We present results on numerical regulator design for sampled-data nonlinear plants via their approximate discrete-time plant models. The regulator design is based on an approximate discrete-time plant model and is carried out either via an infinite horizon optimization problem or via a finite horizon with terminal cost optimization problem. In both cases, we discuss situations when the sampling period T and the integration period h used in obtaining the approximate discrete-time plant model are the same or they are independent of each other. We show that, using this approach, practical and/or semiglobal stability of the exact discrete-time model is achieved under appropriate conditions.