Full Beam Formulation of a Rotating Beam-Mass System

1994 ◽  
Vol 116 (1) ◽  
pp. 93-99 ◽  
Author(s):  
B. Fallahi ◽  
S. H.-Y. Lai ◽  
R. Gupta
Keyword(s):  
Nonlinear Term ◽  
Cross Coupling ◽  
Automatic Generation ◽  
Shape Functions ◽  
Rotating Beam ◽  
Mass System ◽  
Computational Implementation ◽  
Geometric Stiffening ◽  
Rigid Body Motions ◽  
Tip Mass

In this study a comprehensive approach for modeling flexibility for a beam with tip mass is presented. The method utilizes a Timoshenko beam with geometric stiffening. The element matrices are reported as the integral of the product of shape functions. This enhances their utility due to their generic form. They are utilized in a symbolic-based algorithm for the automatic generation of the element matrices. The time-dependent terms are factored after assembly for better computational implementation. The effect of speed and tip mass on cross coupling between the elastic and rigid body motions represented by Coriolis, normal and tangential accelerations is investigated. The nonlinear term (geometric stiffening) is modeled by introducing a tensor which plays the same role as element matrices for the linear terms. This led to formulation of the exact tangent matrix needed to solve the nonlinear differential equation.

scholarly journals Improved model predictive load frequency control of interconnected power system with synchronized automatic generation control loops

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Abdullahi Bala Kunya ◽  
Mehmet Argin ◽  
Yusuf Jibril ◽  
Yusuf Abubakar Shaaban
Keyword(s):  
Frequency Control ◽  
Cross Coupling ◽  
Absolute Error ◽  
Automatic Generation ◽  
Load Frequency Control ◽  
Automatic Generation Control ◽  
Control Vector ◽  
Interconnected Power System ◽  
Control Scheme ◽  
Generation Control

Abstract Background Automatic generation control (AGC) of multi-area interconnected power system (IPS) is often designed with negligible cross-coupling between the load frequency control (LFC) and automatic voltage regulation (AVR) loops. This is because the AVR loop is considerably faster than that of LFC. However, with the introduction of slow optimal control action on the AVR, positive damping effect can be achieved on the LFC loop thereby improving the frequency control. In this paper, LFC synchronized with AVR in three-area IPS is proposed. Model predictive controller (MPC) configured in a dense distributed pattern, due to its online set-point tacking is used as the supplementary controller. The dynamics of the IPS subjected to multi-area step and random load disturbances are studied. The efficacy of the developed scheme is ascertained by simulating the disturbed system in MATLAB/Simulink. Results Based on the comparative analysis on the system responses, it is established that by cross-coupling the LFC loop with AVR, reductions of 66.45% and 59.09% in the frequency and tie-line power maximum deviations respectively are observed, while the respective settling times are found to be reduced by 29.68% and 22.77% when compared with the uncoordinated control scheme. In addition, the standard deviation and variance of the integral time absolute error of the system’s responses have reduced by 23.21% and 20.83% respectively compared to those obtained in a similar study. Conclusions The reduction in the maximum deviations and settling times in the system states indicates that introducing the voltage control via AVR loop has improved the frequency control significantly. While the lower standard deviation and variance of the integral time absolute error signify improvement in the robustness of the developed algorithm. However, this improvement is at the detriment of the controller size and computational complexity. In the uncoordinated control scheme, the control vector is one-dimensional, while in the coordinated scheme, the control vector is two-dimensional for each CA.

Dynamic modeling of a rotating beam having a tip mass

2008 ◽  
Author(s):  
Shengjian Bai ◽  
Pinhas Ben-Tzvi ◽  
Qingkun Zhou ◽  
Xinsheng Huang
Keyword(s):  
Dynamic Modeling ◽  
Rotating Beam ◽  
Tip Mass

Period Doubling Motions of a Nonlinear Rotating Beam at 1:1 Resonance

2014 ◽  
Vol 24 (12) ◽  
pp. 1450159 ◽  
Author(s):  
Fengxia Wang ◽  
Yuhui Qu
Keyword(s):  
Harmonic Balance ◽  
Floquet Theory ◽  
Harmonic Balance Method ◽  
Period Doubling ◽  
Balance Method ◽  
Rotating Beam ◽  
Period 2 ◽  
Geometric Stiffening ◽  
Torsional Excitation ◽  
The Galerkin Method

A rotating beam subjected to a torsional excitation is studied in this paper. Both quadratic and cubic geometric stiffening nonlinearities are retained in the equation of motion, and the reduced model is obtained via the Galerkin method. Saddle-node bifurcations and Hopf bifurcations of the period-1 motions of the model were obtained via the higher order harmonic balance method. The period-2 and period-4 solutions, which are emanated from the period-1 and period-2 motions, respectively, are obtained by the combined implementation of the harmonic balance method, Floquet theory, and Discrete Fourier transform (DFT). The analytical periodic solutions and their stabilities are verified through numerical simulation.

Non-Linear Effects in Transient Dynamic Analysis of Flexible Multibody Systems

1995 ◽  
Author(s):  
Madeleine Pascal
Keyword(s):  
Multibody Systems ◽  
Transient Dynamic Analysis ◽  
Flexible Bodies ◽  
Open Questions ◽  
Centrifugal Stiffening ◽  
Higher Order Terms ◽  
Geometric Stiffening ◽  
Slender Bodies ◽  
Linear Effects ◽  
Rigid Body Motions

Abstract Some open questions arising in the dynamical formulation of systems of hinge-connected flexible bodies are discussed. The first one deals with the choice of the “floating reference frame” associated to a body under-going large rigid body motions but small elastic deformations. The second one is concerned by the so-called geometric stiffening (or centrifugal stiffening) effects. It is shown that in the most cases, these effects have to be taken into account only for slender bodies like beams or plates when they are subjected to axial or inplane forces. The last problem is concerned by the eventual appearance of higher order terms in the kinetic energy of the system for large rates and large accelerations.

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