Aufbau und Regelung des Labormodells Scheibe mit schwerer Kette

This master thesis treats systems with heavy chains, where on the one hand the chain is linearly-guided and on the other hand rotatory-guided. In terms of modelling the extended Hamilton principle is applied to obtain the equation of motion, where the systems are considered to be infinite-dimensional and, thus, are described by partial differential equations. For the simulation a finite-dimensional approximation is derived with the Rayleigh-Ritz method. The system with the rotatory-guided chain is constructed as a laboratory model. The parameters of the system are determined based upon measurement information and verified by simulation. As a control strategy for the laboratory model first a time-discrete time-invariant LQR control law is calculated for the special case of a rigid chain. As it is shown the control law does not lead to the desired results. Finally a finite-dimensional control law based on damping injection in combination with the backstepping method is created. It is worth mentioning that this controller rests upon the infinite-dimensional system description.