Reduced-Order Model-Based Feedback Control of Flow Over an Obstacle Using Center Manifold Methods

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Coşku Kasnakoğlu ◽  
R. Chris Camphouse ◽  
Andrea Serrani
Keyword(s):  
Boundary Control ◽  
Center Manifold ◽  
Controller Design ◽  
Tracking Error ◽  
Reduced Order Model ◽  
Order System ◽  
Linear Quadratic ◽  
Order Model ◽  
Control Effort ◽  
Reduced Order

In this paper, we consider a boundary control problem governed by the two-dimensional Burgers’ equation for a configuration describing convective flow over an obstacle. Flows over obstacles are important as they arise in many practical applications. Burgers’ equations are also significant as they represent a simpler form of the more general Navier–Stokes momentum equation describing fluid flow. The aim of the work is to develop a reduced-order boundary control-oriented model for the system with subsequent nonlinear control law design. The control objective is to drive the full order system to a desired 2D profile. Reduced-order modeling involves the application of an L2 optimization based actuation mode expansion technique for input separation, demonstrating how one can obtain a reduced-order Galerkin model in which the control inputs appear as explicit terms. Controller design is based on averaging and center manifold techniques and is validated with full order numerical simulation. Closed-loop results are compared to a standard linear quadratic regulator design based on a linearization of the reduced-order model. The averaging∕center manifold based controller design provides smoother response with less control effort and smaller tracking error.

Control of Asymmetric Systems Using Complex Modes

1991 ◽  
Author(s):  
G. W. Fan ◽  
H. D. Nelson
Keyword(s):  
Normal Modes ◽  
Original System ◽  
High Order ◽  
Reduced Order Model ◽  
Order System ◽  
Matrix Transformations ◽  
Linear Quadratic ◽  
Order Model ◽  
Reduced Order ◽  
Complex Modes

Abstract The complex modal approach is introduced for the optimal vibration control (Linear Quadratic Regulator) of high-order nonsymmetric discrete systems. An LQ regulator is designed based on a reduced-order model obtained by neglecting high-frequency complex modes of the original system. The matrix transformations between physical coordinates and complex coordinates are derived. A 52 degree-of-freedom finite element based rotordynamic system is used for illustration. Simulation results show that an LQ regulator based on a reduced-order system obtained by using normal modes of a high-order system with asymmetric models can possibly destabilize the original system i.e., the spill-over problem (Ulsoy, 1984), however, this problem might be avoided by applying complex modes which provides a more accurate reduced-order model than obtained by normal modes. Comparison of the reduced-order models using normal modes and complex modes is presented. Frequency, time transient and steady state responses of the controlled and uncontrolled systems are also shown.

scholarly journals Optimal Reduced Order Model of Single- Shaft Heavy Duty Gas Turbine Power Plants

2020 ◽  
Vol 5 (9) ◽  
pp. 1090-1098
Author(s):  
M. Ramasubramanian ◽  
M. Thirumarimurugan ◽  
P. Ananthi
Keyword(s):  
Gas Turbine ◽  
Optimization Technique ◽  
Higher Order ◽  
Reduced Order Model ◽  
Order System ◽  
Heavy Duty ◽  
Order Model ◽  
Reduced Order ◽  
Particle Swarm Optimization Technique ◽  
Heavy Duty Gas Turbine

Design of controller and analyzing the response of higher order system in real time environment would be very complex and expensive. Therefore, an attempt has been made in this paper to obtain the reduced order model of single-shaft Heavy duty gas turbine plants ranging from 18.2 to 106.7 MW by using various model order reduction techniques. The step response of Heavy duty gas turbine model using the reduced order models are compared with that of the original MATLAB/ Simulink model. Various time domain specifications and performance index criteria have been considered for analyzing the responses. The simulation results show that the response obtained by Routh approximation-Pade approximation technique based reduced order model mimics the original, higher order Heavy Duty gas turbine response. It is also proposed in this paper to improve the response by optimizing the co-efficients of reduced order model using Particle Swarm Optimization technique. On comparing the simulation results, Particle Swarm Optimization technique based reduced order model yield better transient and steady state response as close to original higher order system and hence it is identified as an optimal reduced order model for all Heavy Duty gas turbine plants in grid connected operation

scholarly journals Higher Order Reduction of Uncertain Systems: Affine Arithmeti

2021 ◽  
Vol 08 (1&2) ◽  
pp. 1-4
Author(s):  
H Mallesam Dora ◽  
Keyword(s):  
Uncertain Systems ◽  
Order Reduction ◽  
Reduced Order Model ◽  
Order System ◽  
Effective Algorithm ◽  
Order Model ◽  
Reduced Order ◽  
Numerical Examples ◽  
Rigorous Study ◽  
Lower Order System

In this paper the Modified Routh Approximation (MRA) and Affine Arithmetic (AA) methods are investigates for obtaining the reduced order model (ROM) of SISO, discrete & MIMO uncertain systems into lower order system. Rigorous study and analysis of physical system direct to the outcome of systems with uncertainty instead of certain coefficients. Thus, systems having uncertain but bounded parameters known as uncertain systems are under consideration in this paper. An effective algorithm to determine the reduced order model is proposed here. This proposed methodology is verified using numerical examples available from the literature.

Experimental Study on Arrangements of Setting Points of an Actuator and Sensor for the Vibration Control of Flexible Structures

1994 ◽  
Vol 6 (4) ◽  
pp. 292-297
Author(s):  
Kazuto Seto ◽  
◽  
Katsuhiko Ezure ◽  
Keyword(s):  
Experimental Study ◽  
Vibration Control ◽  
Vibration Mode ◽  
Controller Design ◽  
Flexible Structures ◽  
Reduced Order Model ◽  
Displacement Sensor ◽  
Order Model ◽  
Reduced Order ◽  
Dynamic Absorber

This paper proposes an experimental study on the arrangements between the setting points of an actuator and sensor for the vibration control of a flexible structure, when a vibration controller is mounted at an arbitrary position on the structure. The important vibration mode of the structure to be controlled is its first mode, because it is excited most sensitively by strong winds. It is therefore necessary to make a reduced-order model represented by a one-degree-of-freedom system at an arbitrary location, in consideration of preventing spillover instability. In this paper, non-observability is used for making the reduced-order model, and the LQ control theory is used for controller design. For controlling vibration, a reduced-order model is constructed at the setting point of a hybrid dynamic absorber, and a displacement sensor is set at the vibration node of the second vibration mode. Then, the setting point of the sensor is changed to compare control effects by means of this model. It is demonstrated experimentally that a hybrid dynamic absorber, designed by this method, is capable of controlling vibration well without causing spillover instability. In addition, it is considered that the setting point of the sensor influences the robustness of the control system.

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