Flatness Based Control of Linear and Nonlinear Systems

The property of flatness has become quite popular especially for the class of lumped parameter systems since its introduction about 20 years ago. Challenging design problems like planning of optimal trajectories, stabilization of equilibria or trajectories by state feedback are significantly easier to solve for flat systems than for non flat ones. E.g. two point boundary problems, which appear in trajectory planning or in optimal system design, simplify, and the stabilization problem, formulated in flat coordinates, can be solved by linear methods. This contribution presents a short introduction into flatness and related control loop design problems for the class of nonlinear lumped parameter systems and applies the presented theory to the design of time optimal trajectories for a single mast stacker crane.