Lerp Issue

I've recently discovered that I'm using lerp wrong. This is my current code to set the speed of my vehicle:

Code (CSharp):

1. targetSpeed = Slider.value;
2. currentSpeed = Mathf.Lerp(currentSpeed, targetSpeed,Time.deltaTime);

I like the effect it makes, but it isn't framerate independent. To try and replicate it using the correct method I got this:

Code (CSharp):

1. lastFrameSpeed = targetSpeed;
2. targetSpeed = Slider.value;
3.  
4. if(lastFrameSpeed != targetSpeed ) //if the slider has changed
5. {
6.     rate = 0;  //reset timer
7.     startSpeed = currentSpeed;
8. }
9.  
10. rate+=time.deltaTime;
11. currentSpeed= Mathf.Lerp(startSpeed,targetSpeed ,rate);

What this does is reset the lerp if the slider that controls the speed has changed. It works good if I go from one value to another and leave it, but if I keep changing the slider by dragging it, the lerp is continually reset and the speed stays the same.

Is there a better way of doing this, that keeps the smooth slow down, is framerate independent and also allows the slider to be continually changed by the player? Thanks.

Edit: Nevermind, seems like smoothdamp is what I was looking for.