The scope of this research is to develop a hyperstable adaptive control system of a direct current (DC) drive speed for effective load torque attenuation. The proposed speed controller is based on the model reference adaptive control framework and integrated into the conventional DC drive cascade control system. Its main features are as follows: (1) the boundedness of the control action signal, as well as the armature current control loop non‐stationarities, are taken into consideration with the help of the reference model hedging technique; (2) its inputs include only measurable signals, thus there is no need to use any kind of state estimators; (3) it attenuates the disturbances, which are matched with its control action signal, particularly, the inertia moment non‐stationarity and load torque. The asymptotic hyperstability of the obtained DC drive control system is proven with the help of Lyapunov’s theorems and Popov’s criterion. The numerical experiments corroborate the obtained results. They include the demonstration of disadvantages of the conventional cascade control system under conditions of the drive parameters’ non‐stationarity and advantages of the proposed solution for different disturbance types and amplitudes.