How can I regulate duty time and frequency of 555 timer output with 2 potentiometers?
Using two pots to adjust the frequency and duty cycle is easy, but there may be interaction between the controls. The simplest method is to have one pot for charge and another for discharge, with diodes steering the current between them. To change duty cycle you turn one pot up and the other down. To change frequency you adjust both in the same direction. That's a lot of interaction!
You can rearrange the pots so one controls duty cycle and the other changes frequency, but there will still be some interaction. Here's a circuit which has minimal interaction and provides a duty cycle range of about 2~98%. The practical frequency range is only about 3:1, and is quite sensitive at the low end.
However there is a way to get wide frequency range with 0~100% duty cycle and no interaction, using the same number of parts! It uses the 555 as a triangle wave generator, and an opamp or comparator to control the duty cycle.