scholarly journals Nonlinear Global Stabilization Control for the Underactuated WAcrobot System

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Shuli Gong ◽  
Ancai Zhang ◽  
Zhi Liu ◽  
Zhenxing Li ◽  
Chengdong Yang ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Reduced Order Model ◽  
Underactuated System ◽  
Global Stabilization ◽  
Order Model ◽  
Control Laws ◽  
Reduced Order ◽  
Stabilization Control ◽  
Stabilizing Control ◽  
Control Objective

A WAcrobot is an underactuated nonlinear system that has three degrees of freedom (DOF) and two inputs. This paper discusses the global stabilization control problem for this 3-DOF underactuated system. A new control strategy is developed to solve this problem. The strategy first changes the 3-DOF WAcrobot system to be a 2-DOF reduced-order model in finite time. This transforms the stabilizing control of the WAcrobot system into that of the reduced-order model. After that, nonsingular control laws that globally stabilize the reduced-order model at the origin are designed. It guarantees the stabilizing control objective of the WAcrobot to be achieved. Finally, a simulation experimental example demonstrates the validity of the presented theoretical results. Simulation results show the advantage of our strategy over others.

scholarly journals A Reduced Order Model of Mistuning Using a Subset of Nominal System Modes

1999 ◽  
Author(s):  
M.-T. Yang ◽  
J. H. Griffin
Keyword(s):  
Degrees Of Freedom ◽  
Reduced Order Model ◽  
Reduced Order Models ◽  
Order Model ◽  
Disk System ◽  
Element Analysis ◽  
Reduced Order ◽  
Nominal System ◽  
Harmonic Response ◽  
Bladed Disk

Reduced order models have been reported in the literature that can be used to predict the harmonic response of mistuned bladed disks. It has been shown that in many cases they exhibit structural fidelity comparable to a finite element analysis of the full bladed disk system while offering a significant improvement in computational efficiency. In these models the blades and disk are treated as distinct substructures. This paper presents a new, simpler approach for developing reduced order models in which the modes of the mistuned system are represented in terms of a sub-set of nominal system modes. It has the following attributes: the input requirements are relatively easy to generate; it accurately predicts mistuning effects in regions where frequency veering occurs; as the number of degrees of freedom increases it converges to the exact solution; it accurately predicts stresses as well as displacements; and it accurately models the deformation and stresses at the blades’ bases.

Aeroelastic Analysis of Blades Cascades Through Aerodynamic Reduced-Order Modeling

2011 ◽  
Author(s):  
Davide Finamore ◽  
Fred Nitzsche ◽  
Massimo Gennaretti
Keyword(s):  
Reduced Order Model ◽  
Aeroelastic Stability ◽  
Order Model ◽  
Control Laws ◽  
Reduced Order ◽  
Aerodynamic Model ◽  
Blade Cascade ◽  
Aeroelastic Analysis ◽  
Direct Use ◽  
High Computational Efficiency

An aerodynamic Reduced-Order Model (ROM) is introduced to describe the aeroelastic behavior of a blade cascade of a turbomachine. This is obtained coupling an aerodynamic model with a semi-rigid 2D model for the description of the structure dynamics. The advantages of using an aerodynamic reduced-order model concern the high computational efficiency compared to the direct use of a CFD code, and the applicability of control laws to reduce, for instance, blades vibrations. ROMs are identified from both an analytical aerodynamic model and a numerical CFD solver. The aeroelastic stability of a blade cascade is examined with the presence or not of mistuning.

Nonlinear Dynamic Analysis of Cantilever Beam Using POD Based Reduced Order Model

2015 ◽  
Vol 786 ◽  
pp. 398-403 ◽  
Author(s):  
Kulkarni Atul Shankar ◽  
Manoj Pandey
Keyword(s):  
Dynamic Analysis ◽  
Large Deformation ◽  
Cantilever Beam ◽  
Nonlinear Dynamic ◽  
Degrees Of Freedom ◽  
Numerical Technique ◽  
Nonlinear Dynamic Analysis ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order

In this paper, a reduced order model is obtained for nonlinear dynamic analysis of a cantilever beam. Nonlinearity in the system is basically due to large deformation. A reduced order model is an efficient method to formulate low order dynamical model which can be obtained from data obtained from numerical technique such as finite element method (FEM). Nonlinear dynamical models are complex with large number of degrees of freedom and hence, are computationally intensive. With formulation of reduced order models (i.e. Macromodels) number of degrees of freedom are reduced to fewer degrees of freedom by using projection based method like Galerkin’s projection, so as to make system computationally faster and cost effective. These macromodels are obtained by extracting global basis functions from fully meshed model runs. Macromodels are generated using technique called proper orthogonal decomposition (POD) which gives good linear fit for the nonlinear systems. Using POD based macromodel, response of system can be computed using fewer modes instead of considering all modes of system. Macromodel is generated to obtain the response of cantilever beam with large deformation and hence, simulation time is reduced by factor of 90 approximately with error of order of 10-4. Further, method of POD based reduced order model is aplied to beam with different loading conditions to check the robustness of the macromodel. POD based macromodel response gives good agreement with FEA model response for a cantilever beam.

Reduced Order Model for the Geometric Nonlinear Response of Complex Structures

2012 ◽  
Author(s):  
Ricardo Perez ◽  
X. Q. Wang ◽  
Andrew Matney ◽  
Marc P. Mignolet
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Behavior ◽  
Reduced Order Model ◽  
Model Parameters ◽  
Complex Structures ◽  
Order Model ◽  
Plate Structures ◽  
Reduced Order ◽  
Nonlinear Static ◽  
Selection Of

This paper focuses on the development of nonlinear reduced order modeling techniques for the prediction of the response of complex structures exhibiting “large” deformations, i.e. a geometrically nonlinear behavior, and modeled within a commercial finite element code. The present investigation builds on a general methodology successfully validated in recent years on simpler beam and plate structures by: (i) developing a novel identification strategy of the reduced order model parameters that enables the consideration of the large number of modes (> 50 say) that would be needed for complex structures, and (ii) extending an automatic strategy for the selection of the basis functions used to represent accurately the displacement field. The above novel developments are successfully validated on the nonlinear static response of a 9-bay panel structure modeled with 96,000 degrees of freedom within Nastran.

A Reduced-Order Model of Mistuning Using a Subset of Nominal System Modes

1999 ◽  
Vol 123 (4) ◽  
pp. 893-900 ◽  
Author(s):  
M.-T. Yang ◽  
J. H. Griffin
Keyword(s):  
Degrees Of Freedom ◽  
Reduced Order Model ◽  
Reduced Order Models ◽  
Order Model ◽  
Disk System ◽  
Element Analysis ◽  
Reduced Order ◽  
Nominal System ◽  
Harmonic Response ◽  
Bladed Disk

Reduced-order models have been reported in the literature that can be used to predict the harmonic response of mistuned bladed disks. It has been shown that in many cases they exhibit structural fidelity comparable to a finite element analysis of the full bladed disk system while offering a significant improvement in computational efficiency. In these models the blades and disk are treated as distinct substructures. This paper presents a new, simpler approach for developing reduced-order models in which the modes of the mistuned system are represented in terms of a subset of nominal system modes. It has the following attributes: the input requirements are relatively easy to generate; it accurately predicts mistuning effects in regions where frequency veering occurs; as the number of degrees-of-freedom increases it converges to the exact solution; it accurately predicts stresses as well as displacements; and it accurately models the deformation and stresses at the blades’ bases.

Reduced-Order Model of a Mistuned Multi-Stage Bladed Rotor

2007 ◽  
Author(s):  
Alok Sinha
Keyword(s):  
Degrees Of Freedom ◽  
Maximum Amplitude ◽  
Reduced Order Model ◽  
Order Model ◽  
Mass Model ◽  
Reduced Order ◽  
Multi Stage ◽  
Bladed Rotor ◽  
The Impact ◽  
Three Degrees Of Freedom

This paper deals with a reduced-order model of a multi-stage rotor in which each stage has a different number of blades. In particular, it is shown that a reduced-order model can be developed on the basis of tuned modes of certain bladed disks. The validity of this algorithm is shown for a spring-mass model with three degrees of freedom per sector. In addition, the statistical distributions of the peak maximum amplitude are generated via Monte Carlo simulations, and the impact of mistuning is examined for a two-stage rotor.

Reduced Order Model of a Bladed Rotor With Geometric Mistuning: Comparison Between Modified Modal Domain Analysis and Frequency Mistuning Approach

2011 ◽  
Author(s):  
Yasharth Bhartiya ◽  
Alok Sinha
Keyword(s):  
Degrees Of Freedom ◽  
Domain Analysis ◽  
Forced Response ◽  
Reduced Order Model ◽  
Mode Shapes ◽  
Order Model ◽  
Reduced Order ◽  
Young’S Moduli ◽  
Stiffness Matrices ◽  
Bladed Rotor

Mistuning has traditionally been modeled through the changes in Young’s moduli of blades, or equivalently through perturbations in the stiffness matrices associated with blades’ degrees of freedom. Such a mistuning is termed as Frequency Mistuning because it alters the blade alone frequencies without altering the mode shapes component associated with the blades. Many reduced order models have been developed for frequency mistuning [1–7]. Although frequency mistuning has been developed for Young’s Modulus mistuning, it is applied to geometric mistuning in the literature. In this paper frequency mistuning is applied to a geometrically mistuned system and the results from Subset of Nominal Modes (SNM) [5] technique, a reduced order model based on frequency mistuning, are compared with those from Modified Modal Domain Analysis (MMDA). It is shown that frequency mistuning analysis is unable to capture the effects of geometric mistuning in general, whereas MMDA provides accurate estimates of natural frequencies, mode shapes and forced response.

A Reduced Order Approach for the Vibration of Mistuned Bladed Disk Assemblies

1997 ◽  
Vol 119 (1) ◽  
pp. 161-167 ◽  
Author(s):  
M.-T. Yang ◽  
J. H. Griffin
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Reduced Order Model ◽  
Order Model ◽  
Disk System ◽  
Element Analysis ◽  
Reduced Order ◽  
Bladed Disk

A reduced order approach is introduced in this paper that can be used to predict the steady-state response of mistuned bladed disks. This approach takes results directly from a finite element analysis of a tuned system and, based on the assumption of rigid blade base motion, constructs a computationally efficient mistuned model with a reduced number of degrees of freedom. Based on a comparison of results predicted by different approaches, it is concluded that: The reduced order model displays structural fidelity comparable to that of a finite element model of the entire bladed disk system with significantly improved computational efficiency; and under certain circumstances both the finite element model and the reduced order model predict quite different response from simple spring-mass models.

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