What type of system uses LVDT's to sense the spool position?

A closed inner-loop system is designed to automatically adjust its operation based on feedback. In this context, an LVDT (Linear Variable Differential Transformer) serves as a highly precise sensor to determine the position of a spool, which is a component often found in hydraulic or pneumatic systems.

The LVDT provides continuous feedback by translating the position of the spool into a corresponding electrical signal that indicates the position. This signal is then used in conjunction with a control mechanism to either maintain or adjust the spool's position based on the system's requirements, thus ensuring that the system operates effectively and efficiently.

In contrast, open-loop systems do not utilize feedback to adjust operations; instead, they execute a pre-set action without regard to the actual outcome or condition of the system. Manual systems rely on human intervention to adjust components rather than utilizing automated feedback mechanisms like an LVDT. Therefore, the closed inner-loop system is the most appropriate choice since it incorporates an automated feedback mechanism for better control and precision.