This paper is focused on orthogonal function approximation technique FAT-based adaptive backstepping control of a geared DC motor coupled with a rotational mechanical component. It is assumed that all parameters of the actuator are unknown including the torque-current constant (i.e., unknown input coefficient) and hence a control system with three motor control modes is proposed: 1) motor torque control mode, 2) motor current control mode, and 3) motor voltage control mode. The proposed control algorithm is a powerful tool to control a dynamic system with an unknown input coefficient. Each uncertain parameter/term is represented by a linear combination of weighting and orthogonal basis function vectors. Chebyshev polynomial is used as a strong approximator for estimation of uncertainty. The designed control law includes three terms: a feedforward term, a feedback term and a robust term for compensation of modeling error. Lyapunov stability is used to prove the validity of the proposed controller and to derive the update laws for the weighting vectors of orthogonal Chebyshev approximators. A case study of a geared DC motor in connection with a rotating output load is simulated to prove the effectiveness of the proposed controller structure.
