Application of the symplectic group in a novel branch of soft computing for controlling of electro-mechanical devices

An application of a special approach aiming at the development of a new branch of soft computing (SC) for the adaptive control of approximately and partially known electromechanical systems is reported. Like "traditional" SC it uses "uniform structures" for modeling, but these structures are obtained from the symplectic group (SG). This approach can considerably reduce the number of free parameters in the model in comparison e.g. with that of the neural networks or ample sets of fuzzy rules. It also replaces the process of parameter tuning with simple, lucid, and explicit algebraic operations of limited steps. While in the previous approaches SG was utilized as an inner symmetry of classical mechanical systems, in the present one it is used in a formal way not utilizing mechanical symmetries. Furthermore, SG is not the internal symmetry of electrical, that is of electro-mechanical systems. In the present paper the new formal approach is demonstrated in the adaptive control of a 3 mechanical DOF SCARA-type robot arm actuated by DC motors together forming a 6 DOF electromechanical system. It is concluded on the basis of simulations that the control designed for the 3 DOF mechanical degrees of freedom can efficiently compensate for the behavior of the electrical degrees of freedom not modeled by the controller.