We propose a controller architecture for soft-landing control with quantized input. The objective of the soft-landing problem is to achieve precise positioning of a moving object at a target position, while ensuring the velocity decreases as the target is approached. In this paper, we formulate the soft-landing problem as a constrained control problem. Our approach combines traditional convex model predictive control with a rounding rule that quantizes the input. The rounding rule is designed to minimize the error between the requested and quantized inputs. A robust control invariant set is used to ensure that the rounding errors do not lead to constraint violations. We demonstrate our approach for a transportation system case study.