The H2 Control Problem: State-space and Transfer-function Solutions

2006 ◽  
Author(s):  
Vladimir Kucera
Keyword(s):  
Transfer Function ◽  
Control Problem ◽  
State Space ◽  
H2 Control

Transfer Function Analysis of Non-Uniformly Distributed Parameter Systems

1993 ◽  
Author(s):  
Bingen Yang ◽  
Houfei Fang
Keyword(s):  
Distributed Systems ◽  
Transfer Function ◽  
State Space ◽  
Fundamental Matrix ◽  
Function Analysis ◽  
Distributed Parameter Systems ◽  
System Response ◽  
Distributed Parameter ◽  
Transfer Function Analysis ◽  
Function Formulation

Abstract This paper studies a transfer function formulation for general one-dimensional, non-uniformly distributed systems subject to arbitrary boundary conditions and external disturbances. The purpose is to provide an useful alternative for modeling and analysis of distributed parameter systems. In the development, the system equations of the non-uniform system are cast into a state space form in the Laplace transform domain. The system response and distributed transfer functions are derived in term of the fundamental matrix of the state space equation. Two approximate methods for evaluating the fundamental matrix are proposed. With the transfer function formulation, various dynamics and control problems for the non-uniformly distributed system can be conveniently addressed. The transfer function analysis is also applied to constrained/combined non-uniformly distributed systems.

scholarly journals Dynamical modeling and optimal control of landfills

2016 ◽  
Vol 26 (05) ◽  
pp. 901-929 ◽  
Author(s):  
Alain Rapaport ◽  
Terence Bayen ◽  
Matthieu Sebbah ◽  
Andres Donoso-Bravo ◽  
Alfredo Torrico
Keyword(s):  
Optimal Control ◽  
Simple Model ◽  
Control Problem ◽  
State Space ◽  
Optimal Strategy ◽  
Dynamical Modeling ◽  
Minimal Time ◽  
Time Control ◽  
Switching Curve ◽  
Singular Arc

We propose a simple model of landfill and study a minimal time control problem where the re-circulation leachate is the manipulated variable. We propose a scheme to construct the optimal strategy by dividing the state space into three subsets [Formula: see text], [Formula: see text] and the complementary. On [Formula: see text] and [Formula: see text], the optimal control is constant until reaching target, while it can exhibit a singular arc outside these two subsets. Moreover, the singular arc could have a barrier. In this case, we prove the existence of a switching curve that passes through a point of prior saturation under the assumption that the set [Formula: see text] intersects the singular arc. Numerical computations allow then to determine the switching curve and depict the optimal synthesis.

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