Assisted Analyze of the Extenics Dependent Functions in 1<i>D</i>, 2<i>D</i>, 3<i>D</i> and n<i>D</i> Dimensions with LabVIEW Instrumentation

Abstract

Assisted analyze of the Extenics dependent functions theory is necessary to study easily all influences of the current point in to the space of nR dimensions. The Extenics theory was defined by prof. Cai Wen in 1983 and his collaborators in the mathematical, philosophy and logical models [1-. This paper inspired from the Extenics theory try to transfer the mathematical formalism in to the virtual LabVIEW instrumentation what can be easily establish, by on-line calculus of the dependent functions, the affiliation of one class or interval in the nR dimensions and validate all Extenics conditions. The research established the complex field of the dependent functions, when the work point is inside, outside, symmetrical or asymmetrical position versus the optimal area. In the Extenics theory wasnt defined in this new form the nR dimensions. It is defined also in this paper the attraction field instead of the attraction point defined in [. The paper show the study case of the 2D and 3D dependent on-line functions with define finally the attraction field like the optimized place of the working point.

Assisted Methods for Optimization in Robotics

“…After applying the mathematical model of the Extenics dependent function for 2D dimension and increasing/ decreasing transformations were obtained some results, figs.3. The Extenics theory was accomplished with the proper remarks and concepts [9]. We remark that the partial solution is not singular inside of the minimal attraction field.…”

“…Some of the data must be increasing and other decreasing, finally defined the minimal working attraction field [9]. The other way of the research was to define different values of the factor.…”

“…In the proper research paper [9] was shown that the working point obtained by Extenics theory is formed by x coordinate of the precision limit point and y coordinate of the stability limit point, because the y coordinate determine the increasing of the proper frequency with effect to the increasing the precision and decreasing the stability and x determine the increasing of the damper factor with effect to the increasing of stability and decreasing the precision. In this case (partial solving case) the solution of the contradictory problem can be written in the following form …”

“…After applying the Extenics theory and the assisted determination of the dependent 2D formula for each of these points, we were obtained the results from (2). The applied values were determined by apply the logical Extenics theory with AND function between the goals and conditions matter-elements [9]. [19], [20].…”

“…The virtual instruments were achieved in the LabVIEW TM soft 8.2 from National Instruments, USA. The VI-s simulates the open and closed loop of the DC servo systems, and the data acquisition of the velocity and acceleration and generate the Fourier spectrum with the final goal to compare simulation results with the real results [4]- [9]. This method will be possible to be used in the assisted research of the many other mechanical applications where it is necessary to know the dynamic behavior, the vibration spectrum and how the constructive and functional parameters of the DC servo systems and the movements cases (the equilibrium of the robot's arm) determine the major changes of the spectrum and of the dynamic behavior.…”