Handbook for the Direct Statistical Analysis of Missile Guidance Systems via CADET (Trademark) (Covariance Analysis Describing Function Technique)

1975 ◽  
Author(s):  
James H. Taylor
Keyword(s):  
Statistical Analysis ◽  
Covariance Analysis ◽  
Function Technique ◽  
Missile Guidance ◽  
Describing Function ◽  
Guidance Systems

A new direct statistical analysis of nonlinear systems: CAUTDET

2017 ◽  
Vol 233 (1) ◽  
pp. 382-389
Author(s):  
Hong-Xia Li ◽  
Hui-Jie Li ◽  
Yuan-Li Cai
Keyword(s):  
Nonlinear System ◽  
System Analysis ◽  
Covariance Analysis ◽  
Function Technique ◽  
Analysis Method ◽  
Describing Function ◽  
Analysis Problem ◽  
Unscented Transform ◽  
Time Calculation ◽  
System Input

This paper investigates the nonlinear system analysis problem for achieving higher computational efficiency and accuracy. A novel and efficient technique, covariance analysis unscented transform describing function technique (CAUTDET), is proposed. This method combines linear system covariance analysis algorithm with describing function method based on unscented transform. Furthermore, the quasi-linearization of the nonlinear system are derived to approximate the nonlinearity, while there is no requirement of the probability density function of the nonlinear system input and needs only one time calculation. Moreover, the proposed technique can be viewed as a generalization method of the nonlinear system design and analysis. Finally, simulations are presented to illustrate the effectiveness of the presented analysis method.

Integrating Accessible Multiplication Games into Inclusive Classrooms

2012 ◽  
pp. 273-292
Author(s):  
Cindy L. Anderson
Keyword(s):  
Elementary School ◽  
Statistical Analysis ◽  
School District ◽  
Universal Design ◽  
Fourth Grade ◽  
Inclusive Classrooms ◽  
Covariance Analysis ◽  
Analysis Of Covariance ◽  
Elementary School District ◽  
Multiplication Facts

Two accessible games were the focus of a study involving inclusive fourth grade classrooms in a suburban Chicago elementary school district. The games were created using software with universal design capability and were designed to teach multiplication facts. Data were collected that compared the classes using the software with classes that did not use the software. The statistical analysis used in the design of the study was analysis of covariance using a pretest assessment of multiplication facts as the covariate. Students used the games twice a week for four weeks during a period of 40 minutes a day. Results indicated a gain in accuracy of multiplication facts on the part of the groups using the games, but not enough to demonstrate significance. In addition to the analysis of covariance analysis, selected classes filled out surveys designed to measure the students’ opinions of the games and their effectiveness. Results of the surveys indicated that the students were somewhat unsure about their effectiveness as a tool to learn multiplication facts but found them enjoyable to play. Interpretation of both of these results is provided.

Vehicle-Follower Longitudinal Control for Automated Transit Vehicles

1977 ◽  
Vol 99 (4) ◽  
pp. 241-248 ◽  
Author(s):  
R. J. Caudill ◽  
W. L. Garrard
Keyword(s):  
Steady State ◽  
Function Technique ◽  
Steady State Response ◽  
Describing Function ◽  
Transient Responses ◽  
Longitudinal Control ◽  
Transit Systems ◽  
State Response ◽  
Acceleration And Deceleration ◽  
And Control

This paper examines the effects of spacing policy and control system nonlinearities on the dynamic response of strings of automated transit vehicles operating under automatic velocity and spacing control. Both steady-state and transient responses are studied. Steady-state response is examined by a modification of the describing function technique and transient response is studied by Liapunov procedures. It is shown that a nonlinearity commonly encountered in automated transit vehicles, a limiter on acceleration and deceleration, can result in string instabilities even though a linearized analysis indicates that the string is stable. Although this paper is specifically focused on automated transit systems, some of the results obtained also appear to be applicable to strings of automobiles on freeways.

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