Adaptive controller for systems with internal point delays providing asymptotic stability

1994 ◽  
Vol 25 (2) ◽  
pp. 269-290 ◽  
Author(s):  
M. DE LA SEN
Keyword(s):  
Asymptotic Stability ◽  
Adaptive Controller ◽  
Internal Point ◽  
Point Delays

scholarly journals On the Global Asymptotic Stability of Switched Linear Time-Varying Systems with Constant Point Delays

2008 ◽  
Vol 2008 ◽  
pp. 1-31 ◽  
Author(s):  
M. de la Sen ◽  
A. Ibeas
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Linear Time ◽  
Time Varying ◽  
System Matrix ◽  
Almost Everywhere ◽  
Time Varying Systems ◽  
The Matrix ◽  
Delayed System ◽  
Point Delays

This paper investigates the asymptotic stability of switched linear time-varying systems with constant point delays under not very stringent conditions on the matrix functions of parameters. Such conditions are their boundedness, the existence of bounded time derivatives almost everywhere, and small amplitudes of the appearing Dirac impulses where such derivatives do not exist. It is also assumed that the system matrix for zero delay is stable with some prescribed stability abscissa for all time in order to obtain sufficiency-type conditions of asymptotic stability dependent on the delay sizes. Alternatively, it is assumed that the auxiliary system matrix defined for all the delayed system matrices being zero is stable with prescribed stability abscissa for all time to obtain results for global asymptotic stability independent of the delays. A particular subset of the switching instants is the so-called set of reset instants where switching leads to the parameterization to reset to a value within a prescribed set.

scholarly journals Stability and assignment of spectrum in systems with discrete time lags

2006 ◽  
Vol 2006 ◽  
pp. 1-8 ◽  
Author(s):  
M. De la Sen
Keyword(s):  
Asymptotic Stability ◽  
Closed Loop ◽  
Pole Placement ◽  
Time Lags ◽  
Matrix Inequalities ◽  
Delayed Systems ◽  
Spectrum Assignment ◽  
Discrete Delays ◽  
Identical Number ◽  
Point Delays

The asymptotic stability with a prescribed degree of time delayed systems subject to multiple bounded discrete delays has received important attention in the last years. It is basically proved that theα-stability locally in the delays (i.e., all the eigenvalues have prefixed strictly negative real parts located inRe⁡s≤−α<0) may be tested for a set of admissible delays including possible zero delays either through a set of Lyapunov's matrix inequalities or, equivalently, by checking that an identical number of matrices related to the delayed dynamics are all stability matrices. The result may be easily extended to check theε-asymptotic stability independent of the delays, that is, for all the delays having any values, the eigenvalues are stable and located inRe⁡s≤ε→0−. The above referred number of stable matrices to be tested is2rfor a set of distinctrpoint delays and includes all possible cases of alternate signs for summations for all the matrices of delayed dynamics. The manuscript is completed with a study for prescribed closed-loop spectrum assignment (or “pole placement”) under output feedback.

Implementation of Minimal Control Synthesis on a Servo-Hydraulic Testing Machine

1992 ◽  
Vol 206 (3) ◽  
pp. 189-194 ◽  
Author(s):  
D P Stoten
Keyword(s):  
Asymptotic Stability ◽  
Prior Knowledge ◽  
Closed Loop ◽  
Testing Machine ◽  
Adaptive Controller ◽  
Hydraulic Testing ◽  
Technical Note ◽  
Control Synthesis ◽  
Dynamic Parameters ◽  
Closed Loop System

The minimal control synthesis (MCS) algorithm is an adaptive controller that requires no prior knowledge of plant dynamic parameters, and yet is guaranteed to provide global asymptotic stability of the closed-loop system. The algorithm has been implemented on a variety of plant, ranging from laboratory-based rigs to industrial machines. The purpose of this technical note is to present the results of the first known implementation of the algorithm on a servo-hydraulically actuated machine. The results of the MCS implementation will be seen to compare very favourably with those of a conventional (P + I) implementation.

scholarly journals WIND DISTURBANCE CANCELLATION FOR SMALLER ALT-AZIMUTH TELESCOPES

2021 ◽  
Vol 53 ◽  
pp. 29-34
Author(s):  
A. C. Unal ◽  
G. Kararsiz ◽  
C. T. Yilmaz ◽  
O. Keskin ◽  
C. Yesilyaprak
Keyword(s):  
Mathematical Model ◽  
Asymptotic Stability ◽  
Numerical Study ◽  
Adaptive Controller ◽  
Wind Gust ◽  
Wind Disturbance ◽  
Lyapunov Approach ◽  
Unknown Amplitude ◽  
Disturbance Cancellation ◽  
The Mathematical Model

This study focuses on eliminating unknown amplitude wind disturbance for 2-DOF alt-azimuth configuration small telescopes. An adaptive controller is designed to overcome wind disturbance as a set and forget system. The mathematical model is derived based on 2-DOF alt-azimuth configuration. The wind disturbance is modeled as a sum of sinusoidal with unknown amplitude, frequency and phase by using Wind-Gust model. The controller aims to cancel the effect of the disturbance on the altitude and azimuth angles of the telescope while positioning or staying static on a dedicated configuration. The asymptotic stability is proven with the Lyapunov approach. The numerical study is illustrated to success of the proposed controller.

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