<p>The presence of faults within control systems often results in elevated operational costs, diminished performance efficiency, compromised safety, and a substantial reduction in overall system reliability. Timely and accurate fault diagnosis can prevent undesirable consequences and ensure the safe and stable operation of the system. In this paper, a discrete-time model-free data-driven fault diagnosis system (FDS) and adaptive sliding mode controller (ASMC) are proposed for a class of practical engineering systems. The proposed FDS consists of two main components: a detector and an estimator. The fault detection component is innovatively designed based on a robust nonlinear sliding mode observer (SMO) and performs detection using a variable threshold mechanism. Compared to conventional methods, it significantly reduces the incidence of false alarms. The proposed fault estimator is innovatively designed based on a fractional-order radial basis function neural network (FORBFNN). The learning algorithm in the proposed approach is innovatively formulated based on fractional-order derivatives and implemented using a fractional gradient method. The novel characteristics of the FORBFNN include enhanced convergence, memory-based learning, improved accuracy with reduced error, and increased robustness against noise and uncertainties. The stability of the control system under the proposed method has been analyzed and verified using a Lyapunov-based approach. The performance of the proposed FDS was evaluated through simulations, and the results demonstrated improvements of 24% under normal conditions, 26% in the presence of noise, and 30% under internal uncertainty, compared to the conventional approach.</p>