On the stability preserving property of the double bilinear transformation on a class of 2-D transfer functions

1996 ◽  
Vol 7 (2) ◽  
pp. 211-220
Author(s):  
Sandra A. Yost ◽  
Peter H. Bauer ◽  
Kasyapa Balemarthy
Keyword(s):  
Transfer Functions ◽  
Bilinear Transformation ◽  
Double Bilinear Transformation ◽  
The Stability

An Evaluation of Stability Indices Using Sensitivity Functions for Active Magnetic Bearing Supported High-Speed Rotor

2006 ◽  
Vol 129 (2) ◽  
pp. 230-238 ◽  
Author(s):  
Naohiko Takahashi ◽  
Hiroyuki Fujiwara ◽  
Osami Matsushita ◽  
Makoto Ito ◽  
Yasuo Fukushima
Keyword(s):  
High Speed ◽  
Transfer Functions ◽  
Mimo System ◽  
Magnetic Bearing ◽  
Singular Value ◽  
Active Magnetic Bearing ◽  
Sensitivity Functions ◽  
Phase Lags ◽  
The Stability ◽  
Stability Indices

In active magnetic bearing (AMB) systems, stability is the most important factor for reliable operation. Rotor positions in radial direction are regulated by four-axis control in AMB, i.e., a radial system is to be treated as a multi-input multioutput (MIMO) system. One of the general indices representing the stability of a MIMO system is “maximum singular value” of a sensitivity function matrix, which needs full matrix elements for calculation. On the other hand, ISO 14839-3 employs “maximum gain” of the diagonal elements. In this concept, each control axis is considered as an independent single-input single-output (SISO) system and thus the stability indices can be determined with just four sensitivity functions. This paper discusses the stability indices using sensitivity functions as SISO systems with parallel/conical mode treatment and/or side-by-side treatment, and as a MIMO system with using maximum singular value; the paper also highlights the differences among these approaches. In addition, a conversion from usual x∕y axis form to forward/backward form is proposed, and the stability is evaluated in its converted form. For experimental demonstration, a test rig diverted from a high-speed compressor was used. The transfer functions were measured by exciting the control circuits with swept signals at rotor standstill and at its 30,000 revolutions/min rotational speed. For stability limit evaluation, the control loop gains were increased in one case, and in another case phase lags were inserted in the controller to lead the system close to unstable intentionally. In this experiment, the side-by-side assessment, which conforms to the ISO standard, indicates the least sensitive results, but the difference from the other assessments are not so great as to lead to inadequate evaluations. Converting the transfer functions to the forward/backward form decouples the mixed peaks due to gyroscopic effect in bode plot at rotation and gives much closer assessment to maximum singular value assessment. If large phase lags are inserted into the controller, the second bending mode is destabilized, but the sensitivity functions do not catch this instability. The ISO standard can be used practically in determining the stability of the AMB system, nevertheless it must be borne in mind that the sensitivity functions do not always highlight the instability in bending modes.

Stability and resonance analysis of a general non-commensurate elementary fractional-order system

2020 ◽  
Vol 23 (1) ◽  
pp. 183-210 ◽  
Author(s):  
Shuo Zhang ◽  
Lu Liu ◽  
Dingyu Xue ◽  
YangQuan Chen
Keyword(s):  
Fractional Order ◽  
Transfer Functions ◽  
Order Parameters ◽  
Fractional Order System ◽  
Order System ◽  
Stability Conditions ◽  
Order Restriction ◽  
Resonance Analysis ◽  
General Kind ◽  
The Stability

AbstractThe elementary fractional-order models are the extension of first and second order models which have been widely used in various engineering fields. Some important properties of commensurate or a few particular kinds of non-commensurate elementary fractional-order transfer functions have already been discussed in the existing studies. However, most of them are only available for one particular kind elementary fractional-order system. In this paper, the stability and resonance analysis of a general kind non-commensurate elementary fractional-order system is presented. The commensurate-order restriction is fully released. Firstly, based on Nyquist’s Theorem, the stability conditions are explored in details under different conditions, namely different combinations of pseudo-damping (ζ) factor values and order parameters. Then, resonance conditions are established in terms of frequency behaviors. At last, an example is given to show the stable and resonant regions of the studied systems.

Transfer Function Modeling of Distributed Piezoelectric Vibration Energy Harvesters

2009 ◽  
Author(s):  
Chin An Tan ◽  
Heather L. Lai
Keyword(s):  
Transfer Function ◽  
Transfer Functions ◽  
Vibration Energy ◽  
System Response ◽  
Distributed Parameter ◽  
Domain Modeling ◽  
Vibration Energy Harvesting ◽  
Energy Harvesters ◽  
Adjoint Systems ◽  
The Stability

Extensive research has been conducted on vibration energy harvesting utilizing a distributed piezoelectric beam structure. A fundamental issue in the design of these harvesters is the understanding of the response of the beam to arbitrary external excitations (boundary excitations in most models). The modal analysis method has been the primary tool for evaluating the system response. However, a change in the model boundary conditions requires a reevaluation of the eigenfunctions in the series and information of higher-order dynamics may be lost in the truncation. In this paper, a frequency domain modeling approach based in the system transfer functions is proposed. The transfer function of a distributed parameter system contains all of the information required to predict the system spectrum, the system response under any initial and external disturbances, and the stability of the system response. The methodology proposed in this paper is valid for both self-adjoint and non-self-adjoint systems, and is useful for numerical computer coding and energy harvester design investigations. Examples will be discussed to demonstrate the effectiveness of this approach for designs of vibration energy harvesters.

Analysis of the Idling Start of the Moving Coil Linear Compressor

2008 ◽  
Author(s):  
Yingbai Xie ◽  
Xiuzhi Huang ◽  
Liyong Lun ◽  
Ganglei Sun
Keyword(s):  
Closed Loop ◽  
Transfer Functions ◽  
Load Condition ◽  
Open Loop ◽  
Reciprocating Compressor ◽  
Piston Motion ◽  
Linear Compressor ◽  
Simulation Results ◽  
The Stability ◽  
Stability Time

The linear compressor is driven by a linear motor. Because it has no crankcase, the piston motion and its control of the linear compressor are differing from that of the conventional reciprocating compressor. For a moving coil linear compressor, mechanical and electromagnetism system are modeled. The open loop and closed loop transfer functions of the system in no-load condition are obtained derived from these equations. The Matlab software is applied to analyze the stability, time domain and frequency domain of the system. Simulation results show that the linear compressor is stable, but the overshoot is relative high, which must be adjusted. This conclusion will be benefit for the design of the idling start of the moving coil linear compressor.

The Stability and Transfer Functions of Rail Vehicles

1975 ◽  
Vol 4 (2-3) ◽  
pp. 159-165
Author(s):  
LADISLAV RUS
Keyword(s):  
Transfer Functions ◽  
Rail Vehicles ◽  
The Stability

Disturbance Elimination of Buck-Converter with Resonant LPF via ILQ Servo-System

2014 ◽  
Vol 492 ◽  
pp. 493-498
Author(s):  
Shuhei Shiina ◽  
Sidshchadhaa Aumted ◽  
Hiroshi Takami
Keyword(s):  
Transfer Functions ◽  
Design Method ◽  
Servo System ◽  
State Equation ◽  
Buck Converter ◽  
Linear Quadratic ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Low Pass ◽  
The Stability

The proposed optimal control on the basis of both current and voltage of the buck-converter is designed to be based on Inverse Linear Quadratic (ILQ) design method with the resonant low pass filter, which eliminates the disturbance by appended disturbance compensator. The designed scheme is composed of the state equation, an optimal ILQ solution, the ILQ servo-system with the disturbance elimination, the optimal basic gain, the optimal condition, the transfer functions and the disturbance compensator. Our results show the proposed strategy is the stability and robust control and has been made to improve ILQ control for the disturbance elimination of the output response, which guarantees the optimal gains on the basis of polynomial pole assignment.

scholarly journals Frequency Weighted Discrete-Time Controller Order Reduction Using Bilinear Transformation

2011 ◽  
Vol 62 (1) ◽  
pp. 44-48 ◽  
Author(s):  
Paknosh Karimaghaee ◽  
Navid Noroozi
Keyword(s):  
Discrete Time ◽  
Closed Loop ◽  
Linear Time ◽  
Order Reduction ◽  
Bilinear Transformation ◽  
Reduced Order ◽  
Linear Time Invariant ◽  
The Stability ◽  
Controllability And Observability ◽  
Time Invariant

Frequency Weighted Discrete-Time Controller Order Reduction Using Bilinear TransformationThis paper addresses a new method for order reduction of linear time invariant discrete-time controller. This method leads to a new algorithm for controller reduction when a discrete time controller is used to control a continuous time plant. In this algorithm, at first, a full order controller is designed ins-plane. Then, bilinear transformation is applied to map the closed loop system toz-plane. Next, new closed loop controllability and observability grammians are calculated inz-plane. Finally, balanced truncation idea is used to reduce the order of controller. The stability property of the reduced order controller is discussed. To verify the effectiveness of our method, a reduced controller is designed for four discs system.

scholarly journals On the Essential Instabilities Caused by Fractional-Order Transfer Functions

2008 ◽  
Vol 2008 ◽  
pp. 1-13 ◽  
Author(s):  
Farshad Merrikh-Bayat ◽  
Masoud Karimi-Ghartemani
Keyword(s):  
Transfer Function ◽  
Fractional Order ◽  
Characteristic Equation ◽  
Stability Condition ◽  
Transfer Functions ◽  
Branch Points ◽  
The Stability ◽  
Unstable Branch

The exact stability condition for certain class of fractional-order (multivalued) transfer functions is presented. Unlike the conventional case that the stability is directly studied by investigating the poles of the transfer function, in the systems under consideration, the branch points must also come into account as another kind of singularities. It is shown that a multivalued transfer function can behave unstably because of the numerator term while it has no unstable poles. So, in this case, not only the characteristic equation but the numerator term is of significant importance. In this manner, a family of unstable fractional-order transfer functions is introduced which exhibit essential instabilities, that is, those which cannot be removed by feedback. Two illustrative examples are presented; the transfer function of which has no unstable poles but the instability occurred because of the unstable branch points of the numerator term. The effect of unstable branch points is studied and simulations are presented.

Modeling Support Effects: Finite Element and Experimental Modal Methods

1996 ◽  
Author(s):  
Jonathan R. Buckles ◽  
Keith E. Rouch ◽  
John R. Baker
Keyword(s):  
Finite Element ◽  
High Speed ◽  
Transfer Functions ◽  
Coupling Effects ◽  
Support Effects ◽  
Critical Speeds ◽  
Modal Data ◽  
The Stability ◽  
Direct Use ◽  
Reduced Matrices

The effects of support/foundation dynamics are often significant in high speed turbomachinery, and can affect the stability and response to unbalance. In some cases additional critical speeds are introduced, related to resonances in the foundation or interaction with rotor resonances of foundation resonances. This paper reviews several methods for representing these effects, including (1) reduced matrices from finite element substructures (ANSYS, for example), (2) matrices generated from modal data, and (3) direct use of experimental transfer functions. These methods are implemented in a finite element rotor program in a PC-DOS environment. The application of the methods to two laboratory rotor configurations described and results presented. Situations with a foundation resonance above and near the rotor critical are included. The importance of including coupling effects between supports is shown.

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