Practical Finite-Time Command Filtered Backstepping With its Application to DC Motor Control Systems

In this article, a practical finite-time command filtered backstepping control method is proposed for a class of uncertain nonlinear systems with unknown control direction coefficients, unmodeled dynamics, and external disturbances. In this approach, practical finite-time command filters are proposed to get the differential estimations of the system signals, and such estimations are used to construct the approximations of the system uncertainties. In order to address the design difficulties caused by the system unknown control direction coefficients, a virtual control direction method is presented by using a system equivalence transformation. Based on practical finite-time Lyapunov stability criterion, it can be proved that the system tracking error is practical finite-time stable with convergence rate faster than exponential. Finally, this method is applied to a direct current motor control system, and experimental results demonstrate the effectiveness of the proposed control scheme.