A Stability Model for Flexible Rotors With Magnetic Bearings

1992 ◽  
Vol 114 (1) ◽  
pp. 172-175 ◽  
Author(s):  
E. H. Maslen ◽  
J. R. Bielk
Keyword(s):  
Computer Software ◽  
Magnetic Bearing ◽  
System Stability ◽  
Matrix Differential Equation ◽  
Linear Modeling ◽  
Substantial Impact ◽  
First Order ◽  
Flexible Rotors ◽  
Stability Model ◽  
Matrix Differential

A direct linear modeling scheme is described for magnetic bearing supported rotors. The model includes the effect of controller bandwidth as well as sensor-actuator noncollocation. These effects, commonly ignored in simpler formulations, can have substantial impact on system stability. Based on a first order matrix differential equation form, the model is very suitable for stability analysis using widely available computer software.

scholarly journals ON CONDITIONING FOR A GENERAL SYSTEM OF FOUR POINT BOUNDARY VALUE PROBLEMS

1996 ◽  
Vol 27 (3) ◽  
pp. 219-225
Author(s):  
M. S. N. MURTY
Keyword(s):  
Differential Equation ◽  
Fundamental Matrix ◽  
Close Relationships ◽  
General System ◽  
Point Boundary ◽  
Matrix Differential Equation ◽  
Growth Behaviour ◽  
First Order ◽  
Matrix Differential ◽  
The Stability

In this paper we investigate the close relationships between the stability constants and the growth behaviour of the fundamental matrix to the general FPBVP'S associated with the general first order matrix differential equation.

Rotor Dynamics of Flywheel Energy Storage Systems

1991 ◽  
Vol 113 (1) ◽  
pp. 11-18 ◽  
Author(s):  
C. P. Jayaraman ◽  
J. A. Kirk ◽  
D. K. Anand ◽  
M. Anjanappa
Keyword(s):  
Control Systems ◽  
Degrees Of Freedom ◽  
Magnetic Bearing ◽  
System Stability ◽  
Dynamic Equations ◽  
Dynamic Coupling ◽  
First Order ◽  
Torque Response ◽  
Resonance Frequencies ◽  
Computer Simulation Program

This paper deals with the dynamic analysis of the magnetic bearing stack system. The stack consists of a single flywheel supported by two magnetic bearings. To model the system, the dynamic equations of a magnetically suspended flywheel are derived. Next, the four control systems controlling the four degrees-of-freedom of the stack are incorporated into the model. The resulting dynamic equations are represented as first-order differential equations in a matrix form. A computer simulation program was then used to simulate the working of the magnetic bearing stack. Real time plots from the simulation are used to show the effect of dynamic coupling on torque response. Frequency response is used to determine the resonance frequencies of the stack system. It is found that system stability depends on flywheel speed. On the basis of the above results suggestions are made to improve stability and allow the stack to be spun beyond 60,000 rpm.

scholarly journals Stability Analysis of Linear Sylvester System of First Order Differential Equations

2020 ◽  
Vol 9 (11) ◽  
pp. 25252-25259
Author(s):  
Kasi Viswanadh V. Kanuri ◽  
SriRam Bhagavathula ◽  
K.N. Murty
Keyword(s):  
Differential Equation ◽  
Stability Analysis ◽  
Differential Equations ◽  
Stability Criteria ◽  
Matrix Differential Equation ◽  
Bounded Solutions ◽  
First Order ◽  
Matrix Differential ◽  
First Order Differential Equations

    In this paper, we establish stability criteria of the linear Sylvester system of matrix differential equation using the new concept of bounded solutions and deduce the existence of -bounded solutions as a particular case.

Oscillation Criteria for Matrix Differential Equations

1967 ◽  
Vol 19 ◽  
pp. 184-199 ◽  
Author(s):  
H. C. Howard
Keyword(s):  
Existence Theorems ◽  
Symmetric Matrix ◽  
Order System ◽  
Matrix Differential Equation ◽  
First Order ◽  
The Matrix ◽  
Matrix Differential Equations ◽  
Matrix Differential ◽  
Image Position

We shall be concerned at first with some properties of the solutions of the matrix differential equation1.1whereis an n × n symmetric matrix whose elements are continuous real-valued functions for 0 < x < ∞, and Y(x) = (yij(x)), Y″(x) = (y″ ij(x)) are n × n matrices. It is clear such equations possess solutions for 0 < x < ∞, since one can reduce them to a first-order system and then apply known existence theorems (6, Chapter 1).

scholarly journals Sliding Mode Control of Magnetic Bearings: a Hardware Perspective

1999 ◽  
Author(s):  
Eric Maslen ◽  
Dominick Montie
Keyword(s):  
Sliding Mode Control ◽  
High Speed ◽  
Sliding Mode ◽  
Magnetic Bearing ◽  
Strong Impact ◽  
Substantial Impact ◽  
Mode Control ◽  
Flexible Rotors ◽  
State Observers ◽  
Linear State

The physical hardware of magnetic bearing systems has a very strong impact on the application of sliding mode control to this technology. Finite current slew rates affect the character of achievable reaching conditions; flexible rotors demand the use of state observers which then affect achievable robustness; finite controller throughput and use of switching power amplifiers has substantial impact on how chatter should be addressed. This paper formulates the sliding mode control problem for realistic rotor/magnetic actuator systems considering rotor flexibility and finite amplifier voltages. The structure of the resulting class of controllers is examined for both rigid and for flexible rotors. It is demonstrated that, fundamentally, these controllers are conventional linear state observer based controllers acting through high speed switching amplifiers as in conventional magnetic bearing technology.

Sliding Mode Control of Magnetic Bearings: A Hardware Perspective

1999 ◽  
Vol 123 (4) ◽  
pp. 878-885 ◽  
Author(s):  
E. Maslen ◽  
D. Montie
Keyword(s):  
Sliding Mode Control ◽  
High Speed ◽  
Sliding Mode ◽  
Magnetic Bearing ◽  
Strong Impact ◽  
Substantial Impact ◽  
Mode Control ◽  
Flexible Rotors ◽  
State Observers ◽  
Linear State

The physical hardware of magnetic bearing systems has a very strong impact on the application of sliding mode control to this technology. Finite current slew rates affect the character of achievable reaching conditions; flexible rotors demand the use of state observers which then affect achievable robustness; finite controller throughput and use of switching power amplifiers has substantial impact on how chatter should be addressed. This paper formulates the sliding mode control problem for realistic rotor/magnetic actuator systems considering rotor flexibility and finite amplifier voltages. The structure of the resulting class of controllers is examined for both rigid and for flexible rotors. It is demonstrated that, fundamentally, these controllers are conventional linear state observer-based controllers acting through high-speed switching amplifiers as in conventional magnetic bearing technology.

scholarly journals Thermal Disturbances in Twinned Orthotropic Thermoelastic Material

2018 ◽  
Vol 23 (4) ◽  
pp. 897-910 ◽  
Author(s):  
L. Rani ◽  
V. Singh
Keyword(s):  
Fourier Transforms ◽  
Crystallographic Axis ◽  
Physical Domain ◽  
Matrix Differential Equation ◽  
Special Cases ◽  
Eigen Value ◽  
Basic Equations ◽  
Matrix Differential ◽  
Thermally Conducting ◽  
Vector Matrix

Abstract This paper deals with deformation in homogeneous, thermally conducting, single-crystal orthotropic twins, bounded symmetrically along a plane containing only one common crystallographic axis. The Fourier transforms technique is applied to basic equations to form a vector matrix differential equation, which is then solved by the eigen value approach. The solution obtained is applied to specific problems of an orthotropic twin crystal subjected to triangular loading. The components of displacement, stresses and temperature distribution so obtained in the physical domain are computed numerically. A numerical inversion technique has been used to obtain the components in the physical domain. Particular cases as quasi-static thermo-elastic and static thermoelastic as well as special cases are also discussed in the context of the problem.

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