What is better approach for non blocking pid algorithm?
The main issue you have is that pulseIn() is completely blocking - and your while loop doesn't help much either.

The "proper" (or what I would consider the "proper") way of dealing with this is to use a timer in gated mode. Actually you need two timers, but the Arduino already provides you micros() that will do for one of them.

Basically your pulsed signal is input into the gate input of a timer. That timer, when the gate input is HIGH, will count the number of ticks from whatever clock source you configure it for (system clock, etc, with or without prescaler, etc). It also needs to be configured so that the timer triggers an interrupt at the falling edge of the gate. 

That interrupt reads the count from the timer and resets the count to 0 ready for the next pulse. It also uses micros() to work out the time between successive falling edges (should be about 1100us).  A little bit of maths is needed to calculate the time from the count.

It's not something I have ever done with an Arduino - I have only used a PIC32 for it - though I assume that AVR timers have a gated mode (they should have; they are fairly comprehensive timers). Check the datasheet to be sure - as well as for how to configure it.  On the PIC32 I used two timers both running at the same speed from the same clock source - one in gated mode to count the HIGH time and one in free-running mode to count the full period time. The duty % is then the ratio of the two counts and you don't care about the actual time in human-created units.

Of course, it goes without saying that you need a gated timer for each servo you want to sense...