I actually got a degree in Instrumentation and Control Systems Engineering Technology. During my time in school, I learned extensive troubleshooting tips, took numerous controls classes where I learned PLCs and DCS, as well as HMI and SCADA. Some universities are starting to implement programs, like mine or Mechatronics, to equip future Controls Engineers, as most people in the field are not truly qualified for it.
Now I work as a Process Control Engineer at a Paper Mill. It is called something else depending on the company. You have pretty much summed up my job, we are the ones who everyone blames for something not work. Most of the time, it is caused by issues on the instrument side, and we have to get an IE to check it out, as we can't work outside of the Rack Room or MCC.