Stability of a CFSTR with two consecutive reactions by the Liapunov direct method

1989 ◽  
Vol 6 (3) ◽  
pp. 200-205 ◽  
Author(s):  
Chongyoup Kim ◽  
Hyun-Ku Rhee
Keyword(s):  
Direct Method ◽  
Consecutive Reactions ◽  
Liapunov Direct Method

Thermally Induced Instability of Laminated Beams and Plates

1996 ◽  
Vol 63 (4) ◽  
pp. 884-890 ◽  
Author(s):  
A. Tylikowski ◽  
R. B. Hetnarski
Keyword(s):  
Stochastic Stability ◽  
Direct Method ◽  
Wide Band ◽  
Temperature Fields ◽  
Time And Space ◽  
Thermally Induced ◽  
Stability Problems ◽  
Linear Elastic ◽  
Liapunov Direct Method ◽  
Short Time

A theoretical investigation of dynamic stability for linear elastic structures due to non-uniform, time and space-dependent stochastic temperature fields is presented. The study is based on the reformulation of stochastic stability problems as a stability of Itoˆ type equations in some appropriate Hilbert space and is adopted for stability problems of structures with time and space-dependent stochastic coefficients. Uniform stochastic stability criteria of the structure equilibrium are derived using the Liapunov direct method. The energy-like functional and the generalized ltoˆ lemma are used to derive the sufficient stability conditions of the equilibrium state. A symmetrically laminated crossply plate subjected to the wide-band Gaussian temperature distribution and a laminated beam subjected to local short-time heatings are analysed in detail.

Liapunov direct method in approaching bifurcation problems

1976 ◽  
Vol 108 (1) ◽  
pp. 211-226 ◽  
Author(s):  
F. Marchetti ◽  
P. Negrini ◽  
L. Salvadori ◽  
M. Scalia
Keyword(s):  
Direct Method ◽  
Liapunov Direct Method ◽  
Bifurcation Problems

NON-LINEAR DYNAMIC BUCKLING OF A SIMPLE MODEL VIA THE LIAPUNOV DIRECT METHOD

1996 ◽  
Vol 193 (5) ◽  
pp. 1091-1097 ◽  
Author(s):  
A.N. Kounadis
Keyword(s):  
Simple Model ◽  
Direct Method ◽  
Dynamic Buckling ◽  
Linear Dynamic ◽  
Liapunov Direct Method ◽  
Non Linear

scholarly journals Multivariable Adaptive Control for Turbojet Engines

1993 ◽  
Author(s):  
Jin-Quan Huang ◽  
Jian-Guo Sun
Keyword(s):  
Adaptive Control ◽  
Direct Method ◽  
Pressure Ratio ◽  
Operating Conditions ◽  
Stall Margin ◽  
Acceleration Time ◽  
Engine Simulation ◽  
Liapunov Direct Method ◽  
Flight Envelope ◽  
Model Reference Adaptive

Integrated flight and propulsion control systems will require propulsion systems to reduce in time to accelerate engine and to improve transient performance for a full flight envelope operation. A multivariate model reference adaptive control (MRAC) scheme is proposed in this paper. Acceleration time is reduced by uptrimming engine pressure ratio in some operating conditions and in parts of the flight envelope where excess stall margin and turbine temperature margin exist. The MRAC scheme is obtained by using Liapunov direct method. Simulation studies are performed for a two-spool turbojet engine. The satisfactory transient responses are obtained at different operating points from idle to maximum dry power in flight envelope which shows good robustness for unmodelled dynamics of nonlinear engine. Simulation results also show the good effectiveness of reducing interaction in multivariable system with significant coupling. Using the Multivariable MRAC controller, the engine acceleration time is reduced about 16 percent in comparison with the conventional engine controller.

STABILITY OF RATE GYRO IN A VEHICLE WITH UNCERTAIN ANGULAR VELOCITY AND ACCELERATION

1995 ◽  
Vol 19 (4) ◽  
pp. 417-433
Author(s):  
Zheng-Ming Ge ◽  
Heng-Hui Chen
Keyword(s):  
Angular Velocity ◽  
Numerical Method ◽  
Fourth Order ◽  
Direct Method ◽  
Space Vehicle ◽  
Stability Of Motion ◽  
Liapunov Direct Method ◽  
Rate Gyro ◽  
The Stability ◽  
Analytical Relations

Using the Liapunov direct method, we study the stability of motion of a single-axis rate gyro mounted on a space vehicle which is simultaneously accelerating (ω)x(t)) with respect to the output axis and rotating (ωz(t)) about the spin axis of gyro. The analytical relations, which must be satisfied by the gyro parameters, are obtained for the asymptotical stability of the gimbal motion. In addition, by using a fourth-order Runge-Kutta numerical method, the trajectories of motions of a rate gyro are obtained to verify its stability.

Estimates Based on First Order Inequalities 1: Liapunov Direct Method

2020 ◽  
pp. 45-73
Author(s):  
James N. Flavin ◽  
Salvatore Rionero
Keyword(s):  
Direct Method ◽  
First Order ◽  
Liapunov Direct Method

Stability Analysis of the Motion of a Tuned Gyroscope

1988 ◽  
Vol 12 (1) ◽  
pp. 31-37
Author(s):  
Zheng-Ming Ge
Keyword(s):  
Stability Analysis ◽  
Direct Method ◽  
Input Rate ◽  
Stability Of Motion ◽  
Damping Coefficients ◽  
Liapunov Direct Method ◽  
The Stability ◽  
Rotor Winding ◽  
Elastically Supported

In this paper, we use the Liapunov direct method to study the stability of motion of the rotor of a single-gimbal, elastically supported tuned gyroscope with the input rate ø̇1 = ø̇2 = 0 in three cases: (1) rotor-gimbal damping coefficients D1 = D2 = 0, rotor winding coefficient Dw = 0; (2) D1 ≠ 0, D2 ≠ 0, Dw = 0; (3) D1 ≠ 0, D2 ≠0, Dw ≠ 0.

STABILITY OF EULER, LAGRANGE AND KOVALEVSKAYA GYROS IN A NEWTONIAN CENTRAL FORCE FIELD WITH SECOND ORDER TERMS

1996 ◽  
Vol 20 (1) ◽  
pp. 41-53
Author(s):  
Zheng-Ming Ge ◽  
Fu-Neng Ku
Keyword(s):  
Fixed Point ◽  
Force Field ◽  
Direct Method ◽  
High Accuracy ◽  
Second Order ◽  
Central Force ◽  
Central Force Field ◽  
Liapunov Direct Method ◽  
Permanent Rotation ◽  
The Stability

The stability of the permanent rotation of the Euler, Lagrange and Kovalevskaya gyros about a fixed point in the Newtonian central force field is investigated by Liapunov direct method, which improve Leimanis’ and Rumiantsev’s result of stability conditions. For the sake of high accuracy, the first and second order terms of R-1 expressed by potential energy of the Newtonian central force field have been considered, where the R is the distance from the fixed point to the center of attraction.

UNIFORM DISSIPATIVENESS, ROBUST SYNCHRONIZATION AND LOCATION OF THE ATTRACTOR OF PARAMETRIZED NONAUTONOMOUS DISCRETE SYSTEMS

2011 ◽  
Vol 21 (02) ◽  
pp. 513-526 ◽  
Author(s):  
HILDEBRANDO M. RODRIGUES ◽  
JIANHONG WU ◽  
LUÍS R. A. GABRIEL
Keyword(s):  
Direct Method ◽  
Liapunov Function ◽  
Discrete Systems ◽  
Step Size ◽  
Uniform Estimates ◽  
Bounded Set ◽  
Liapunov Direct Method ◽  
Autonomous Case ◽  
Time Periodic ◽  
Secured Communication

In this series of papers, we study issues related to the synchronization of two coupled chaotic discrete systems arising from secured communication. The first part deals with uniform dissipativeness with respect to parameter variation via the Liapunov direct method. We obtain uniform estimates of the global attractor for a general discrete nonautonomous system, that yields a uniform invariance principle in the autonomous case. The Liapunov function is allowed to have positive derivative along solutions of the system inside a bounded set, and this reduces substantially the difficulty of constructing a Liapunov function for a given system. In particular, we develop an approach that incorporates the classical Lagrange multiplier into the Liapunov function method to naturally extend those Liapunov functions from continuous dynamical system to their discretizations, so that the corresponding uniform dispativeness results are valid when the step size of the discretization is small. Applications to the discretized Lorenz system and the discretization of a time-periodic chaotic system are given to illustrate the general results. We also show how to obtain uniform estimation of attractors for parametrized linear stable systems with nonlinear perturbation.

Liapunov Stability Criteria for Continuous Systems Under Parametric Excitation

1972 ◽  
Vol 39 (1) ◽  
pp. 244-250 ◽  
Author(s):  
T. H. Lee ◽  
C. S. Hsu
Keyword(s):  
Parametric Excitation ◽  
Direct Method ◽  
Continuous Systems ◽  
Panel Flutter ◽  
Stability Criteria ◽  
Use Of Time ◽  
Liapunov Direct Method ◽  
Liapunov Functionals ◽  
Adjoint Operators ◽  
Extremal Properties

A Liapunov direct method is developed here to derive stability criteria for continuous systems under parametric excitation. The method makes use of time-dependent Liapunov functionals and the extremal properties of Rayleigh quotients of self-adjoint operators. The application of the method entails solving an eigenvalue problem with the variable t appearing in the problem strictly as a parameter. As examples of application the method is applied to (a) a clamped column under the action of periodic axial load, and (b) the panel flutter problem with the panel also subjected to periodic in-plane load. The calculated results for the first example show improvement over those obtained previously.

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