Lumped approximation of distributed systems and controllability questions

The approximation of a distributed system by a lumped system using both exact analysis and qualitative reasoning is studied in some detail for the lossless LC transmission line, and with much less detail for an RC line, a towed cable, and a deep-sea mining hauling pipe. We delimit, at least partly, the region of validity of the approximation, especially in analysing controllability questions. We also suggest why a form of nonuniform lumping may be more appropriate for the towed cable and the deep-sea mining hauling pipe.