Modelling, stability, and control of DAE numerical integration

This thesis deals with the integration of differential algebraic equations systems. Generally speaking the execution of numerical integration algorithms may introduce some errors, which could propagate ending up in a wrong description of system dynamics. This issue, named drifting, will be highlighted by dealing with a specific constrained mechanical system presenting. Such system consists of a looper, which is a mechanism used in the steel production to sense and control the tension acting on the material. The thesis unfolds as follows: a first section model the looper and inspects the main properties related to its joint space and singularities. A brief introduction to stability analysis on multidof systems is proposed. Then, the thesis proceeds analysing looper stability properties, eventually finding a globally asymptotic stable configuration. Lastly, the drifting is highlighted by numerical simulations. To solve this issue two control algorithms are proposed: the first is the Baumgarte algorithm and the second consists of a nonlinear stabilizer. A performance comparison of both algorithms is then presented at the end of the implementation description.