What is the difference between active tip clearance control system and passive tip clearance control system in turbine?
This is kind of half an answer, but the difference between active tip clearance control and passive tip clearance control is in the definition of “active” and “passive”. An active system has some way of determining the clearance, and then making adjustments to achieve a desired gap. So, it has a feedback loop in the control system. A passive system has no feedback, it just operates “blind”.

Turbine blade tip clearance is usually achieved by blowing cool or hot air onto the turbine casing, to make it contract, and move closer to the blade tips (when cool air is being used), or expand (when using hot air). A passive system will just blow x amount of air at temperature y, during a given portion of the mission (say the climb), without actually knowing what the actual clearance is.  It was up to the designers to make sure the values for x and y result in the right tip clearance. In comparison, l expect an active system has some feedback so it modulates the flow to achieve a desired clearance.

Here is a scientific paper that describes a concept for active tip clearance. The paper uses the term “open loop” to describe a passive system. An active system would be “closed loop”, because there is a signal going back to the controller, telling it how well it is achieving its target tip clearance. It appears in this paper, this signal is not an actual measure of the tip clearance, but rather a prediction from a thermal model of the casing &amp; blade.