This thesis report is focused on the design of a guidance and control system that is able to minimize the deviation from the desired impact point for a firing range of 1 kilometer, given a 30mm spinning gun-launched projectile with a novel actuator design. This actuator is fixed on the projectile and offers a single force that can only be switched on or off. In order to test the effectiveness of the guidance, navigation and control (GNC) system, an accurate model for both the projectile and the proposed actuator are constructed. These models will serve as a substitute for testing with working prototypes. The model for the projectile dynamics is constructed based on existing nonlinear 6-DOF rigid-body models that are widely-used and validated. A new, simplified second order model that approximates the dynamics of the actuator, based on available measurements, is constructed. The overall structure of the GNC loop is defined, with the guidance method of choice being the pre-calculation of a reference trajectory towards the intended target. This method serves to alleviate under-actuation and computation time problems. One of the most important contributions of the thesis is made with the description of a method for transforming the input from a single binary input signal towards two continuous virtual input forces. This method uses a discretization of the rolling motion of the projectile, such that an optimization can be done which results in a transformation from the binary on/off signal to two virtual force inputs. These two virtual force represent the steering forces in the directions perpendicular to the forwards motion that would have the same effect as the binary on/off signal if directly applied on the projectile. The restructuring of the input allows for the use of PD-controllers to track the pre-defined trajectory. Using a grid-search method, the controller gains are found that best satisfy the design goal of minimizing the dispersion, which is defined by the sum of the mean error and the standard deviation of the impact points. Analysis of the integrated solution shows that the proposed solution with the input transformation and the PD-controller is able to significantly reduce the projectile dispersion from standard deviations of about 50 cm to just a few cm. The exact performance depends on the frequency of the actuator and the spin rate of the projectile. The best performance is reached with high spin rates and actuator frequencies high enough to match these spin rates.