For one of my projects, I recently bought on Aliexpress (see links at end of article) a Chinese fan speed controller board.
I was struggling to understand how this board can be set, the instructions found on Aliexpress being nearly of no help. The Chinese to English translation is....   :-)
Here is what I found ...
fan speed pcb

This board can be used WITHOUT or WITH the temperature sensor.
WITHOUT sensor, it acts like a simple fan speed controller running all time at the same speed.

WITH sensor, it permits to vary the fan speed in relation with the temperature of the sensor.
There is one theshold temperature (Tu) under which the fan runs at its low speed, and above this threshold it gradually increases the speed with increasing temperature until it reaches the maximum speed at the temperature of (threshold Tu + accelaration window Td). The fan runs than if like powered at supply voltage.
Ie : Tu = 40°C and Td = 30°C. The fan will accelerate from 40 to 70 °C.

The 3 LEDs on the module are indicating various informations as per table below.
The left column gives information about the module working state.
The 2nd column gives the Tu threshold temperature.
The 3rd column gives the acceleration window width.

fan speed table

The normal operation mode is indicated by a steady lightning of the center LED.
The right or left LED can also light simultaneously in this mode indicating that the module is set to MAX or MIN fan speed.

SETTING the low speed : (also permanent speed in mode without sensor)
Press shortly the pushbutton once to enter in setting mode, the center LED should blink fast.

One short press shown by a short blink of the right LED increases the speed by 5 %. When the maximum speed is reached, the right LED lights permanently.
Two short presses shown by a short blink of the left LED decreases the speed by 5 %. When the minimum speed is reached the left LED lights permanently.

Once satisfied, wait for 20s until the center LED stops blinking, the module stores the value and goes back into normal operation.
icons8 error 16When setting the lowest speed, you should take care that the fan restarts when you stop it by hand or restart the module !

SETTING the threshold temperature (Tu) :
Make a long press on the pushbutton until some LEDs are blinking slowly. We are now in THRESHOLD setting mode.
The blinking LEDs are displaying the threshold temperature according to the second column of the table.
The simple and double presses increases or decreases the temperature as above.

Once the desired temperature set, you can wait 20s to save and exit OR make another long press to enter the temperature window mode shown by a fast blinking. (see below)

SETTING the acceleration window temperature :
Once in threshold setting mode (slow blinking), make another long press to enter this mode (fast blinking)
The blinking LEDs are displaying the window width according to the third column of the table.
The simple and double presses increases or decreases the temperature as above.

Wait 20s to save/exit.

Fan shutdown strategy setting :
To enter in this mode, you have to turn the power OFF then turn the power ON while pressing simultaneously the pushbutton for a few seconds until one LED is blinking rapidely.

If LED 1 blinks : the module will never switch the fan OFF and use the low speed instead.
If LED 2 blinks : the module will turn the fan OFF when the temperature is lower than the threshold by at least 2°C
If LED 3 blinks : the module will turn the fan OFF when the temperature is lower than the threshold by at least 5°C

A long press will save and exit.

Links :
Aliexpress seller 1
Aliexpress seller 2