Phase-plane method for solving one-dimensional stationary problems of radiation gas dynamics

1972 ◽  
Vol 7 (1) ◽  
pp. 131-141
Author(s):  
V. V. Aleksandrov
Keyword(s):  
Gas Dynamics ◽  
Phase Plane ◽  
Plane Method ◽  
One Dimensional ◽  
Phase Plane Method ◽  
Stationary Problems ◽  
Radiation Gas Dynamics

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

Phase plane analysis of left ventricular hemodynamics

2001 ◽  
Vol 90 (6) ◽  
pp. 2238-2244 ◽  
Author(s):  
Stephanie A. Eucker ◽  
Jennifer B. Lisauskas ◽  
Jasvindar Singh ◽  
Sándor J. Kovács
Keyword(s):  
Ventricular Function ◽  
Phase Plane ◽  
Pressure Rise ◽  
Left Ventricular ◽  
Time Dependent ◽  
Phase Plane Analysis ◽  
Plane Method ◽  
Plane Analysis ◽  
Pressure Contour ◽  
Phase Plane Method

We sought to extract additional physiological information from the time-dependent left ventricular (LV) pressure contour and thereby gain new insights into ventricular function. We used phase plane analysis to characterize high-fidelity pressure data in selected subjects undergoing elective cardiac catheterization. The standard hemodynamic indexes of LV systolic and diastolic function derived from the time-dependent LV pressure contour could be easily obtained using the phase plane method. Additional novel attributes of the phase plane pressure loop, such as phase plane pressure loop area, graphical representation of the isovolumic relaxation time constant, and quantitative measures of beat-to-beat systolic-diastolic coupling were characterized. The asymmetry between the pressures at which maximum isovolumic pressure rise and pressure fall occur, as well as their load dependence, were also easily quantitated. These results indicate that the phase plane method provides a novel window for physiological discovery and has theoretical and applied advantages in quantitative ventricular function characterization.

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