scholarly journals The Linear Quadratic Regulator Problem for a Class of Controlled Systems Modeled by Singularly Perturbed Itô Differential Equations

2012 ◽  
Vol 50 (1) ◽  
pp. 448-470 ◽  
Author(s):  
Vasile Dragan ◽  
Hiroaki Mukaidani ◽  
Peng Shi
Keyword(s):  
Differential Equations ◽  
Linear Quadratic Regulator ◽  
Singularly Perturbed ◽  
Linear Quadratic ◽  
Regulator Problem ◽  
Controlled Systems

Linear quadratic regulator problem governed by granular neutrosophic fractional differential equations

2020 ◽  
Vol 97 ◽  
pp. 296-316 ◽  
Author(s):  
Nguyen Thi Kim Son ◽  
Nguyen Phuong Dong ◽  
Hoang Viet Long ◽  
Le Hoang Son ◽  
Alireza Khastan
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Regulator Problem ◽  
Fractional Differential

Control of a thermoelastic beam using heat actuation

2016 ◽  
Vol 23 (20) ◽  
pp. 3309-3326 ◽  
Author(s):  
Ilhan Tuzcu ◽  
Joshua K Moua ◽  
Joe G Olivares
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Rectangular Cross Section ◽  
Linear Quadratic Regulator ◽  
Elastic Displacement ◽  
Thermoelastic Damping ◽  
Linear Quadratic ◽  
Partial Differential ◽  
Control Effort ◽  
Thermoelastic Beam

This paper explores the idea of using heat as an actuator to simultaneously control vibration and temperature of a thermoelastic beam. We first model the beam as a slender, uniform cantilever beam of rectangular cross-section subject to heat through heat patches on the lower and upper surfaces at some discrete spanwise locations. The governing equations of the model are two coupled partial differential equations: one governing the elastic bending displacement and one governing the two-dimensional heat conduction of the beam. Through a discretization, the partial differential equations are replaced by a set of ordinary differential equations in a compact state-space form. We show that the coupling is actually between elastic displacement and those components of temperature contributing to the thickness-wise gradient at the midplane. The linear quadratic regulator in conjunction with the Kalman–Bucy filter is used for the control design to simultaneously damp out the displacement and the gradient. In a numerical example, we show the presence of thermoelastic damping due to the coupling. We also show that the displacement and gradient can simultaneously be controlled by using displacement measurements only, and that for less control effort it is also necessary to include some temperature measurements in the feedback.

scholarly journals Singularly Perturbed Modeling and LQR Controller Design for a Fuel Cell System

Energies ◽  
2020 ◽  
Vol 13 (11) ◽  
pp. 2735
Author(s):  
Kliti Kodra ◽  
Ningfan Zhong
Keyword(s):  
Time Scales ◽  
Gas Flow ◽  
Proton Exchange Membrane ◽  
Controller Design ◽  
Linear Quadratic Regulator ◽  
Cell System ◽  
Proton Exchange ◽  
Singularly Perturbed ◽  
Singular Perturbation Theory ◽  
Linear Quadratic

Modeling and control of proton-exchange membrane fuel cells (PEMFC) has become a very popular research topic lately due to the increasing use of renewable energy. Despite this fact, most of the work in the current literature only studies standard dynamical models without taking into consideration possible parasitics such as small gas flow perturbations that could be available in the system. This paper addresses this issue by elaborating on time-scale modeling of an augmented eighteenth-order PEMFC-reformer system via singular perturbation theory. The latter captures time scales that arise in the model due to the presence of small perturbations. Specifically, a novel and efficient algorithm that helps identify the presence of different time-scales is developed. In addition, the method converts an implicit singularly perturbed model into an explicit equivalent where the time-scales are evident. Using this algorithm, a complete singularly perturbed dynamic model of the augmented eighteenth-order PEMFC-reformer system is obtained. Modeling of the PEMFC-reformer system is followed by linear quadratic regulator (LQR) design for the individual time-scales present in the system.

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