This article proposes a generalized Udwadia-Kalaba control method to simultaneously handle equality and speed inequality constraints. First, a dynamic model that includes both of these constraints is established, and the state transformation is carried out through diffeomorphism state transition theory. At the same time, limitations are imposed on the difference between the estimated state variables designed in this article and the actual state variables. Then, a robust control strategy is designed to ensure that the equality constraints and speed inequality constraints are satisfied. By utilizing the Lyapunov approach, the uniform boundedness and uniform ultimate boundedness of the dynamical system are demonstrated. Finally, the feasibility of the proposed method was verified through an uncertain long-distance belt conveyor system.