How to properly stabilize the voltage of a transformer?

Question

Batteries

There is a 12V transformer. When connected to a diode bridge, it produces a floating voltage of 9-10V. After connecting a 10V 1000uf capacitor in parallel (to reduce ripple), this system started putting out 13.5V. How to make this system output 12V or a little less (needed to power the arduino and motors).

Answer 1

1) Power the logic by installing linear voltage regulators 7805/7812, etc., and motors can be driven from 13.5V, especially if the current through the motor is controlled by PWM.
2) It's a bad idea to put linear voltage regulators on everything, getting an iron along the way. :)
3) Put DC-DC converters at the output of the transformer for the required voltage and power.
4) Arduina for the most part can easily withstand 14V at the input, the engine too. If you need to reduce the voltage from the trash by 1-2 Volts, then you can put diodes in series with consumers, about 1V will fall on them.
And yes, since such a question, it is worth noting that the output voltage of the transformer under load will sag, and with a very powerful load, the first transformer that comes to hand may not overpower it (load). It would be worthwhile to indicate what and how you are going to twist.

Answer 2

How do you generally measure? Something tells me that you measure the 12V change as a constant voltage, hence 9-10 volts. Install a voltage smoothing filter and a linear regulator L7812CV.