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Recent Developments of Electrical Drives - Part 10

Recent Developments of Electrical Drives - Part 10. The book stating the recent developments of electrical drives, can be useful for engineers and researchers investigating and designing electrical and electronic devices as well as for students and young researchers dealing with electrical and electronic engineering, computer sciences (advanced computer modelling, sophisticated control systems with artificial intelligence tools applied, optimal design bye use of classical and genetic algorithms employed), applied mathematics and all the topics where electromagnetic, thermal, mechanical phenomena occur | 76 Rembowski and Pelikant Figure 3. Generated meshes for the shit larger than one third of the air gap width. Taking into account the stator node with number j neighboring with nodes i and i 1 of the rotor mesh f the linear interpolation the equation for this node can be described as follows 5 Vj M - V Y - Vi 1 A0 - y 0 5 Where A0 is the angle between nodes with the numbers i and i 1 and y is the angle between the stator mesh node j and the rotor mesh node i. Figure 4. Part of the one level z const. of the mesh with the overlapping region parts of electrodes dashed dimensions enlarge symmetrical air gap. 77 I-7. Analysis of Electrostatic Microactuators Figure 5. Part of the one level z const. of the mesh with the overlapping region parts of electrodes dashed dimensions enlarge nonsymmetrical air gap. In the nonsymmetrical model nodes of the stator and the rotor meshes for overlapping bounds have different angle 0 and radius r Fig. 5 . The stator mesh node with number j neighbors with four nodes i i 1 i k and i k 1 of the rotor mesh. The equation describing the value of the potential in the j node can be written down using bilinear interpolation function in the following form 6 Vj Yi ri aoyiri aiY a i a3 6 Using equation 6 for each node at both boundaries outer for the rotor mesh and inner for the stator mesh one obtains sub matrix of main matrix M containing five nonzero elements for each row. As a result one gets nonsymmetrical system of linear equations which is solved using LDU decomposition method with permutation matrix 7 . M P L U P 7 Presented algorithm was implemented in a numerical program which allows determining a field distribution for every angular position of the rotor and every possible movement of its rotation axis. Integral parameters The application allows calculating integral parameters for every position of the rotor in particular the system energy that can be written down in general in form 8 W iii wdti if D dE dti Q Q 0 8 78 Rembowski and .