Control of Weakly Damped Finite and Infinite Dimensional Euler-Lagrange Systems

This contribution presents the control of a certain kind of mechanical systems based on energy considerations. The plants under investigation are underactuated lumped and distributed parameter systems, which consist of two masses and an elastic element. After a brief introduction of the used mathematical objects, the proposed controller design method is applied to a simple introductory example - the Mass-Spring-Mass system. After that, an infinite dimensional system - the Mass-Beam-Mass system - is under consideration. In this case, the elastic element is given by a Bernoulli-Euler beam. Finally some simulation results demonstrate the improvements gained by the introduced control structure.