Solid Element Rotordynamic Modeling of a Rotor on a Flexible Support Structure Utilizing Multiple-Input and Multiple-Output Support Transfer Functions

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Lingnan Hu ◽  
Alan Palazzolo
Keyword(s):  
State Space ◽  
Transfer Functions ◽  
State Space Model ◽  
Computation Time ◽  
Support Structure ◽  
Polynomial Degree ◽  
Space Model ◽  
Flexible Support ◽  
Multiple Input ◽  
Rotor Support

The authors present an improved modeling approach to analyze the coupled rotor-support dynamics by modeling the rotor with solid finite elements (FEs) and utilizing multiple-input and multiple-output transfer functions (TFs) to represent the flexible support. A state-space model is then employed to perform general rotordynamic analyses. Transfer functions are used to simulate dynamic characteristics of the support structure, including cross-coupling between degrees-of-freedom. These TFs are derived by curve-fitting the frequency response functions of the support model at bearing locations. The impact of the polynomial degree of the TF on the response analysis is discussed, and a general rule is proposed to select an adequate polynomial degree. To validate the proposed approach, a comprehensive comparison between the complete solid FE rotor-support model (CSRSM) and the reduced state-space model (RSSM) is presented. Comparisons are made between natural frequencies, critical speeds, unbalance response, logarithmic decrement, and computation time. The results show that the RSSM provides a dynamically accurate approximation of the solid FE model in terms of rotordynamic analyses. Moreover, the computation time for the RSSM is reduced to less than 20% of the time required for the CSRSM. In addition, the modes up to 100,000 cpm are compared among the super-element, beam element, and RSSM. The results show that the RSSM is more accurate in predicting high-frequency modes than the other two approaches. Further, the proposed RSSM is useful for applications in vibration control and active magnetic bearing systems.

Solid Element Rotordynamic Modeling of a Rotor on a Flexible Support Structure Utilizing MIMO Support Transfer Functions

2016 ◽  
Author(s):  
Lingnan Hu ◽  
Alan Palazzolo
Keyword(s):  
State Space ◽  
State Space Model ◽  
Computation Time ◽  
Support Structure ◽  
Space Model ◽  
Flexible Support ◽  
Rotor Support ◽  
Rotor Model ◽  
Reduced State ◽  
Support Model

The accurate modeling of a rotor system is essential for effective design and troubleshooting in rotating machinery. The beam-type finite element (FE) may be inadequate for modeling a rotor or support structure with complex shapes. In addition, the isolated support impedance methods may be inaccurate for modeling the support structure that has modes that are highly coupled between bearings and directions at the bearing locations. The solid FE method is a good replacement of the beam FE and support impedance approaches. However, a drawback for this method is the significant amount of computation time required to obtain accurate solutions due to the large number of nodes in the solid FE analysis. The authors present an improved approach to analyze the coupled rotor-support dynamics, by modeling the rotor with solid elements and utilizing transfer functions (TFs) to represent the flexible support. A state-space model is then employed to perform general rotordynamic analyses. The solid FE rotor model includes the gyroscopic effects and the asymmetric and cross-coupled stiffness coefficients of the bearing. A series of rational TFs are used to simulate dynamic characteristics of the support structure, including the cross-coupling between degrees of freedom (DOFs). These TFs are derived by curve-fitting the frequency response functions (FRFs) of the solid FE support model at the bearing locations. The impact of the polynomial degree of the TF on the unbalance response analysis is discussed, and a general rule is proposed to select an adequate polynomial degree. To validate the proposed modeling approach, a comprehensive comparison among the complete solid FE rotor-support model and the solid FE rotor model with the TFs representing the flexible support (the reduced state-space model) are presented. Comparisons are made between natural frequencies, critical speeds, unbalance response, logarithmic decrement (log dec), and computation time. The results of these comparisons show that the reduced state-space rotor-support model provides a dynamically accurate approximation of the solid FE rotor-support model in terms of general rotordynamic analyses. Moreover, the computation time for the proposed modeling approach is reduced to 2.5 minutes, compared to 14 minutes for the complete solid FE modeling. The reduction of the computation time may vary with different number of DOFs of the rotor model and the support structure model. In addition, the modes up to 100,000 cpm are compared among the beam rotor with the solid FE support model, the solid FE rotor with the super-element support model, and the reduced state-space model. The results show that the reduced state-space model is more accurate in predicting high-frequency modes than the beam rotor-support and super-element support models. Further, the proposed approach with the state-space model is useful for applications in vibration control and active magnetic bearing (AMB) systems.

Motion Response Control of the DWSC Spar Based on State-Space Model

2012 ◽  
Author(s):  
Xiaochuan Yu ◽  
Jeffrey Falzarano
Keyword(s):  
State Space ◽  
Transfer Functions ◽  
State Space Model ◽  
Development Program ◽  
Naval Research ◽  
Hydrodynamic Coefficients ◽  
Time Step ◽  
Response Control ◽  
Motion Response ◽  
Space Model

In 2007, the Office of Naval Research (ONR) started a technology development program called STLVAST (Small to Large Vessel At-Sea Transfer), in order to develop ‘enabling capabilities’ in the realm of logistic transfer (i.e. stores, equipment, vehicles) between a large transport vessel and a smaller T-craft ship, using a Deep Water Stable Crane (DWSC) spar between them. In this paper, the equation of motions of the single DWSC spar is initially expressed as the standard state-space model. Then the ODE solver of Matlab is directly employed to obtain the motion responses at each time step. Two levels of approximation of hydrodynamic coefficients are considered in this study. One is the Constant Coefficient Method (CCM), and the other one is the Impulse Response Function (IRF) method, with fluid memory effects considered. WAMIT software is used to calculate the hydrodynamic coefficients, including the added mass, radiation damping, IRF, the first order and second order waves loads transfer functions, etc. The motion response control is achieved by assuming the thrusters can provide the optimal feedback force derived from Linear Quadratic Regulator (LQR) method.

scholarly journals Multiple-Input Single-Output Polynomial Nonlinear State-Space Model of the Li-ion Battery’s Short-term Dynamics

2018 ◽  
Vol 51 (15) ◽  
pp. 497-502
Author(s):  
Rishi Relan ◽  
Koen Tiels ◽  
Jean-Marc Timmermans ◽  
Johan Schoukens
Keyword(s):  
State Space ◽  
State Space Model ◽  
Short Term ◽  
Space Model ◽  
Single Output ◽  
Multiple Input ◽  
Li Ion ◽  
Nonlinear State

A NONLINEAR UNIFIED STATE-SPACE MODEL FOR SHIP MANEUVERING AND CONTROL IN A SEAWAY

2005 ◽  
Vol 15 (09) ◽  
pp. 2717-2746 ◽  
Author(s):  
THOR I. FOSSEN
Keyword(s):  
State Space ◽  
Transfer Functions ◽  
State Space Model ◽  
Low Frequency ◽  
Ship Maneuvering ◽  
Frequency Model ◽  
Space Model ◽  
Classic Theory ◽  
Space Formulation ◽  
And Control

This article presents a unified state-space model for ship maneuvering, station-keeping, and control in a seaway. The frequency-dependent potential and viscous damping terms, which in classic theory results in a convolution integral not suited for real-time simulation, is compactly represented by using a state-space formulation. The separation of the vessel model into a low-frequency model (represented by zero-frequency added mass and damping) and a wave-frequency model (represented by motion transfer functions or RAOs), which is commonly used for simulation, is hence made superfluous.

Development of L1-norm sliding mode observer for sensor fault diagnosis of an industrial gas turbine

2021 ◽  
pp. 095965182199617
Author(s):  
Mahyar Akbari ◽  
Abdol Majid Khoshnood ◽  
Saied Irani
Keyword(s):  
Fault Detection ◽  
State Space ◽  
Gas Turbine ◽  
Sliding Mode ◽  
State Space Model ◽  
Sensor Fault ◽  
Space Model ◽  
Decision Logic ◽  
Sensor Fault Detection ◽  
Industrial Gas Turbine

In this article, a novel approach for model-based sensor fault detection and estimation of gas turbine is presented. The proposed method includes driving a state-space model of gas turbine, designing a novel L1-norm Lyapunov-based observer, and a decision logic which is based on bank of observers. The novel observer is designed using multiple Lyapunov functions based on L1-norm, reducing the estimation noise while increasing the accuracy. The L1-norm observer is similar to sliding mode observer in switching time. The proposed observer also acts as a low-pass filter, subsequently reducing estimation chattering. Since a bank of observers is required in model-based sensor fault detection, a bank of L1-norm observers is designed in this article. Corresponding to the use of the bank of observers, a two-step fault detection decision logic is developed. Furthermore, the proposed state-space model is a hybrid data-driven model which is divided into two models for steady-state and transient conditions, according to the nature of the gas turbine. The model is developed by applying a subspace algorithm to the real field data of SGT-600 (an industrial gas turbine). The proposed model was validated by applying to two other similar gas turbines with different ambient and operational conditions. The results of the proposed approach implementation demonstrate precise gas turbine sensor fault detection and estimation.

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