scholarly journals Linear feedback stabilization of point-vortex equilibria near a Kasper wing

2017 ◽  
Vol 827 ◽  
pp. 121-154 ◽  
Author(s):  
R. Nelson ◽  
B. Protas ◽  
T. Sakajo
Keyword(s):  
Feedback Control ◽  
Point Vortex ◽  
Basins Of Attraction ◽  
Feedback Stabilization ◽  
Linear Feedback ◽  
Linear Quadratic ◽  
Linear Control Theory ◽  
Single Plate ◽  
Point Vortex Equilibria ◽  
Almost All

This paper concerns feedback stabilization of point-vortex equilibria above an inclined thin plate and a three-plate configuration known as the Kasper wing in the presence of an oncoming uniform flow. The flow is assumed to be potential and is modelled by the two-dimensional incompressible Euler equations. Actuation has the form of blowing and suction localized on the main plate and is represented in terms of a sink–source singularity, whereas measurement of pressure across the plate serves as system output. We focus on point-vortex equilibria forming a one-parameter family with locus approaching the trailing edge of the main plate and show that these equilibria are either unstable or neutrally stable. Using methods of linear control theory we find that the system dynamics linearized around these equilibria is both controllable and observable for almost all actuator and sensor locations. The design of the feedback control is based on the linear–quadratic–Gaussian (LQG) compensator. Computational results demonstrate the effectiveness of this control and the key finding of this study is that Kasper wing configurations are in general not only more controllable than their single-plate counterparts, but also exhibit larger basins of attraction under LQG feedback control. The feedback control is then applied to systems with additional perturbations added to the flow in the form of random fluctuations of the angle of attack and a vorticity shedding mechanism. Another important observation is that, in the presence of these additional perturbations, the control remains robust, provided the system does not deviate too far from its original state. Furthermore, except in a few isolated cases, introducing a vorticity-shedding mechanism enhanced the effectiveness of the control. Physical interpretation is provided for the results of the controllability and observability analysis as well as the response of the feedback control to different perturbations.

scholarly journals Force-enhancing vortex equilibria for two parallel plates in uniform flow

2012 ◽  
Vol 468 (2140) ◽  
pp. 1175-1195 ◽  
Author(s):  
Takashi Sakajo
Keyword(s):  
Stationary Point ◽  
Design Problem ◽  
Flow Problem ◽  
Point Vortex ◽  
Uniform Flow ◽  
Point Vortices ◽  
Multiply Connected Domains ◽  
Parallel Plates ◽  
Single Plate ◽  
Point Vortex Equilibria

A two-dimensional potential flow in an unbounded domain with two parallel plates is considered. We examine whether two free point vortices can be trapped near the two plates in the presence of a uniform flow and observe whether these stationary point vortices enhance the force on the plates. The present study is an extension of previously published work in which a free point vortex over a single plate is investigated. The flow problem is motivated by an airfoil design problem for the double wings. Moreover, it also contributes to a design problem for an efficient wind turbine with vertical blades. In order to obtain the point-vortex equilibria numerically, we make use of a linear algebraic algorithm combined with a stochastic process, called the Brownian ratchet scheme. The ratchet scheme allows us to capture a family of stationary point vortices in multiply connected domains with ease. As a result, we find that stationary point vortices exist around the two plates and they enhance the downward force and the counter-clockwise rotational force acting on the two plates.

Feedback control of three-dimensional optimal disturbances using reduced-order models

2011 ◽  
Vol 677 ◽  
pp. 63-102 ◽  
Author(s):  
ONOFRIO SEMERARO ◽  
SHERVIN BAGHERI ◽  
LUCA BRANDT ◽  
DAN S. HENNINGSON
Keyword(s):  
Boundary Layer ◽  
Feedback Control ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Spanwise Direction ◽  
Linear Quadratic ◽  
Sensors And Actuators ◽  
Reduced Order ◽  
Linear Control Theory ◽  
Optimal Disturbances

The attenuation of three-dimensional wavepackets of streaks and Tollmien–Schlichting (TS) waves in a transitional boundary layer using feedback control is investigated numerically. Arrays of localized sensors and actuators (about 10–20) with compact spatial support are distributed near the rigid wall equidistantly along the spanwise direction and connected to a low-dimensional (r = 60) linear quadratic Gaussian controller. The control objective is to minimize the disturbance energy in a domain spanned by a number of proper orthogonal decomposition modes. The feedback controller is based on a reduced-order model of the linearized Navier–Stokes equations including the inputs and outputs, computed using a snapshot-based balanced truncation method. To account for the different temporal and spatial behaviour of the two main instabilities of boundary-layer flows, we design two controllers. We demonstrate that the two controllers reduce the energy growth of both TS wavepackets and streak packets substantially and efficiently, using relatively few sensors and actuators. The robustness of the controller is investigated by varying the number of actuators and sensors, the Reynolds number and the pressure gradient. This work constitutes the first experimentally feasible simulation-based control design using localized sensing and acting devices in conjunction with linear control theory in a three-dimensional setting.

CONTINUOUS FEEDBACK CONTROL STRATEGY WITH MAXIMAL CAPTURE ZONE IN A CLASS OF PURSUIT GAMES

2005 ◽  
Vol 07 (01) ◽  
pp. 1-24 ◽  
Author(s):  
VLADIMIR TURETSKY ◽  
VALERY Y. GLIZER
Keyword(s):  
Feedback Control ◽  
Differential Game ◽  
Linear Feedback ◽  
Capture Zone ◽  
State Variables ◽  
Linear Quadratic ◽  
Kinematical Model ◽  
Continuous Feedback ◽  
Feedback Control Strategy ◽  
Noisy Measurements

An interception problem of a highly maneuverable target is considered using a linearized kinematical model with first order acceleration dynamics of the interceptor and the target. The problem is interpreted as a differential game of pursuit. An admissible pursuer (interceptor) feedback strategy, continuous with respect to the state variables and having a maximal capture zone, is constructed. This strategy is the saturated version of a linear feedback control, obtained from the solution of an auxiliary linear-quadratic differential game with cheap controls. This strategy is evaluated by Monte-Carlo simulation of the interception with noisy measurements.

Optimization approach to the constrained regulation problem for linear continuous-time fractional-order systems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Xindong Si ◽  
Hongli Yang
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
State Feedback Control ◽  
Invariant Sets ◽  
Linear Feedback ◽  
Control Law ◽  
Optimization Approach ◽  
Fractional Order Systems ◽  
Linear Feedback Control ◽  
Computational Point

AbstractThis paper deals with the Constrained Regulation Problem (CRP) for linear continuous-times fractional-order systems. The aim is to find the existence conditions of linear feedback control law for CRP of fractional-order systems and to provide numerical solving method by means of positively invariant sets. Under two different types of the initial state constraints, the algebraic condition guaranteeing the existence of linear feedback control law for CRP is obtained. Necessary and sufficient conditions for the polyhedral set to be a positive invariant set of linear fractional-order systems are presented, an optimization model and corresponding algorithm for solving linear state feedback control law are proposed based on the positive invariance of polyhedral sets. The proposed model and algorithm transform the fractional-order CRP problem into a linear programming problem which can readily solved from the computational point of view. Numerical examples illustrate the proposed results and show the effectiveness of our approach.

FREQUENCY-DOMAIN CRITERIA FOR GLOBAL SYNCHRONIZATION OF MULTISCROLL CHAOTIC SYSTEMS UNDER LINEAR FEEDBACK CONTROL

2010 ◽  
Vol 20 (07) ◽  
pp. 2165-2177 ◽  
Author(s):  
XIAOFENG WU ◽  
ZHIFANG GUI ◽  
GUANRONG CHEN
Keyword(s):  
Feedback Control ◽  
Frequency Domain ◽  
Chaotic Systems ◽  
Linear Feedback ◽  
Error Feedback ◽  
Linear Feedback Control ◽  
Global Synchronization ◽  
General Mathematical Model ◽  
Linear State ◽  
Absolute Stability Theory

This paper provides a unified approach for achieving and analyzing global synchronization of a class of master-slave coupled multiscroll chaotic systems under linear state-error feedback control. A general mathematical model for such a class of multiscroll chaotic systems is first established. Based on some special properties of such systems, two less-conservative frequency-domain criteria for the desirable global synchronization are rigorously proven by means of the absolute stability theory. The analysis is then applied to two master-slave coupled modified Chua's circuits, obtaining the corresponding simple and precise algebraic criteria for global synchronization, which are finally verified by numerical simulations.

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