Various methods of adaptive control of a high-order system with variable or unknown parameters have been analysed. The design of the model reference adaptive control algorithm with parameter adaptation based on the Lyapunov stability and Popov hyperstability criterion has been discussed. A simplified adaptive control algorithm with few adjustable system state variables and a reference model of a lower order than the system has been developed. Compensation of the referent signal level influence on the adaptive system has been achieved by signal normalization. An analytic procedure for error weight coefficients determination based on reference model parameters, has been developed. Other adaptation coefficients have been determined by computer optimization. A modified reference model adaptive control algorithm with parameter adaptation has been applied for the control of the thyristor-supplied DC motor drive. Compensation of the angular speed response due to variations of the moment of inertia was the major task of the developed algorithm. An algorithm has been tested with computer simulation. The simplified adaptation algorithm with the third-order discrete reference model and system output variable has been implemented by means of a digital signal processor, and was used for the control of DC drive angular speed. The simulation results of the system with a moment of inertia two times smaller than the nominal value demonstrated a 50 to 100 fold decrease in transient error compared with the nonadaptive system. The adaptive algorithm has been tested on the laboratory model of a DC drive with signal noise and nonlinearities and limitations. The testing has been performed using a two fold gain over nominal value of the closed armature current loop, which is equivalent to moment of the inertia two times lower than the nominal value. The measured error signal has been 4 times decreased in respect to nonadaptive system.