We discuss the model of a quantum bit driven by an external classical field without decay in the rotating wave approximation. In such a model, the whole evolution of the qubit states takes place on the Bloch sphere. We reformulate the model as a unitless set of real ordinary differential equations and use the normalized external field as a feedback control parameter. The closed-loop algorithm is designed in the form of the speed gradient, driving the dynamical system towards minimizing a given nonnegative goal function expressed via the qubit variables. We investigate the achievability of the control goal, and focus on the most important features of the speed gradient algorithm applied to a quantum system in comparison with classical systems. Our approach is valid for the control over the ground and excited population levels, and over the qubit phase variables. The paper was presented at PhysCon2024.