Numerical Three-Sliding Manifold and Lyapunov Analysis of Rotor Angle with Brushless Machine Construction

This paper presents the comprehensive numerical analysis of three-sliding manifold control algorithm to estimate rotor angle/position, θe , sensorlessly in brushless DC synchronous machine. The Lyapunov stability and convergence in the discrete time is also analyzed for each of these algorithms for both continuous and discontinuous controls. The algorithm has also been examined for computation cost and complexity given by the upper bound, Big O. The control estimation algorithm is irrespective of the machine construction but this paper also elaborates 7.5 Hp (5.5 kW) brushless machine construction with winding table in a non-salient eight pole rotor, double layer wye-winding with 48 slots.