Efficiency and Accuracy of Semi-Discretization Schemes for Time Delayed Feedback Control Systems

2003 ◽  
Author(s):  
Ozer Elbeyli ◽  
J. Q. Sun
Keyword(s):  
Feedback Control ◽  
Order Approximation ◽  
Control Design ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Approximation Schemes ◽  
Zeroth Order ◽  
First Order ◽  
Periodic Linear ◽  
First Order Approximation

Semi-discretization is an effective method for analysis and control design of time-invariant as well as periodic linear systems with time delay. This paper briefly describes various approximation schemes in conjunction to the semi-discretization method. Comparison measures making use of the stability bounds of control gains and the controlled response of the system are presented. The accuracy and efficiency of the method with the zeroth order, improved zeroth order and first order approximations are compared through numerical simulations. Another first order approximation of the system with multiple time delays under a non-delayed feedback leads to integro-differential equations where a simple approximation is utilized to generate discrete maps. It is found that the first order approximation provides substantial improvements in accuracy and efficiency for feedback control design of LTI and periodic systems.

Chaos Control of a Sprott Circuit Using Non-Linear Delayed Feedback Control Via Sliding Mode

2007 ◽  
Author(s):  
Hoda Sadeghian ◽  
Kaveh Merat ◽  
Hassan Salarieh ◽  
Aria Alasty
Keyword(s):  
Feedback Control ◽  
High Performance ◽  
Sliding Mode ◽  
Chaotic Behavior ◽  
Electrical Circuit ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Unstable Periodic Orbits ◽  
Parameter Uncertainties ◽  
First Order

In this paper a nonlinear delayed feedback control is proposed to control chaos in a nonlinear electrical circuit which is known as Sprott circuit. The chaotic behavior of the system is suppressed by stabilizing one of its first order Unstable Periodic Orbits (UPOs). Firstly, the system parameters assumed to be known, and a nonlinear delayed feedback control is designed to stabilize the UPO of the system. Then the sliding mode scheme of the proposed controller is presented in presence of model parameter uncertainties. The effectiveness of the presented methods is numerically investigated by stabilizing the unstable first order periodic orbit and is compared with a typical linear delayed feedback control. Simulation results show the high performance of the methods for chaos elimination in Sprott circuit.

Improved first-order approximation of eigenvalues and eigenvectors

AIAA Journal ◽  
1998 ◽  
Vol 36 ◽  
pp. 1721-1727
Author(s):  
Prasanth B. Nair ◽  
Andrew J. Keane ◽  
Robin S. Langley
Keyword(s):  
Order Approximation ◽  
Eigenvalues And Eigenvectors ◽  
First Order ◽  
First Order Approximation

Analytical solution for unsteady flow behind ionizing shock wave in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field

2021 ◽  
Vol 76 (3) ◽  
pp. 265-283
Author(s):  
G. Nath
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Analytical Solution ◽  
Axial Magnetic Field ◽  
Order Approximation ◽  
Ideal Gas ◽  
Field Region ◽  
First Order ◽  
First Order Approximation ◽  
Flow Variables

Abstract The approximate analytical solution for the propagation of gas ionizing cylindrical blast (shock) wave in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field is investigated. The axial and azimuthal components of fluid velocity are taken into consideration and these flow variables, magnetic field in the ambient medium are assumed to be varying according to the power laws with distance from the axis of symmetry. The shock is supposed to be strong one for the ratio C 0 V s 2 ${\left(\frac{{C}_{0}}{{V}_{s}}\right)}^{2}$ to be a negligible small quantity, where C 0 is the sound velocity in undisturbed fluid and V S is the shock velocity. In the undisturbed medium the density is assumed to be constant to obtain the similarity solution. The flow variables in power series of C 0 V s 2 ${\left(\frac{{C}_{0}}{{V}_{s}}\right)}^{2}$ are expanded to obtain the approximate analytical solutions. The first order and second order approximations to the solutions are discussed with the help of power series expansion. For the first order approximation the analytical solutions are derived. In the flow-field region behind the blast wave the distribution of the flow variables in the case of first order approximation is shown in graphs. It is observed that in the flow field region the quantity J 0 increases with an increase in the value of gas non-idealness parameter or Alfven-Mach number or rotational parameter. Hence, the non-idealness of the gas and the presence of rotation or magnetic field have decaying effect on shock wave.

FIRST-ORDER APPROXIMATION OF THE NUMBER-PROJECTED SO(2N) TAMM-DANCOFF EQUATION AND ITS REDUCTION BY THE SCHUR FUNCTION

1999 ◽  
Vol 08 (05) ◽  
pp. 461-483
Author(s):  
SEIYA NISHIYAMA
Keyword(s):  
Wave Function ◽  
Order Approximation ◽  
Approximate Equation ◽  
Variation Principle ◽  
Schur Function ◽  
Soliton Theory ◽  
First Order ◽  
Fermion Systems ◽  
Group Manifold ◽  
First Order Approximation

First-order approximation of the number-projected (NP) SO(2N) Tamm-Dancoff (TD) equation is developed to describe ground and excited states of superconducting fermion systems. We start from an NP Hartree-Bogoliubov (HB) wave function. The NP SO(2N) TD expansion is generated by quasi-particle pair excitations from the degenerate geminals in the number-projected HB wave function. The Schrödinger equation is cast into the NP SO(2N) TD equation by the variation principle. We approximate it up to first order. This approximate equation is reduced to a simpler form by the Schur function of group characters which has a close connection with the soliton theory on the group manifold.

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