Stability Analysis of an Aeroelastic System with Actuator Saturation

2012 ◽  
Vol 463-464 ◽  
pp. 1527-1532
Author(s):  
Adrian Mihail Stoica ◽  
Marius Stoia-Djeska ◽  
Gabriela Stroe
Keyword(s):  
Actuator Saturation ◽  
Equations Of Motion ◽  
Stability Domain ◽  
Lagrange Equations ◽  
Aeroelastic System ◽  
Aerospace Vehicles ◽  
Control Laws ◽  
The Stability ◽  
The Mathematical Model ◽  
Weight Structures

Aeroelastic problems of light weight structures of modern aerospace vehicles are the result of interactions between aerodynamics, structural and inertial forces. The mathematical model of the aeroelastic problem is based on the Lagrange equations of motion for the structural dynamics and on a quasi-steady approach of the generalized unsteady incompressible aerodynamic forces. The oscillations of such aeroelastic system can be suppressed using linear active control techniques. In the case when the control is saturated the stability domain shrinks. The describing function method is used in this paper to determine the periodic solutions of an experimental aeroelastic system for two control laws.

Analytical and Experimental Flutter Analysis of a Typical Wing Section Carrying a Flexibly Mounted Unbalanced Engine

2019 ◽  
Vol 19 (02) ◽  
pp. 1950013 ◽  
Author(s):  
A. S. Mirabbashi ◽  
A. Mazidi ◽  
M. M. Jalili
Keyword(s):  
Stability Domain ◽  
Governing Equations ◽  
Lagrange Equations ◽  
Wing Section ◽  
Unbalanced Force ◽  
Engine Thrust ◽  
Finite State Model ◽  
Flutter Analysis ◽  
Finite State ◽  
The Stability

In this paper, both experimental and analytical flutter analyses are conducted for a typical 5-degree of freedon (5DOF) wing section carrying a flexibly mounted unbalanced engine. The wing flexibility is simulated by two torsional and longitudinal springs at the wing elastic axis. One flap is attached to the wing section by a torsion spring. Also, the engine is connected to the wing by two elastic joints. Each joint is simulated by a spring and damper unit to bring the model close to reality. Both the torsional and longitudinal motions of the engine are considered in the aeroelastic governing equations derived from the Lagrange equations. Also, Peter’s finite state model is used to simulate the aerodynamic loads on the wing. Effects of various engine parameters such as position, connection stiffness, mass, thrust and unbalanced force on the flutter of the wing are investigated. The results show that the aeroelastic stability region is limited by increasing the engine mass, pylon length, engine thrust and unbalanced force. Furthermore, increasing the damping and stiffness coefficients of the engine connection enlarges the stability domain.

Electrostatically Actuated Coupled MEMS Resonators

2011 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Kyle N. Taylor
Keyword(s):  
Nonlinear Response ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
System Structure ◽  
Lagrange Equations ◽  
Electrostatically Actuated ◽  
Beam System ◽  
Mems Resonators ◽  
The Mathematical Model ◽  
Steady State Solutions

This paper deals with the nonlinear response of an electrostatically actuated cantilever beam system composed of two micro beam resonators near natural frequency. The mathematical model of the system is obtained using Lagrange equations. The equations of motion are nondimensionalized and then the method of multiple scales is used to find steady state solutions. Both AC and DC actuation voltages of the first beam are considered, while the influence on the system of DC on the second beam is explored. Graphical representations of the influence of the detuning parameters are provided for a typical micro beam system structure.

Pointwise Optimal Control of Dynamical Systems Described by Constrained Coordinates

1999 ◽  
Vol 121 (4) ◽  
pp. 594-598 ◽  
Author(s):  
V. Radisavljevic ◽  
H. Baruh
Keyword(s):  
Optimal Control ◽  
Dynamical Systems ◽  
Feedback Control ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Control Law ◽  
Algebraic Equations ◽  
The Stability ◽  
The Mathematical Model

A feedback control law is developed for dynamical systems described by constrained generalized coordinates. For certain complex dynamical systems, it is more desirable to develop the mathematical model using more general coordinates then degrees of freedom which leads to differential-algebraic equations of motion. Research in the last few decades has led to several advances in the treatment and in obtaining the solution of differential-algebraic equations. We take advantage of these advances and introduce the differential-algebraic equations and dependent generalized coordinate formulation to control. A tracking feedback control law is designed based on a pointwise-optimal formulation. The stability of pointwise optimal control law is examined.

scholarly journals Coupling synchronization principle of two pairs counter-rotating unbalanced rotors in the different resonant conditions

2020 ◽  
pp. 146134842093788
Author(s):  
Liqun Liu ◽  
Ting Liu ◽  
Hongliang Yue ◽  
Xueliang Zhang
Keyword(s):  
Resonant State ◽  
Equations Of Motion ◽  
Phase Relationship ◽  
Resonance Region ◽  
Lagrange Equations ◽  
Absolute Value ◽  
Dimensionless Coupling ◽  
Coupling Dynamic ◽  
The Stability ◽  
The Ideal

The present work investigates the coupling synchronization principle and stability in a vibrating system with two pairs counter-rotating unbalanced rotors (also called exciters). Based on Lagrange equations, the dimensionless coupling differential equations of motion of the system are deduced. The synchronization criterion of two pairs exciters stems from the averaging method, it satisfies the fact that the absolute value of dimensionless residual torque difference between arbitrary two driving motors is less than or equal to the maximum of their dimensionless coupling torques. The stability criterion of the synchronous states complies with Routh-Hurwitz principle. The coupling dynamic characteristics of the system are numerically analyzed in detail, including synchronization and stability ability, maximum of the coupling torque and phase relationship, etc. Some simulation results applying the Runge-Kutta algorithm are performed, it is shown that the motion states of the system can be classified into two types: sub-resonant state and super-resonant state. Generally in engineering, the ideal working points should be selected in sub-resonance region, in this case the expended energy can be saved relatively by 1/5–1/3, which is less than that in super-resonance region under the precondition of the same vibration amplitude value.

Nonlinear Planar Dynamics of Fluid-Conveying Cantilevered Extensible Pipes

2013 ◽  
Author(s):  
Mergen H. Ghayesh ◽  
Michael P. Païdoussis ◽  
Marco Amabili
Keyword(s):  
Flow Velocity ◽  
Trivial Solution ◽  
Equations Of Motion ◽  
Continuation Method ◽  
Time Integration ◽  
Axial Direction ◽  
Transverse Displacement ◽  
Lagrange Equations ◽  
Critical Flow Velocity ◽  
The Stability

This paper for the first time investigates the nonlinear planar dynamics of a cantilevered extensible pipe conveying fluid; the centreline of the pipe is considered to be extensible resulting in coupled longitudinal and transverse equations of motion; specifically, the kinetic and potential energies are obtained in terms of longitudinal and transverse displacements and then the extended version of the Lagrange equations for systems containing non-material volumes is employed to derive the equations of motion. Direct time integration along with the pseudo-arclength continuation method are employed to solve the discretized equations of motion. Bifurcation diagrams of the system are constructed as the flow velocity is increased as the bifurcation parameter. As opposed to the case of an inextensible pipe, an extensible pipe elongates in the axial direction as the flow velocity is increased from zero. At the critical flow velocity, the stability of the system is lost via a supercritical Hopf bifurcation, emerging from the trivial solution for the transverse displacement and non-trivial solution for the longitudinal displacement and leading to a flutter.

scholarly journals Investigations on stability of the synchronous states for three homodromy exciters in the vibrating system with double resonant types

2019 ◽  
Vol 38 (2) ◽  
pp. 312-327
Author(s):  
Xueliang Zhang ◽  
Zhihui Wang ◽  
Jinlin Xu ◽  
Bangchun Wen
Keyword(s):  
Resonant State ◽  
Equations Of Motion ◽  
Lagrange Equations ◽  
Vibrating System ◽  
Rigid Frame ◽  
Exciting Forces ◽  
Dimensionless Coupling ◽  
Simulation Results ◽  
The Stability ◽  
Frequency Ratios

This paper investigates stability of the synchronous states for three homodromy exciters in the vibrating system, some theoretical analyses and simulation results on which are given. Based on Lagrange equations, the differential equations of motion of the system are obtained. Using the average method yields the dimensionless coupling torque balanced equations of three exciters and the simplified analytical expressions for synchronization criterion of the system are deduced, the stability criterion of the synchronous states complies with Routh–Hurwitz principle. The dynamic characteristics of the system for different frequency ratios are discussed numerically. In order to verify the validity of theoretical methods, the simulation results by a Runge–Kutta routine are carried out; it indicates that the motion state of the vibrating system can be classified into two types: sub-resonant state and super-resonant state. The motion type of the rigid frame is strong positive superposition vibration in a sub-resonant state; while in a super-resonant state, the exciting forces of three exciters are mutually cancelled and the rigid frame is motionless. During the design process of the vibrating machines, the ideal working points are only selected in a sub-resonant state, which makes the vibrating machines work efficiently.

scholarly journals Multiobject Holographic Feedback Control of Differential Algebraic System with Application to Power System

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Lanmei Cong ◽  
Xiaocong Li ◽  
Ancai Zhang
Keyword(s):  
Power System ◽  
Algebraic System ◽  
Transient Stability ◽  
Control Method ◽  
Short Circuit ◽  
Dynamic Performance ◽  
Stability Domain ◽  
Control Laws ◽  
Assignment Method ◽  
The Stability

A multiobject holographic feedback (MOHF) control method for studying the nonlinear differential algebraic (NDA) system is proposed. In this method, the nonlinear control law is designed in a homeomorphous linear space by means of constructing the multiobject equations (MOEq) which is in accord with Brunovsky normal form. The objective functions of MOEq are considered to be the errors between the output functions and their references. The relative degree for algebraic system is defined that is key to connecting the nonlinear and the linear control laws. Pole assignment method is addressed for the stability domain of this MOHF control. Since there is no any approximation, the MOHF control is effective in governing the dynamic performance stably both to the small and major disturbance. The application in single machine infinite system (SMIS) shows that this approach is effective in the improvement of stable and transient stability for power system on the disturbance of active power or three-phase short circuit fault.

scholarly journals Modeling and Research of the Controllability of Wheeled Tractors

2019 ◽  
Vol 9 (1) ◽  
pp. 2344-2351
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Equations Of Motion ◽  
Lagrange Equations ◽  
External Disturbances ◽  
The Maximum Principle ◽  
Moving Direction ◽  
The Stability ◽  
Optimal Control Methods ◽  
The Pontryagin Maximum Principle

In this paper we considered the issues of controllability and stability of wheeled tractors on the slopes with the help of mathematical modeling and optimal control. The well-known methods of modeling and research for improving the stability of the tractor do not allow solving the problem of stable motion of the tractor on the slopes, as they do not provide sufficient correction of the moving direction, which depends on the character of external disturbances. The application of modern optimal control methods allows to investigate this problem at the design phase of the machine with using mathematical models. To solve the problem, we created the equations of motion of a wheeled tractor using the Lagrange equations of the second kind. On the basis of the equations of motion we developed models and algorithms for optimal control of a wheeled tractor. The necessary conditions for optimal control of the motion using the Pontryagin maximum principle were investigated. With the help of auxiliary functions of Hamilton-Pontryagin, we have determined the coefficients of stiffness and viscous resistance of wheel tractor tires. The boundary value problem of the maximum principle to determine the transient process motion of the tractor is formulated and on its basis the equations of horizontal and vertical oscillations of the tractor were solved at an uneven distribution of mass between the front and rear driven wheels and the coefficient of adhesion of the wheels and the lateral slip of the tractor in turning were calculated.

Nonlinear Dynamics and Control of an Ideal/Nonideal Load Transportation System With Periodic Coefficients

2006 ◽  
Vol 2 (1) ◽  
pp. 32-39 ◽  
Author(s):  
N. J. Peruzzi ◽  
J. M. Balthazar ◽  
B. R. Pontes ◽  
R. M. L. R. F. Brasil
Keyword(s):  
Equations Of Motion ◽  
Periodic Problem ◽  
Dc Motor ◽  
Transportation System ◽  
Stability Diagrams ◽  
Dynamics And Control ◽  
The Stability ◽  
Load Transportation ◽  
And Control ◽  
The Mathematical Model

In this paper, a loads transportation system in platforms or suspended by cables is considered. It is a monorail device and is modeled as an inverted pendulum built on a car driven by a dc motor. The governing equations of motion were derived via Lagrange’s equations. In the mathematical model we consider the interaction between the dc motor and the dynamical system, that is, we have a so called nonideal periodic problem. The problem is analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, we also analyze the problem quantitatively using the Floquet multipliers technique. Finally, we devise a control for the studied nonideal problem. The method that was used for analysis and control of this nonideal periodic system is based on the Chebyshev polynomial expansion, the Picard iterative method, and the Lyapunov-Floquet transformation (L-F transformation). We call it Sinha’s theory.

scholarly journals A least action principle for interceptive walking

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Soon Ho Kim ◽  
Jong Won Kim ◽  
Hyun Chae Chung ◽  
MooYoung Choi
Keyword(s):  
Social Systems ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Action Principle ◽  
Lagrange Equations ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle ◽  
Principle Of Least Action ◽  
Human Participants

AbstractThe principle of least effort has been widely used to explain phenomena related to human behavior ranging from topics in language to those in social systems. It has precedence in the principle of least action from the Lagrangian formulation of classical mechanics. In this study, we present a model for interceptive human walking based on the least action principle. Taking inspiration from Lagrangian mechanics, a Lagrangian is defined as effort minus security, with two different specific mathematical forms. The resulting Euler–Lagrange equations are then solved to obtain the equations of motion. The model is validated using experimental data from a virtual reality crossing simulation with human participants. We thus conclude that the least action principle provides a useful tool in the study of interceptive walking.

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