I am new member here and I looking about this idea
I need to change the water pump mechanical pressure controller to arduino by using pressure sensor with analog output and I program the arduino to start and stop the pump at specific setting mentioned in the program.
Is this idea easy to do?
Yes. Pick a suitable pressure sensor and motor controller and come back if you have specific questions.
I think this type of pressure sensor is Ok
but, now is it possible to program the mille ampere in the analog input and configure it as a digital output to start & stop the motor?
Yes, you can read the 4-20 mA sensor output using a 200 Ohm resistor to generate a voltage.
What pump and pump controller do you intend to use?
The pump is CALPIDA 2 hp, but why I need pump controller? The arduino can not generate digital output to start and stop the pump by relay as example
A relay can be a "pump controller", but an Arduino cannot directly control most relays, or any pump.
An Arduino can directly control many types of Solid State Relay (SSR), which in turn can switch a 2 HP pump.