Planning and control for autonomous vehicles are often treated as two independent problems in the literature. However, due to their level of abstraction and modeling, they are in fact highly intertwined: for example, the controller tracks the output trajectory of the motion planner without taking into account the surrounding obstacles. Therefore, an ill-designed planning and control architecture of the vehicle might lead to hazardous situations such as infeasible trajectories to follow. Some existing works in the literature have considered both problems simultaneously, but usually they either lack some guarantees on the feasibility of the computed trajectory or are non robust to modeling errors. Therefore, the present paper proposes to combine a 10Hz motion planner based on a kinematic bicycle Model Predictive Control (MPC) and a 100Hz closed-loop Proportional-Integral-Derivative (PID) controller to cope with normal driving situations. Its novelty consists in ensuring the feasibility of the computed trajectory by the motion planner through a limitation of the steering angle depending on the speed. This ensures the validity of the kinematic bicycle model at any time. The architecture is tested on a high-fidelity simulation model on a challenging track with small curve radius, with and without surrounding obstacles.