Adaptive Cascade Control of DC Motor under Condition of Parametric Uncertainty Using Lyapunov Stability Criterion

Abstract

A problem of a DC motor control under the conditions of parametric uncertainty is the scope of this research. It is solved for a cascade control system, in which the armature current and motor speed controllers are adjusted using the model reference adaptive control scheme. The stability of this system is proved using the Lyapunov criterion. Robustness of the adaptive armature current and speed controllers are provided by means of a back-EMF compensation and the e-modification respectively. A mathematical model of a real DC motor is used as a plant. Its inertia moment and an armature winding resistance values are changed from their nominal ones by two and 1.5 times respectively. The results of the mathematical modeling show that the obtained adaptive control system adjusts the parameters of both the above-mentioned controllers effectively and provide the required control quality when the speed setpoint is: 1) implemented as a signal, which meets the condition of the "persistent excitation" (PE), and 2) a conventional step-like signal, which does not meet the PE condition.