A Lorentz-group based adaptive control for electro-mechanical systems

An efficient approach for the adaptive control of approximately and partially known mechanical systems, like traditional soft computing, uses "uniform structures" for modeling, but these structures are obtained from certain Lie groups as the symplectic group or the generalized Lorentz group. This approach considerably reduces the number of free parameters in the model. Until now its efficiency was investigated for mechanical uncertainties and external dynamic interactions. In this paper the behavior of the electric drives are also included in the investigations. A 1-DOF mechanical system, a pendulum driven by a DC motor in a computed torque control, is investigated via simulation. The necessary torque is calculated from a formal primitive mechanical model and an adaptivity rule. For adaptivity real number scaling and the generalized Lorentz group elements are used. It is concluded that a single adaptive loop can compensate for the mechanical and the electrical uncertainties simultaneously