Stability analysis for a class of linear controllers under control constraints

1995 ◽  
Vol 5 (2) ◽  
pp. 191-203 ◽  
Author(s):  
R. M. Dolphus ◽  
W. E. Schmitendorf
Keyword(s):  
Stability Analysis ◽  
Control Constraints ◽  
Linear Controllers

Non-normality and its consequences in active control of thermoacoustic instabilities

2011 ◽  
Vol 670 ◽  
pp. 130-149 ◽  
Author(s):  
RAHUL KULKARNI ◽  
KOUSHIK BALASUBRAMANIAN ◽  
R. I. SUJITH
Keyword(s):  
Stability Analysis ◽  
Simple Model ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Nonlinear Effects ◽  
Transient Growth ◽  
Rijke Tube ◽  
Thermoacoustic Instabilities ◽  
Low Amplitude ◽  
Linear Controllers

Non-normality can cause transient growth of perturbations in thermoacoustic systems with stable eigenvalues. This can cause low-amplitude perturbations to grow to amplitudes high enough to make nonlinear effects significant, and the system can become nonlinearly unstable, even though it is stable under classical linear stability. In this paper, we have demonstrated that this feature can lead to the failure of the traditional controllers that were designed on the basis of classical linear stability analysis. We have also shown in a simple model that it is possible to prevent ‘nonlinear driving’ by controlling transient growth, using linear controllers. The analysis is performed in the context of a horizontal Rijke tube.

Finite element analysis of the constrained Dirichlet boundary control problem governed by the diffusion problem

2020 ◽  
Vol 26 ◽  
pp. 78
Author(s):  
Thirupathi Gudi ◽  
Ramesh Ch. Sau
Keyword(s):  
Finite Element ◽  
Control Problem ◽  
Dirichlet Boundary ◽  
A Priori ◽  
Diffusion Problem ◽  
Discrete Control ◽  
Optimal Order ◽  
Control Constraints ◽  
Element Analysis ◽  
Dirichlet Boundary Control

We study an energy space-based approach for the Dirichlet boundary optimal control problem governed by the Laplace equation with control constraints. The optimality system results in a simplified Signorini type problem for control which is coupled with boundary value problems for state and costate variables. We propose a finite element based numerical method using the linear Lagrange finite element spaces with discrete control constraints at the Lagrange nodes. The analysis is presented in a combination for both the gradient and the L2 cost functional. A priori error estimates of optimal order in the energy norm is derived up to the regularity of the solution for both the cases. Theoretical results are illustrated by some numerical experiments.

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