Hinf Tracking for a Class of Second-Order Dynamical Systems

2011 ◽  
Vol 52-54 ◽  
pp. 589-594
Author(s):  
L. Huang ◽  
Bo You ◽  
W.L. Li
Keyword(s):  
Dynamical Systems ◽  
Upper Bound ◽  
Parametric Design ◽  
Reference Model ◽  
Tracking Error ◽  
Second Order ◽  
Controlled System ◽  
Controller Gain ◽  
Exogenous Disturbance ◽  
Sylvester Matrix Equations

The problem of tracking for second-order dynamical systems subject to disturbance input is considered by using a complete parametric design approach. The goal of this problem is to design a controller such that the output of the controlled system robustly asymptotically tracks the output of the reference model, and the transfer function from the exogenous disturbance to the tracking error meets a prescribed norm upper bound constraint. Based on the complete parametric solution to a class of generalized second-order Sylvester matrix equations, complete parameterizations for all the controller gain matrices are established in terms of two set of freedom parameters. Also, based on these parametric gain matrices, the prescribed norm upper bound constraint is transformed into an equivalent constraint condition which restricts the choice of the freedom parameters. An example is utilized to show the effect of the proposed approach.

Integrable two-dimensional dynamical systems and the characteristic Lie algebras

2007 ◽  
Vol 5 ◽  
pp. 195-200
Author(s):  
A.V. Zhiber ◽  
O.S. Kostrigina
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Second Order ◽  
System Of Equations ◽  
Two Dimensional ◽  
Finite Dimensional ◽  
Dimensional Dynamical System

In the paper it is shown that the two-dimensional dynamical system of equations is Darboux integrable if and only if its characteristic Lie algebra is finite-dimensional. The class of systems having a full set of fist and second order integrals is described.

scholarly journals A Robust Observer—Based Adaptive Control of Second—Order Systems with Input Saturation via Dead-Zone Lyapunov Functions

Computation ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 82
Author(s):  
Alejandro Rincón ◽  
Gloria M. Restrepo ◽  
Fredy E. Hoyos
Keyword(s):  
Lyapunov Functions ◽  
Dead Zone ◽  
Tracking Error ◽  
Input Saturation ◽  
Chemical Reactor ◽  
Second Order ◽  
Control Law ◽  
Compact Set ◽  
State Variables ◽  
Robust Observer

In this study, a novel robust observer-based adaptive controller was formulated for systems represented by second-order input–output dynamics with unknown second state, and it was applied to concentration tracking in a chemical reactor. By using dead-zone Lyapunov functions and adaptive backstepping method, an improved control law was derived, exhibiting faster response to changes in the output tracking error while avoiding input chattering and providing robustness to uncertain model terms. Moreover, a state observer was formulated for estimating the unknown state. The main contributions with respect to closely related designs are (i) the control law, the update law and the observer equations involve no discontinuous signals; (ii) it is guaranteed that the developed controller leads to the convergence of the tracking error to a compact set whose width is user-defined, and it does not depend on upper bounds of model terms, state variables or disturbances; and (iii) the control law exhibits a fast response to changes in the tracking error, whereas the control effort can be reduced through the controller parameters. Finally, the effectiveness of the developed controller is illustrated by the simulation of concentration tracking in a stirred chemical reactor.

A Class of Bounded and Partially Bounded Nonlinear Controllers for First and Second Order Dynamical Systems

2021 ◽  
pp. 1-1
Author(s):  
Eddie Clemente ◽  
M. C. Rodriguez-Linan ◽  
Marlen Meza-Sanchez ◽  
Luis Monay-Arredondo ◽  
Leonardo Herrera
Keyword(s):  
Dynamical Systems ◽  
Second Order ◽  
Nonlinear Controllers

scholarly journals Second-order dynamical systems associated to variational inequalities

2016 ◽  
Vol 96 (5) ◽  
pp. 799-809 ◽  
Author(s):  
Radu Ioan Boţ ◽  
Ernö Robert Csetnek
Keyword(s):  
Dynamical Systems ◽  
Variational Inequalities ◽  
Second Order

The Simulation Analysis of Semi-Active Suspension System in Vehicle Based on Sliding Mode Control with Varying Structure

2011 ◽  
Vol 216 ◽  
pp. 96-100
Author(s):  
Jing Jun Zhang ◽  
Wei Sha Han ◽  
Li Ya Cao ◽  
Rui Zhen Gao
Keyword(s):  
Control Method ◽  
Simulation Analysis ◽  
Reference Model ◽  
Sliding Mode ◽  
Tracking Error ◽  
Active Suspension ◽  
Suspension System ◽  
Sliding Mode Controller ◽  
Error Dynamics ◽  
Dynamic Quality

A sliding mode controller for semi-active suspension system of a quarter car is designed with sliding model varying structure control method. This controller chooses Skyhook as a reference model, and to force the tracking error dynamics between the reference model and the plant in an asymptotically stable sliding mode. An equal near rate is used to improve the dynamic quality of sliding mode motion. Simulation result shows that the stability of performance of the sliding-mode controller can effectively improve the driving smoothness and safety.

scholarly journals The Second Order Upper Bound for the Ground Energy of a Bose Gas

2009 ◽  
Vol 136 (3) ◽  
pp. 453-503 ◽  
Author(s):  
Horng-Tzer Yau ◽  
Jun Yin
Keyword(s):  
Upper Bound ◽  
Bose Gas ◽  
Second Order ◽  
Ground Energy

A case study in bifurcation theory

2017 ◽  
Vol 28 (08) ◽  
pp. 1750104 ◽  
Author(s):  
Youssef Khmou
Keyword(s):  
Dynamical Systems ◽  
Bifurcation Theory ◽  
Chaotic Behavior ◽  
Numerical Study ◽  
Logistic Map ◽  
Logistic Function ◽  
Second Order ◽  
Short Paper ◽  
Chaotic Region

This short paper is focused on the bifurcation theory found in map functions called evolution functions that are used in dynamical systems. The most well-known example of discrete iterative function is the logistic map that puts into evidence bifurcation and chaotic behavior of the topology of the logistic function. We propose a new iterative function based on Lorentizan function and its generalized versions, based on numerical study, it is found that the bifurcation of the Lorentzian function is of second-order where it is characterized by the absence of chaotic region.

Sign in / Sign up

Export Citation Format

Share Document