Analysis and synthesis of underactuated non-minimum phase systems: the inverted pendulum on a cart case

The following dissertation aims to make a thorough analysis and study of the inverted pendulum on a cart. This apparently simple system is largely used in the control field as a benchmarking problem in order to test new control techniques. First of all, an analysis of the system in the state space will be presented. Starting form the modeling, continuing with the linearization, stability, controllability and reachability study. Next the system is brought into normal form, here again it will be studied in all its parts until a controller can be easily implemented based on the backstepping technique. Finally, in the last chapter, an overall global controller is defined. It makes use of the swing-up technique in order to destabilize the system and bring it into the region of validity of the previously designed controller.