Effective diffusion in time‐periodic linear planar flow

1993 ◽  
Vol 5 (10) ◽  
pp. 2563-2566 ◽  
Author(s):  
Alexandra Indeikina ◽  
Hsueh‐Chia Chang
Keyword(s):  
Effective Diffusion ◽  
Planar Flow ◽  
Periodic Linear ◽  
Time Periodic

DISCRETE PROCEDURE OF OPTIMAL STABILIZATION FOR PERIODIC LINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS

2018 ◽  
pp. 891-906
Author(s):  
Roman Ivanovich Shevchenko ◽  
Yuri Filippovich Dolgii
Keyword(s):  
Differential Equations ◽  
Discrete Time ◽  
Periodic Problem ◽  
Optimal Stabilization ◽  
Systems Of Differential Equations ◽  
Special Procedure ◽  
Periodic Linear ◽  
System States ◽  
Linear Periodic Systems ◽  
Time Periodic

We propose procedure to solve the optimal stabilization problem for linear periodic systems of differential equations. Stabilizing controls, formed as a feedback, are defined by the system states at the fixed instants of time. Equivalent discrete-time linear periodic problem of optimal stabilization is considered. We propose a special procedure for the solution of discrete periodic Riccati equation. We investigate the relation between continuous-time and discrete-time periodic optimal stabilization problems. The proposed method is used for stabilization of mechanical systems.

Effects of time-periodic linear coupling on two-component Bose–Einstein condensates in two dimensions

2008 ◽  
Vol 372 (10) ◽  
pp. 1631-1638 ◽  
Author(s):  
H. Susanto ◽  
P.G. Kevrekidis ◽  
B.A. Malomed ◽  
F.Kh. Abdullaev
Keyword(s):  
Two Dimensions ◽  
Linear Coupling ◽  
Periodic Linear ◽  
Two Component ◽  
Bose Einstein ◽  
Time Periodic

Reduced Order Controller Design for Nonlinear Systems With Periodic Coefficients

2009 ◽  
Author(s):  
Amit P. Gabale ◽  
Subhash C. Sinha
Keyword(s):  
Controller Design ◽  
Linear Part ◽  
Eigenvalue Decomposition ◽  
Order System ◽  
Time Varying ◽  
Periodic Coefficients ◽  
Reduced Order ◽  
Periodic Linear ◽  
Time Invariant ◽  
Time Periodic

This study provides a methodology for reduced order controller design for nonlinear dynamic systems with time-periodic coefficients. System equations are represented by quasi-linear differential equations in state space, containing a time-periodic linear part and nonlinear monomials of states with periodic coefficients. The Lyapunov-Floquet (L-F) transformation is used to transform the time-varying linear part of the system into a time-invariant form. Eigenvalue decomposition of the time-invariant linear part can then be used to identify the dominant/ non-dominant dynamics of the system. The non-dominant states of the system are expressed as a nonlinear, time-periodic, manifold relationship in terms of the dominant states. As a result, the original large system can be expressed as a lower order system represented only by the dominant states. A reducibility condition is derived to provide conditions under which a nonlinear order reduction is possible. Then a proper coordinate transformation and state feedback can be found under which the reduced order system is transformed into a linear, time-periodic, closed-loop system. This permits the design of a time-varying feedback controller in linear space to guarantee the stability of the system. The proposed methodology is illustrated by designing a reduced order controller for a 4-dof, inverted pendulum subjected to a periodic follower force. Treatment for the time-invariant case is also included as a subset of the problem.

Ornithopter Trajectory Generation With Stabilization

2008 ◽  
Author(s):  
John M. Dietl ◽  
Ephrahim Garcia
Keyword(s):  
Feedback Control ◽  
Discrete Time ◽  
Trajectory Generation ◽  
Flight Dynamics ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Flight Stabilization ◽  
Rate Feedback ◽  
Periodic Linear ◽  
Time Periodic

Ornithopter flight dynamics and a method for developing flight trajectories are described. These are used to study the unstable modes in hovering ornithopter flight. Stabilization is accomplished through three strategies: pitch-rate feedback control, linear quadratic regulator, and discrete-time periodic linear quadratic regulator. The discrete time controller is the only controller tested that was capable of stabilizing position of the vehicle in hover.

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