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Most firms have their own symbols that are related to the standards. So your employer is the key.

There are plenty of manuals on the web, but it might be better to contact the supplier

Your controller is programable, and it can handle 11 different types of sensors. Type B : 0-1820 C

That's the sort of question asked by someone who doesn't understand the complexity of automation involving interface with separate systems such as analyzers.

https://www.fluke.com/en-us/learn/blog/predictive-maintenance/beyond-the-multimeter-part-2

Is the short present with both ends of the cable are disconnected? Advanced cable testers are available that test for cable faults electronically and report the fault location.

Unlikely just a cable failure as such. What is the wiring gage, and insulation type, voltage rating.

"Usually, controllers have software that detects sensor failure." Perhaps for some failures, but not all. In some processes, multiple sensors from different suppliers are mandated, with Quintuple CPU and memory redundancies to avoid catastropic control failures. "What is a problem is coarse...

In parallel with what?

Least we forget, all these strategies, presume a linear system, 100% realiability of all sensors, control devices, and a stable process response to all changes large or small.

They are coupled, as part of a closed loop, though the dynamic response of your sensor, the dynamic response of your controlled device, and the dynamic response of the process you are aiming to control!

Are they independent? No! Ki (Integration) increases the control adjustment the longer the process variable deviated from your set point. Kd (differentiation) immediately bumps the control command intended to reduce the time needed to achive the set point. Both can lead to instability depending...

You'll nesd to contact the manufacturer "Setra"

Just do an internet search for "Plug-In O-Ring Quick Connects "

Oil leaks suggest worn bearing seals

45 mA circuits havent been used in 50+ years, but it is a simple matter to translate the current to commonly used voltage inputs

Laser light curtains are commonly used to reduce hazard.

A photograph and a supplier drawing of the reed switch location is a good start

Consult the IEEE standards

Given the variety of control panels, working in a panel shop or in engineering construction is a good start.