var smoothing_factor = 0.1;
...

camera.pan += ang(turnangle-camera.pan)*smoothing_factor*time_step;
camera.tilt += ang(turnangle-camera.tilt)*smoothing_factor*time_step;

EDIT: You can limit the speed with clamp, too:

var smoothing_factor = 0.1;
var smoothing_limit = 10;
...

camera.pan += clamp(ang(turnangle-camera.pan)*smoothing_factor,-smoothing_limit,smoothing_limit)*time_step;
camera.tilt += clamp(ang(turnangle-camera.tilt)*smoothing_factor,-smoothing_limit,smoothing_limit)*time_step;