This is definitely doable with a RPi.
Telling us which type of PLCS might help us help a little better. Some ideas.
- the PI has delicate digital inputs, so you will need some extra hardware to protect it. The Pi inputs are max 3.3 V. There are a lot of different solutions which you can buy ready-made for not a lot of money.
- the PI has Digital inputs (on or off), but with extra hardware (there is quite a market with a lot to choose from) you can read real-world digital and analog signals and connect serially to devices using as example RS232. There are solutions available to allow the RPi to connect to as example Modbus used by PLC-s.
- remote connection to the PI through internet is quite possible. It might require a bit of setup in routers and such. As the RPi is a full Linux computer, almost anything is possible.
- the PI could run a "web server application" allowing you to connect with any web browser. There are a number of starting points for this that may save you a lot of programming. One example is node red (see nodered.org ) as well as lot of other so called IOT frameworks. I like a module called node-red-dashboard.
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Not a full answer, but feel welcome.