An Adaptation of a Sliding Mode Classical Observer to a Fractional-Order Observer for Disturbance Reconstruction of a UAV Model: A Riemann–Liouville Fractional Calculus Approach

Abstract

This paper proposes a modification of a Sliding Mode Classical Observer (SMCO) to adapt it to the fractional approach. This adaptation involves using a set of definitions based on fractional calculus theory, particularly the approach developed by Riemann–Liouville, resulting in a Sliding Mode Fractional Observer (SMFO). Both observers are used to perform disturbance reconstruction considered additive in a Quadrotor Unmanned Aerial Vehicle (UAV) model. Then, this work presents the fractional-order sliding mode observer’s mathematical formulation and integration into the Quadrotor UAV model. To validate the quality of the disturbance reconstruction process of the proposed SMFO observer scheme, numerical simulations are carried out, where a reconstruction quality indicator (BQR) is proposed based on the analysis of performance indices such as the Mean Square Error (MSE), the First Probability Moment (FPM), and Second Probability Moment (SPM), which were obtained for both the SMCO and the SMFO. The simulation results demonstrate the efficacy of the proposed observer in accurately reconstructing disturbances under various environmental conditions. Comparative analyses with SMCO highlight the advantages of the fractional-order approach in terms of reconstruction accuracy and improvement of its transitory performance. Finally, the presented SMFO offers a promising avenue for enhancing the reliability and precision of disturbance estimation, ultimately contributing to the advancement of robust control strategies for Quadrotor UAV systems.

Fractional-Order Sliding Mode Observer for Actuator Fault Estimation in a Quadrotor UAV

“…The QUAV has a main operating point, which corresponds to the point where the QUAV is fixed at coordinates x, y, z. This operating point occurs when the acceleration on the z axis and the angles of the QUAV are zero, corresponding to an equilibrium point ϕ, θ, ψ, .. z = (0, 0, 0, 0) [41]. The resulting linear model is expressed in state-space form:…”

“…Compared to existing SMOs, the proposed method achieves weaker chattering, faster response times, and higher estimation accuracy. In [41], an SMO is modified to employ a fractional-order approach for estimating disturbances in a QUAV. This adaptation exhibits superior transient performance compared to the classical observer.…”

“…To verify this assumption, we simulate the closedloop system subject to the initial conditions Z = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] ∈ R 12 , and the operation parameters shown in Table 1. These parameters were obtained from [41]. Figure 2 shows the simulation results of using the linear quadratic regulator (LQR).…”