My actual work experience using analog computers was brief, but it had a large impact on my subsequent career.
While I was in graduate school in 1966-1967, I got a job advising a Fibreboard paper mill facility in Antioch, CA. (The mill is long gone since it was an environmental disaster.) I had two main assignments. One was teaching computer programming to their engineering staff. They did not have an on-site computer so I arranged to get them terminals (old teletype machines) to a remote time-sharing service using the BASIC language. Twice a week I drove to Antioch and taught BASIC to their engineers.
The second part of the job was particularly interesting. Fibreboard was having problems with "exploding" milk carton material. They produced paperboard material coated with polyethylene. This material was later assembled into a milk carton and sealed by applying enough heat to melt the polyethylene. If the moisture levels in the paper were too high, the heat of sealing the carton's seams caused the moisture to boil causing a bubble that weakens the container. My assignment was to find a way that computers could help in reducing this problem.
I started by touring the paper mill. Logs arrived by barges on the San Joaquin River, were turned into pulp, which was then fed into a Fourdrinier continuous-flow paper machine, which was many hundred feet long. At the far end of the machine giant rolls of paper appeared. The key component for my purposes was the drying section where the wet paper passed through a maze of steam-heated cylinders. Key variables were the moisture content of the paper entering the dryer, the roller temperatures, and the speed of the paper passing through the rollers. Fibreboard periodically sampled these values and recorded them by hand. After the fact, these values could be associated with a particular batch of paper, which was also know to be a good or flawed batch re moisture using post-process sampling.
I soon programmed a heat flow model that, based on measurements from the process, could accurately predict a good batch or a bad batch, and, most importantly, identified how the process parameters needed to be changed on the bad batches. Of course, by the time I could collect the data and run the model, the paper batch was long gone on the way to a customer. What was needed was a real-time process-control computer that could measure, model, predict, and make adjustments as the paper flowed through the rollers. So, I started investigating the state real-time process-control computers.
Finding no statisfactory digital solutions (a long story here, which I'll skip), I turned to analog computers. I learned the concepts of analog computers and visited the sales office of a major analog computer manufacturer (either EAI or Beckman, I believe) in San Francisco. Hoping for a sale, they let me program my model on one of their demo systems. The process input was simulated by potentiometers, and the feedback control was represented by voltmeters. My model seemed to work fine with real-time feedback, but the solution was impractical for Fibreboard. The computer was too environmentally sensitive for the plant floor, it required constant maintenance, and so forth. Plus, I was ready to graduate and they had no one to continue driving this project.
However, I had now fallen in love with the concept of real-time computer control. So, when I learned that IBM in nearby San Jose had a group developing real-time process-control computers, I decided to try to get hired there. I ended up taking a job in the IBM PCSSS (Process Control and Small Scientific Systems) group at San Jose, rejecting many other offers, most offering a higher salary. My initial job was programmer on the MPX operating system for the IBM 1800 process-control computer. (Interestingly, the IBM 1800 was later used in controlling paper mills.)
I won't go into the details here, but joining this particular IBM group turned out to be a great decision and, I believe, was a critical contributor to my later becoming an IBM Fellow.
Actually, the Old Military section has many special purpose analog computers. Almost all bombsights, gunsights, and navigation computers were analog though the 1940's and '50's. This section is for general purpose analog computers.