Luminescence lifetime measurements. Elimination of phototube time shifts with the phase plane method

1985 ◽  
Vol 57 (12) ◽  
pp. 2304-2308 ◽  
Author(s):  
E. R. Carraway ◽  
B. L. Hauenstein ◽  
J. N. Demas ◽  
B. A. DeGraff
Keyword(s):  
Phase Plane ◽  
Luminescence Lifetime ◽  
Lifetime Measurements ◽  
Plane Method ◽  
Phase Plane Method

Analysis and Synthesis of a Fuzzy Controller by the Phase Plane Method

2021 ◽  
Vol 22 (10) ◽  
pp. 507-517
Author(s):  
Y. A. Bykovtsev
Keyword(s):  
Control System ◽  
Automatic Control ◽  
Automatic Control System ◽  
Phase Plane ◽  
Fuzzy Controller ◽  
Piecewise Linear ◽  
Plane Method ◽  
Phase Trajectories ◽  
Analysis And Synthesis ◽  
Phase Plane Method

The article is devoted to solving the problem of analysis and synthesis of a control system with a fuzzy controller by the phase plane method. The nonlinear transformation, built according to the Sugeno fuzzy model, is approximated by a piecewise linear characteristic consisting of three sections: two piecewise linear and one piecewise constant. This approach allows us to restrict ourselves to three sheets of phase trajectories, each of which is constructed on the basis of a second-order differential equation. Taking this feature into account, the technique of "stitching" of three sheets of phase trajectories is considered and an analytical base is obtained that allows one to determine the conditions for "stitching" of phase trajectories for various variants of piecewise-linear approximation of the characteristics of a fuzzy controller. In view of the specificity of the approximated model of the fuzzy controller used, useful analytical relations are given, with the help of which it is possible to calculate the time of motion of the representing point for each section with the involvement of the numerical optimization apparatus. For a variant of the approximation of three sections, a technique for synthesizing a fuzzy controller is proposed, according to which the range of parameters and the range of input signals are determined, at which an aperiodic process and a given control time are provided. On the model of the automatic control system of the drive level of the mechatronic module, it is shown that the study of a fuzzy system by such an approximated characteristic of a fuzzy controller gives quite reliable results. The conducted studies of the influence of the degree of approximation on the quality of control show that the approximated characteristic of a fuzzy controller gives a slight deterioration in quality in comparison with the smooth characteristic of a fuzzy controller. Since the capabilities of the phase plane method are limited to the 2nd order of the linear part of the automatic control system, the influence of the third order on the dynamics of the system is considered using the example of a mechatronic module drive. It is shown that taking into account the electric time constant leads to overshoot within 5-10 %. Such overshoot can be eliminated due to the proposed recommendations for correcting the static characteristic of the fuzzy controller.

Surge Tank Stability by Phase Plane Method

1971 ◽  
Vol 97 (4) ◽  
pp. 489-503
Author(s):  
M. Hanif Chaudhry ◽  
Eugen Ruus
Keyword(s):  
Phase Plane ◽  
Surge Tank ◽  
Plane Method ◽  
Phase Plane Method

scholarly journals Yaw controller design of stratospheric airship based on phase plane method

2016 ◽  
Vol 29 (3) ◽  
pp. 738-745 ◽  
Author(s):  
Jinggang Miao ◽  
Jianghua Zhou ◽  
Ying Nie ◽  
Xin Yang
Keyword(s):  
Phase Plane ◽  
Controller Design ◽  
Plane Method ◽  
Stratospheric Airship ◽  
Phase Plane Method
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