continuous vs discrete systems in control theory
Pete W already provided good insight, let me add a few important:
The use of MCU is usually cheap, easy to implement, easy to modify. They are often the way to go except in some situations.
Speed:
The big drawback of MCU based system is speed. If the control system needs to operate with a low response or high frequency, programmable systems quickly show their limits.
FPGA addresses that to some extent with programmable logic, to some extent, but they are complex to program and you are still limited by the ADC / DAC conversions.
I used to work for a company that was regulating the current on a Xenon flashlamp using a light detector and a PID system. This requires ns response time on the complete control loop and analog was the only way to achieve that.
Reliability:
Another situation is where you want to have a highly reliable system, where MCU can sometimes bug or behave unpredictably.
This can happen either by software bugs, compiler bugs, programming that didn't go right, or processing errors (it does happen).
For instance, one of my designs has an analog timing control on one of the outputs of an MCU to protect the system in case of an MCU malfunction.
You can think of military, aircraft, medical, sometimes it's perhaps easier to pass certification with an analog system (you just measure it) than a software where each instruction of assembly code has to be deeply studied as well as the MCU itself being certified.
Simple System:
Sometimes you need a control system that is fairly simple and it is better to use a discrete system as you do not need to program it, removing one step in the production and a software stack to maintain.
Design / Cost:
If you need a fairly precise control system, handling small signals, designing a whole ADC -&gt; MCU -&gt; DAC chain can be tricky because of noise consideration, correct ADC drive, and so forth. High-performance ADC is expensive and you need a good front-end analog, which altogether can quickly be more expensive and complex than an analog solution.
There is certainly plenty more situation that can be described and it really depends on the specific case.