Input-decoupled discrete-time sliding mode control algorithm for servo multi-field multi-armature DC machine

Abstract

The multivariable modeling of a servo actuating system consisting of multi-field multi-armature direct current (MFMADC) machine is extracted and a novel discrete time nonlinear algorithm is proposed for the corresponding system. The proposed control algorithm demonstrates robustness against modeling uncertainty and by utilizing its novel mathematical structure, decouples the dynamical interactions of the connected motors. The main contribution of this paper is the proposition of a new decoupling control algorithm that in which, the driving (commanding) voltages of the connected driving motors are extracted separately and independently using the Lyapunov principle in discrete time. In fact, the obtained coupled stabilizing convex inequalities of the controlling voltages, resulting from the evaluation of the Lyapunov functions, are analytically decoupled using elementary matrix operations. Consequently, each motor now has the capability to perform its controlling task (position control or torque control) with asymptotic stability and robustness against uncertainty. To assess the performance of the proposed controlling algorithm and its verification, a MFMADC machine is attached to a harmonic drive reducer (HDR) whose flex spline and circular spline are fabricated using viscoelastic polyesters PLA and thermoplastic PLA, respectively. A number of experiments are conducted where in the first test, the MFMADC is controlled in only-position mode while in the second test, the MFMADC is controlled in simultaneous position-torque control mode. Comparative assessments confirm that the MFMADC technology is needed when a high precision tracking of position, under high frequency disturbances, is desired.