finite-dimensional controllers based on the finite-dimensional linear quadratic optimal control theory. Although the finite-dimensional controllers are only sub-optimal for the distributed parameter systems, an estimation for the performance degradation from that of the ideal case is derived for the comparison purpose.