CONTROL OF THE DIFFERENTIALLY FLAT LORENZ SYSTEM

2001 ◽  
Vol 11 (07) ◽  
pp. 1989-1996 ◽  
Author(s):  
JIN MAN JOO ◽  
JIN BAE PARK
Keyword(s):  
Equilibrium State ◽  
Lorenz System ◽  
Degree Of Freedom ◽  
Design Approach ◽  
State Trajectory ◽  
System A ◽  
Full State ◽  
Tracking Controller ◽  
The Lorenz System ◽  
Two Degree Of Freedom

This paper presents an approach for the control of the Lorenz system. We first show that the controlled Lorenz system is differentially flat and then compute the flat output of the Lorenz system. A two degree of freedom design approach is proposed such that the generation of full state feasible trajectory incorporates with the design of a tracking controller via the flat output. The stabilization of an equilibrium state and the tracking of a feasible state trajectory are illustrated.

Two-degree-of-freedom Controller Design for Uncertain Processes Using Input/output Linearization Control Technique

2011 ◽  
Vol 11 (1) ◽  
pp. 16 ◽  
Author(s):  
Pisit Sukkarnkha ◽  
Chanin Panjapornpon
Keyword(s):  
Disturbance Rejection ◽  
Control Structure ◽  
Control Method ◽  
Random Noise ◽  
Degree Of Freedom ◽  
Control Technique ◽  
Input Output ◽  
Tracking Controller ◽  
Two Degree Of Freedom ◽  
Input Output Linearization

In this work, a new control method for uncertain processes is developed based on two-degree-of-freedom control structure. The setpoint tracking controller designed by input/output linearization technique is used to regulate the disturbance-free output and the disturbance rejection controller designed is designed by high-gain technique. The advantage of two-degree-of-freedom control structure is that setpoint tracking and load disturbance rejection controllers can be designed separately. Open-loop observer is applied to provide disturbance-free response for setpoint tracking controller. The process/disturbance-free model mismatches are fed to the disturbance rejection controller for reducing effect of disturbance. To evaluate the control performance, the proposed control method is applied through the example of a continuous stirred tank reactor with unmeasured input disturbances and random noise kinetic parametric uncertainties. The simulation results show that both types of disturbances can be effectively compensated by the proposed control method.

Multistability in the Lorenz System: A Broken Butterfly

2014 ◽  
Vol 24 (10) ◽  
pp. 1450131 ◽  
Author(s):  
Chunbiao Li ◽  
Julien Clinton Sprott
Keyword(s):  
Parameter Space ◽  
Limit Cycles ◽  
Lorenz System ◽  
Dynamical Behavior ◽  
Symmetric Pair ◽  
Physical Systems ◽  
System A ◽  
Plausible Model ◽  
Fluid Convection ◽  
The Lorenz System

In this paper, the dynamical behavior of the Lorenz system is examined in a previously unexplored region of parameter space, in particular, where r is zero and b is negative. For certain values of the parameters, the classic butterfly attractor is broken into a symmetric pair of strange attractors, or it shrinks into a small attractor basin intermingled with the basins of a symmetric pair of limit cycles, which means that the system is bistable or tristable under certain conditions. Although the resulting system is no longer a plausible model of fluid convection, it may have application to other physical systems.

Feedback Linearization of the Lorenz System: Stabilization and Tracking Control

2002 ◽  
Author(s):  
L. G. Crespo ◽  
J. Q. Sun
Keyword(s):  
Feedback Linearization ◽  
Lorenz System ◽  
The State ◽  
Differential Flatness ◽  
State Transformation ◽  
System A ◽  
Excellent Control ◽  
High Control ◽  
The Lorenz System ◽  
Control Study

This paper presents a control study of the Lorenz system by using feedback linearization. The effects of the state transformation on the dynamics of the Lorenz system are studied first. Then, composite controllers are developed for both stabilization and tracking of the system. The controls are designed to overcome the barrier in controllability imposed by the state transformation. The transition through the manifold defined by such a singularity is achieved by inducing the chaotic response within a boundary layer that contains the singularity. Outside this region, a conventional feedback nonlinear control is applied. In this fashion, the authority of the control is enlarged to the whole state space and the need for high control efforts is substantially mitigated. Tracking problems that involve single and cooperative objectives are studied by using the differential flatness property of the system. A good understanding of the system dynamics proves to be invaluable in the design of better controls. In all numerical examples, the proposed approach led to excellent control performances.

Optimization of a Two Degree of Freedom System Acting as a Dynamic Vibration Absorber

2008 ◽  
Vol 130 (1) ◽  
Author(s):  
M. Febbo ◽  
S. A. Vera
Keyword(s):  
Simulated Annealing Algorithm ◽  
Degree Of Freedom ◽  
Vibration Absorber ◽  
Dynamic Vibration Absorber ◽  
Dynamic Vibration ◽  
System A ◽  
Annealing Algorithm ◽  
Minimum Amplitude ◽  
Two Degree Of Freedom ◽  
Heuristic Criterion

This paper deals with the problem of finding the optimal stiffnesses and damping coefficients of a two degree of freedom (2DOF) system acting as a dynamic vibration absorber (DVA) on a beam structure. In this sense, a heuristic criterion for the optimization problem will be developed to contemplate this particular type of DVA. Accordingly, it is planned to minimize the amplitude of vibration in predetermined points of the main structure. Two optimizations will be proposed for two DVAs of 1DOF to compare their performances with the optimized 2DOF system. A simulated annealing algorithm is used to obtain the DVA’s optimal parameters for minimum amplitude in a given point of the beam. The best configuration depends on the location of the absorbers on the beam and, for a fixed location, on the distribution of the stiffness constants.

scholarly journals Lorenz Type Behaviors in the Dynamics of Laser Produced Plasma

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1135 ◽  
Author(s):  
Stefan Andrei Irimiciuc ◽  
Florin Enescu ◽  
Andrei Agop ◽  
Maricel Agop
Keyword(s):  
Experimental Data ◽  
Lorenz System ◽  
Integral Form ◽  
Diagnostic Techniques ◽  
Oscillatory Behavior ◽  
Mathematical Representation ◽  
System A ◽  
Theoretical Predictions ◽  
Fractal Space ◽  
The Lorenz System

An innovative theoretical model is developed on the backbone of a classical Lorenz system. A mathematical representation of a differential Lorenz system is transposed into a fractal space and reduced to an integral form. In such a conjecture, the Lorenz variables will operate simultaneously on two manifolds, generating two transformation groups, one corresponding to the space coordinates transformation and another one to the scale resolution transformation. Since these groups are isomorphs various types isometries become functional. The Lorenz system was further adapted to describe the dynamics of ejected particles as a result of laser matter interaction in a fractal paradigm. The simulations were focused on the dynamics of charged particles, and showcase the presence of current oscillations, a heterogenous velocity distribution and multi-structuring at different interaction scales. The theoretical predictions were compared with the experimental data acquired with noninvasive diagnostic techniques. The experimental data confirm the multi-structure scenario and the oscillatory behavior predicted by the mathematical model.

A Two-Encoder Finger Position Sensing System for a Two-Degree-of-Freedom Robot Hand

1991 ◽  
Author(s):  
Kim-Gau Ng ◽  
Joey K. Parker
Keyword(s):  
Degree Of Freedom ◽  
Robot Hand ◽  
Position Sensing ◽  
Rotary Encoder ◽  
Design And Implementation ◽  
Sensing System ◽  
System A ◽  
Finger Position ◽  
Linear Encoder ◽  
Two Degree Of Freedom

Abstract As part of a robot hand with two independently controlled fingers each having one degree of freedom, a novel two-encoder position sensing system was designed for each of the fingers. In this system, a combination of a linear encoder and a rotary encoder is used to indicate finger position. The linear encoder provides coarse measurements while the rotary encoder provides fine measurements between two adjacent linear encoder counts. This two-encoder system permits more precise measurements than a system with only the linear encoder. The two encoders are connected to an IBM PC through an interface system. This paper presents the complete design and implementation of this two-encoder position sensing system.

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