I had an idea that an analog computer would be better than digital, because work with more characters than 0 and 1

Analog computers already exist, and they are pretty great. AFAIK, they have fallen out of favor due to modern computers being so powerful now. In the older days though, analog computers were a great way to perform complex calculations. They used to use them a lot for things like control systems for automation equipment and stuff like that. One of the big advantages they have is that not only can you compute complex equations with real numbers (actually, complex numbers too) directly without having to rely on a digital representation of them, but they can also simulate dynamic systems in real time. For example, if you had a mechanical systems (like a mechanism or robot), you can simulate its dynamic behavior in real-time using an electrical circuit that replicates it (most mechanical things have an electrical analog, with the movement of electric charge playing the role of the movement of objects and the voltage playing the role of the forces on those objects). Also, things like control systems and signal processing filters are often formulated as dynamic systems that can be realized with an analog electric circuit. So, back in the days when digital computers were just impractical, things like early industrial robots or other similar automated machinery used analog computers (specially designed electric circuits) for the signal processing, control systems and even kinematics and dynamics calculations (for things like model-based control and closed-loop inverse kinematics).

Today, analog signal processing is still a very important first step to any complete signal processing solution, although much of it is now done with digital signal processing (DSP) because those chips have gotten pretty powerful now. The main reason for this is that DSP is a lot more convenient as far as programming and testing the different methods and filters. But DSP has some limitations (sampling rates, analog-to-digital conversion resolution, etc.) and annoying artifacts (like aliasing), which is why the analog filters are used first to clean and demodulate signals before they get to the DSP chip. But all the fancy encodings we have today (e.g., CDMA and stuff like that), you really need a DSP chip to do that kind of stuff. Back in the day of simple unencoded modulation like AM / FM radio, analog systems could do it all, but that just isn't the case anymore.

Also, there are still some low-level control circuits that rely on analog circuitry. It used to be that things like servomotors and hydrolic pistons and stuff like that were controlled by an analog circuit. It's not like that anymore due to the advent of industry-standard digital communication buses, like the CAN bus, and smaller "hobby" digital buses like PWM and I2C. But there are still things that work on analog circuits though. One example is DC motor controllers.

I think that some of the older industrial robots are still largely relying on analog circuitry for a lot of their low-level controls, but I'm not sure, this is a bit of a "trade secret" type of thing.

The main problem with analog computers is that they are tricky to design (especially in terms of electro-magnetic interference problems), and cannot really be changed easily, i.e., they are not really "programmable" (although there are FPAAs, they are not easy to program at all). So, that's why they tend to only appear in limited operations on applications where they can be designed once and mass produced for decades (signal processors, controllers, automated machines, etc.).

Very interesting post, thank you!