Rotordynamic Analysis Using the Complex Transfer Matrix

2012 ◽  
Author(s):  
Philip Varney ◽  
Itzhak Green
Keyword(s):  
Reference Frame ◽  
Transfer Matrix ◽  
Reference Frames ◽  
Detection System ◽  
Numerical Technique ◽  
External Support ◽  
Starting Point ◽  
Rotating Reference Frame ◽  
Rotating Reference Frames ◽  
Lumped Masses

The transfer matrix method is an expedient numerical technique for determining the dynamic behavior of a rotordynamic system (e.g., whirl frequencies, steady-state response to forcing). The typical 8 × 8 transfer matrix suffers from several deficiencies. First, for a system incorporating damping, the method generates a characteristic polynomial of degree 8N for a model of N lumped masses (degree 4N for an undamped model). The high degree of the polynomial results in lengthy computation times and decreased accuracy. Second, as discussed herein, the 8 × 8 formulation fails to distinguish between forward and backward whirl. These deficiencies are overcome by a novel complex-valued state variable redefinition resulting in a 4×4 transfer matrix including external support stiffness and damping. The complex transfer matrix is then modified to account for analysis within a rotating reference frame. Analysis in a rotating reference frame is a judicious means to determine unique system fault characteristics, which serve as a starting point for the development of an on-line fault detection system. Insights into using the complex transfer matrix in a rotating reference frame are discussed. Analytical results in both inertial and rotating reference frames for an overhung rotor model are provided.

scholarly journals Dual Sequence Controller with Delayed Signal Cancellation in the Rotating Reference Frame

2021 ◽  
Author(s):  
Daniel Mota ◽  
Erick Alves ◽  
Elisabetta Tedeschi
Keyword(s):  
Reference Frame ◽  
Reference Frames ◽  
Formal Proof ◽  
Voltage Source ◽  
Phase Measurements ◽  
Current Controller ◽  
Signal Cancellation ◽  
Rotating Reference Frames ◽  
Dsc Method ◽  
Dual Sequence

Manuscript submitted to the Twenty-second IEEE Workshop on Control and Modeling for Power Electronics (COMPEL 2021).<div>Abstract: Dual-sequence current controllers of voltage source converters (VSCs) feature two separate rotating reference frames (RRFs), commonly named dq frames, and rely on techniques that isolate the positive and negative sequences of three-phase measurements. One of these techniques is the delayed signal cancellation (DSC). It is performed in the stationary reference frame (SRF), also known as αβ frame. The DSC combines old values of one axis with new values of the other axis of the SRF. The results are, then, transformed into the RRFs for use in the current controller. This filtering process introduces an extra layer of complexity for dual-sequence current controllers, which could otherwise operate solely in the RRFs. This paper introduces a frequency adaptive DSC method that operates directly in the RRF. Moreover, an averaging of two of the proposed DSC filters with contiguous integer delays is employed for reducing discretization errors caused by grid frequency excursions. A formal proof of the equivalence between the αβ and dq DSC methods is presented. Furthermore, computer simulations of a case study support the interpretation of the results.</div>

scholarly journals Dual Sequence Controller with Delayed Signal Cancellation in the Rotating Reference Frame

2021 ◽  
Author(s):  
Daniel Mota ◽  
Erick Alves ◽  
Elisabetta Tedeschi
Keyword(s):  
Reference Frame ◽  
Reference Frames ◽  
Formal Proof ◽  
Voltage Source ◽  
Phase Measurements ◽  
Current Controller ◽  
Signal Cancellation ◽  
Rotating Reference Frames ◽  
Dsc Method ◽  
Dual Sequence

Manuscript submitted to the Twenty-second IEEE Workshop on Control and Modeling for Power Electronics (COMPEL 2021).<div>Abstract: Dual-sequence current controllers of voltage source converters (VSCs) feature two separate rotating reference frames (RRFs), commonly named dq frames, and rely on techniques that isolate the positive and negative sequences of three-phase measurements. One of these techniques is the delayed signal cancellation (DSC). It is performed in the stationary reference frame (SRF), also known as αβ frame. The DSC combines old values of one axis with new values of the other axis of the SRF. The results are, then, transformed into the RRFs for use in the current controller. This filtering process introduces an extra layer of complexity for dual-sequence current controllers, which could otherwise operate solely in the RRFs. This paper introduces a frequency adaptive DSC method that operates directly in the RRF. Moreover, an averaging of two of the proposed DSC filters with contiguous integer delays is employed for reducing discretization errors caused by grid frequency excursions. A formal proof of the equivalence between the αβ and dq DSC methods is presented. Furthermore, computer simulations of a case study support the interpretation of the results.</div>

Idealisation and Formulation in Structural Dynamics Using Modal Analysis

2011 ◽  
Vol 418-420 ◽  
pp. 1022-1025
Author(s):  
Muhammad Danish ◽  
Vinay Kumar Pingali ◽  
Somnath Chattopadhyaya ◽  
N.K. Singh ◽  
A.K. Ray
Keyword(s):  
Reference Frame ◽  
Structural Dynamics ◽  
Reference Frames ◽  
Dynamic Equilibrium ◽  
Equations Of Motion ◽  
Complex Structure ◽  
Complicated Structure ◽  
Multiple Reference Frames ◽  
Lumped Masses ◽  
Multiple Reference

The crux feature of this paper is the equations of motion in a structural dynamics with respect to single reference frame that can be easily derived, and the results are well defined and converged. However, problem occurs, when the analysis of any complex, complicated structure is considered and its equation of motion is extracted with respect to single reference frame. The results are indecipherable, ambiguous and less converged. Thus, for such a complex structure, the results obtain with respect to multiple reference frames. In present study, an approximated model with a set of lumped masses, properly interconnected, along with discrete spring and damper elements are in consideration for continuous vibrating system. This results in dynamic equilibrium, which in turn results in formulation and idealization. As, rightly said by scientist Steve Lacy- “To me, there is spirit in a reed. It is a living thing, a weed, really and it does not contain spirit of sort. It’s really an ancient vibration”

scholarly journals Reality in a few thermodynamic reference frames: Statistical thermodynamics from Boltzmann via Gibbs to Einstein

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Reference Frame ◽  
Reference Frames ◽  
Statistical Thermodynamics ◽  
Statistical Thermodynamic ◽  
Scientific Theories ◽  
Common Space ◽  
Starting Point ◽  
The Subject ◽  
The Many ◽  
Selection Of

The success of a few theories in statistical thermodynamics can be correlated with their selectivity to reality. These are the theories of Boltzmann, Gibbs, end Einstein.The starting point is Carnot’s theory, which defines implicitly the general selection of reality relevant to thermodynamics. The three other theories share this selection, but specify it further in detail. Each of them separates a few main aspects within the scope of the implicit thermodynamic reality. Their success grounds on that selection. Those aspects can be represented by corresponding oppositions. These are: macroscopic – microscopic; elements – states; relational – non-relational; and observable – theoretical. They can be interpreted as axes of independent qualities constituting a common qualitative reference frame shared by those theories. Each of them can be situated in this reference frame occupying a different place. This reference frame can be interpreted as an additional selection of reality within Carnot’s initial selection describable as macroscopic and both observable and theoretical. The deduced reference frame refers implicitly to many scientific theories independent of their subject therefore defining a general and common space or subspace for scientific theories (not for all).The immediate conclusion is: The examples of a few statistical thermodynamic theories demonstrate that the concept of “reality” is changed or generalized, or even exemplified (i.e. “de-generalized”) from a theory to another.Still a few more general suggestions referring the scientific realism debate can be added: One can admit that reality in scientific theories is some partially shared common qualitative space or subspace describable by relevant oppositions and rather independent of their subject quite different in general. Many or maybe all theories can be situated in that space of reality, which should develop adding new dimensions in it for still newer and newer theories. Its division of independent subspaces can represent the many-realities conception. The subject of a theory determines some relevant subspace of reality. This represents a selection within reality, relevant to the theory in question. The success of that theory correlates essentially with the selection within reality, relevant to its subject.

Allocentric to Egocentric Spatial Switching: Impairment in aMCI and Alzheimer's Disease Patients?

2018 ◽  
Vol 15 (3) ◽  
pp. 229-236 ◽  
Author(s):  
Gennaro Ruggiero ◽  
Alessandro Iavarone ◽  
Tina Iachini
Keyword(s):  
Alzheimer’S Disease ◽  
Alzheimer's Disease ◽  
Reference Frame ◽  
Reference Frames ◽  
Memory Task ◽  
Spatial Representations ◽  
The Novel ◽  
Spatial Memory Task ◽  
Switching Condition ◽  
Normal Controls

Objective: Deficits in egocentric (subject-to-object) and allocentric (object-to-object) spatial representations, with a mainly allocentric impairment, characterize the first stages of the Alzheimer's disease (AD). Methods: To identify early cognitive signs of AD conversion, some studies focused on amnestic-Mild Cognitive Impairment (aMCI) by reporting alterations in both reference frames, especially the allocentric ones. However, spatial environments in which we move need the cooperation of both reference frames. Such cooperating processes imply that we constantly switch from allocentric to egocentric frames and vice versa. This raises the question of whether alterations of switching abilities might also characterize an early cognitive marker of AD, potentially suitable to detect the conversion from aMCI to dementia. Here, we compared AD and aMCI patients with Normal Controls (NC) on the Ego-Allo- Switching spatial memory task. The task assessed the capacity to use switching (Ego-Allo, Allo-Ego) and non-switching (Ego-Ego, Allo-Allo) verbal judgments about relative distances between memorized stimuli. Results: The novel finding of this study is the neat impairment shown by aMCI and AD in switching from allocentric to egocentric reference frames. Interestingly, in aMCI when the first reference frame was egocentric, the allocentric deficit appeared attenuated. Conclusion: This led us to conclude that allocentric deficits are not always clinically detectable in aMCI since the impairments could be masked when the first reference frame was body-centred. Alongside, AD and aMCI also revealed allocentric deficits in the non-switching condition. These findings suggest that switching alterations would emerge from impairments in hippocampal and posteromedial areas and from concurrent dysregulations in the locus coeruleus-noradrenaline system or pre-frontal cortex.

scholarly journals Reference frames in spatial communication for navigation and sports: an empirical study in ultimate frisbee players

2020 ◽  
Vol 5 (1) ◽  
Author(s):  
Steven M. Weisberg ◽  
Anjan Chatterjee
Keyword(s):  
Reference Frame ◽  
Reference Frames ◽  
Spatial Information ◽  
Spatial Reference ◽  
Spatial Reference Frames ◽  
The North ◽  
Communication Task ◽  
Spatial Communication ◽  
Spatial Domains ◽  
Ultimate Frisbee

Abstract Background Reference frames ground spatial communication by mapping ambiguous language (for example, navigation: “to the left”) to properties of the speaker (using a Relative reference frame: “to my left”) or the world (Absolute reference frame: “to the north”). People’s preferences for reference frame vary depending on factors like their culture, the specific task in which they are engaged, and differences among individuals. Although most people are proficient with both reference frames, it is unknown whether preference for reference frames is stable within people or varies based on the specific spatial domain. These alternatives are difficult to adjudicate because navigation is one of few spatial domains that can be naturally solved using multiple reference frames. That is, while spatial navigation directions can be specified using Absolute or Relative reference frames (“go north” vs “go left”), other spatial domains predominantly use Relative reference frames. Here, we used two domains to test the stability of reference frame preference: one based on navigating a four-way intersection; and the other based on the sport of ultimate frisbee. We recruited 58 ultimate frisbee players to complete an online experiment. We measured reaction time and accuracy while participants solved spatial problems in each domain using verbal prompts containing either Relative or Absolute reference frames. Details of the task in both domains were kept as similar as possible while remaining ecologically plausible so that reference frame preference could emerge. Results We pre-registered a prediction that participants would be faster using their preferred reference frame type and that this advantage would correlate across domains; we did not find such a correlation. Instead, the data reveal that people use distinct reference frames in each domain. Conclusion This experiment reveals that spatial reference frame types are not stable and may be differentially suited to specific domains. This finding has broad implications for communicating spatial information by offering an important consideration for how spatial reference frames are used in communication: task constraints may affect reference frame choice as much as individual factors or culture.

OBSERVATION OF THE TRANSVERSE STERN–GERLACH EFFECT IN NEUTRAL POTASSIUM

1967 ◽  
Vol 45 (4) ◽  
pp. 1481-1495 ◽  
Author(s):  
Myer Bloom ◽  
Eric Enga ◽  
Hin Lew
Keyword(s):  
Magnetic Field ◽  
Angular Velocity ◽  
Reference Frame ◽  
Inhomogeneous Magnetic Field ◽  
Time Dependent ◽  
Effective Magnetic Field ◽  
Classical Analysis ◽  
At Resonance ◽  
Rotating Reference Frame

A successful transverse Stern–Gerlach experiment has been performed, using a beam of neutral potassium atoms and an inhomogeneous time-dependent magnetic field of the form[Formula: see text]A classical analysis of the Stern–Gerlach experiment is given for a rotating inhomogeneous magnetic field. In general, when space quantization is achieved, the spins are quantized along the effective magnetic field in the reference frame rotating with angular velocity ω about the z axis. For ω = 0, the direction of quantization is the z axis (conventional Stern–Gerlach experiment), while at resonance (ω = −γH0) the direction of quantization is the x axis in the rotating reference frame (transverse Stern–Gerlach experiment). The experiment, which was performed at 7.2 Mc, is described in detail.

Sign in / Sign up

Export Citation Format

Share Document