Abstract
Due to the elasticity of the links in modern high speed mechanisms, increasing operating speeds often lead to undesirable vibrations, which may render a required accuracy unattainable or, even worse, lead to a failure of the whole process. The dynamic effects e.g. may lead to intolerable deviations from the reference path or even to the instability of the system. Instead of suppressing the vibration by a stiffer design, active control methods may greatly improve the system performance and lead the way to a reduction of the mechanism’s weight. We investigate a four-bar-linkage mechanism and show that by introducing an additional degree of freedom for a controlled actuator and providing a suitable control strategy, the dynamically induced inaccuracies can be substantially reduced. The modelling of the four-bar-linkage mechanism as a hybrid multi body system and the modelling of the complete system (including the actuator) is briefly explained. From the combined feedforward-feedback optimal control approach presented in (v. Stein, Ulbrich, 1998) a time-varying output control law is derived that leads to a very good system performance for this linear discrete time-varying system. The experimental results show the effectiveness of the applied control strategy.
On the existence of a solution for some distributed optimal control hyperbolic system
