Linear-matrix-inequality-based sliding mode control for brushless d.c. motor drives

This paper deals with the robust sliding mode control of a brushless d.c. motor drive. A state-space model of the system is developed. The sliding mode controller is separated into linear and non-linear components. The novelty of the approach is in the rationale and method used to synthesize the linear control component which involves a linear matrix inequality (LMI) optimization. System uncertainty due to changes in load inertia is represented as norm bounded. A robust design approach is developed, yielding a robust controller against system uncertainties. A reaching condition to bring the system states to a sliding surface is developed, and the control burden lies heavily on the linear part to alleviate the chattering problem of conventional sliding mode control. The effect of the non-linear component on system performance is analysed. Testing the proposed controller verifies its effectiveness compared with the conventional one.