How does negative feedback control contribute to homeostasis whereas positive feedback control does not?

Negative feedback by definition is the response to a change in equilibrium in an effort to stop that change and bring you back to normal. For example, if your body registers an increase in blood pressure, a negative feedback mechanism works to bring the blood pressure back down to normal, or at the level it should be at, or homeostasis.

Positive feedback is the opposite. It's the response to a change in equilibrium that will add to the change. In other words, a change happens, which causes a response to add or magnify that change. For example, blood clotting is a positive feedback mechanism. The agglutination of red blood cells together activates more and more platelets to accumulate. And it all starts either with the damage of 1 RBC or the wall of a vessel. The accumulation of the changes drives the overall system away from homeostasis.

Any kind of feedback control is meant to contribute to homeostasis. The positive and negative thing is a direction not a description of the result.  Bear with me here.

Take the blood pressure example...blood pressure goes up..stretch receptors sense this...they talk to the brain...the brain says oh lets relax the vessel walls...and they relax.  this is a negative feedback because the vessel walls were squeezed to tight (constricted) and the action to return to homeostasis was to relax the vessels (dilate).  The action was opposite and thats why its negative (but in the end its a positive experience for the body because its back to normal).

One of the more common examples of positive feedback would be blood clotting.  You got a boo boo and there is a tear in the vessel wall.  It breaks and to fix it (part of how to fix it) platelets start to adhere to the site and each other.  More and more clotting occurs and more platelets aggregate until the area has closed up and bleeding stops (homeostasis).  The thing here is that more and more of the same thing happens (making it positive), as opposed to a negative feedback being less and less (or more of the opposite, like more dilation instead of constriction).

In the end both contribute to homeostasis. Problems happen when feedback loops come into play.