**1. Introduction**

294 Serial and Parallel Robot Manipulators – Kinematics, Dynamics, Control and Optimization

J. D. L. Ree and N. Boules, "Torque production in permanent-magnet synchronous motors,"

J. R. Hendershot and T. J. E. Miller, "Design of Brushless Permanent-Magnet Motors (1995),"

M. Aydin, M. K. Guven, S. Han, T. M. Jahns and W. L. Soong, "Integrated Design Process

N. Bianchi and S. Bolognani, "Design Techniques for Reducing the Cogging Torque in

T. Sebastian, G. R. Slemon and M. A. Rahman, "Design considerations for variable speed

T.Li, and G. Slemon, "Reduction of cogging torque in PM motors," *IEEE Trans. Magnetics*,

Thomas M. Jahns and Wen L. Soong, "Pulsating Torque Minimization Techniques for

and Experimental Verification of a 50 kW Interior Permanent Magnet Synchronous Machine", *17th International Conference on Electrical Machines (ICEM 06)*, Crete,

Surface-Mounted PM Motors", *IEEE Transactions on Industry Applications*, Vol. 38,

permanent magnet motors", *Proceedings of International Conference on Electrical* 

Permanent Magnet AC Motor Drives-A Review", *IEEE Transactions on Industry* 

*IEEE Trans. Industry Applications*, vol. 25, no. 1, pp. 107-112, 1989.

Oxford University Press, ISBN 0198593899, UK.

Greece, 2006.

Motor-CAD v3.1 software manual, April 2006.

No. 5, September/October 2002.

*Machines (ICEM)* 1986, pp.1099-1102.

vol. 24, no. 6, pp 2901-2903, 1988.

SPEED Software, PC-BDC 9.04 User's Manual, February 2010.

*Applications*, pp. Vol. 43, No. 2, April 1996.

Wiener process, as a special mathematical model of Brownian motions, has been investigated and modelling in many probabilistic examples. In the topic literature it is easy to find many procedures of numeric probabilistic simulations of the Wiener process. Fuzzy modelling does not give us more accurate models than probabilistic modelling. Fuzzy knowledge-based modelling allows to determine linguistic description of non-precise relationships between variables and to derive the reasoning procedure from non-crisp facts. More over, using the notions of probabilities of fuzzy events, it is possible to determine a frequency of a conclusion as well as its expected value.

Wiener process and a random walk are very often used for modelling phenomena in physics, engineering and economy. In the area of robot control theory these processes can represent some time-varying parameters of the environments where the object of control operates. Fuzzy models of these processes can constitute a part of a fuzzy model of a tested complex system.

In paragraph 2. of this chapter, the mathematical descriptions of Brownian motions has been reminded, according to the theory of probability and stochastic processes. Some basics of fuzzy modelling has been presented in paragraph 3., to show the method of creating the knowledge base and rules of reasoning. Attention is focused on identification techniques for building empirical probabilities of fuzzy events from input-output data. Exemplary calculations of knowledge bases for real stochastic processes, as well as, some remarks on future works have been presented in paragraphs 4 and 5.
