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In my opinion the best way to learn this stuff on your own would be to build and program a simple automation system. That could be, for example, a garage door system, pool controller, home brewing system, or even just a trainer with some buttons, indicators, sensors and motors.

You'd need basic electrical tools like a multimeter, control screwdrivers and wire strippers.

You would also need common hardware parts like terminals, din rail, 24v power supply and an enclosure. Maybe even some pneumatics if you're willing to spend more. And of course a PLC. If in North America, get a used Allen-Bradley micrologix or similar from ebay. If in Europe, Siemens s7-1200 would be better. You could also get another brand like Automation Direct Click, though that isn't used in industry as much as the two aforementioned industry standards. You'll also need the programming environments for each respective brand. AB has Connected Components Workbench, Siemens has TIA Portal, and AD Click has its own free to download environment.

You can find lots of wiring guides online for how to connect the basics together, it is pretty simple. If you could get your hands on Autocad or similar drafting program (there are free ones) and make electrical prints for your design that would be great to show in an interview. You'll need to be able to read, understand and possibly make your own prints on the job.

Programming PLCs is a different beast than traditional application programming. The most common language is Ladder Logic, which is a graphical representation of digital logic circuits that resemble relay logic wiring diagrams. There is also Structured Text, which is more like traditional text based programming, but in my experience it isn't nearly as popular in the field.

If you get into SCADA systems like Ignition (they have a free or cheap hobbyist package) you'll see more VBA or python scripting along with SQL and things like that. The industry is also being dragged kicking and screaming into the modern age where everything is increasingly networked together, and a little more thought is needed than putting everything on 192.168.1/24 on an open and unsecured network. Understanding networking and security would be a big advantage.

The programming itself is "simple"; constructs like for loops are considered advanced that an inexperienced engineer can do without, and one could have a fulfilling career without ever encountering a sorting algorithm. The challenge is that it isn't just programming, but mechanical, hydraulic, electrical and pneumatic systems that have their own host of challenges. A big could be caused by a programming issue, but it could also be something like a stuck valve, loose wire, or siezed bearing to name a few.

The best way to actually break in and learn would be to get comfortable with the basics and if possible get a job involving travel. Many jobs in the field require extended periods of travel to different plants, not a lot of people want to do that. And I get it, the travel can be brutal. I was just on an especially rough startup in another part of the country, and I pulled over 3 80 hour weeks in a row. I'm young, single and trying to learn so that doesn't bother me, but ymmv. There are plenty of jobs where you'd only be working in one plant, or several within an hour or two of home base. I can say that I learn way more in the field than designing stuff in the office though.

Last but not least, check out r/PLC. Those folks are great.