A curvature cruise controller has been designed to maintain a desired curvature when drilling a curve section of a wellbore. The curvature cruise controller utilizes a model-based controller (such as an LQR controller) to generate steering inputs based on the desired curvature and attitude setpoints and real time measurements. The model-based controller is configured with a wellbore propagation model that characterizes the tool's response dynamics. The curvature cruise controller utilizes real time drilling operation parameters measurements to tune the model-based controller.