Observation-based data driven adaptive control of an electromechanical device

The model-based approach in control engineering works well when a reliable plant model is available. However, in practice, reliable models seldom exist: instead, typical “levels” of limited reliability occur. For instance, Computed Torque Control (CTC) in robotics assumes almost perfect models. The Adaptive Inverse Dynamics Controller (AIDC) and the Slotine Li Adaptive Robot Controller (SLARC) assume absolutely correct analytical model form, and only allows imprecise knowledge regarding the actual values of the model parameters. Neglecting the effects of dynamically coupled subsystems, and allowing the action of unknown external disturbances means a higher level of corrupted model reliability. Friction-related problems are typical examples of this case. In the traditional control literature, such problems are tackled by either drastic “robust” or rather intricate “adaptive” solutions, both designed by the use of Lyapunov´s 2^nd method that is a complicated technique requiring advanced mathematical skills from the designer. As an alternative design methodology, the use of Robust Fixed Point Transformations (RFPT) was suggested, which concentrates on guaranteeing the prescribed details of tracking error relaxation via generation of iterative control signal sequences that converge on the basis of Banach´s Fixed Point Theorem. This approach is essentially based on the fresh data collected by observing the behavior of the controlled systems, rather than in the case of the traditional ones. For the first time, this technique is applied for order reduction in the adaptive control of a strongly nonlinear plant with significant model imprecisions: the control of a DC motor driven arm in dynamic interaction with a nonlinear environment is demonstrated via numerical simulations