Logarithmic Sliding Mode Control with Selective Super-Twisting Algorithm for Trajectory Tracking of a PVTOL Aircraft

We present a logarithmic sliding mode controller (LSMC) combined with a selective super-twisting algorithm (STA) for trajectory tracking of a planar vertical take-off and landing (PVTOL) aircraft subject to persistent disturbances and parasitic input coupling. Each loop in the three-loop cascade uses a logarithmic sliding surface that avoids the singularity of terminal sliding mode while achieving finite-time convergence. A second-order command filter supplies roll-reference derivatives analytically, eliminating noise amplification from numerical differentiation. The STA integrator is applied only to the altitude and attitude loops; we identify explicitly why placing it in the horizontal loop produces oscillatory roll commands that destabilize the cascade. Lyapunov analysis establishes finite-time convergence for altitude and attitude and a closed-form bound on the horizontal position error. Compared with classical SMC and non-singular fast terminal SMC: RMSE_ss,x = 1.65 cm and 68% reduction in altitude IAE under continuous wind disturbances.