We propose a command-filter backstepping controller that integrates a disturbance observer (DO) and a high-gain observer (HGO) to handle unknown internal and external disturbances acting on a quadrotor.
To build the controller, we first define tracking errors between the measured and desired quadrotor outputs. These errors let us rewrite the system in a new set of state variables. Using that transformed model, we apply the Lyapunov theory and derive a backstepping control law. To avoid taking repeated time-derivatives of states and virtual controls, we insert a first-order command filter. Since the controller also needs disturbance estimates, we add a nonlinear DO. Finally, we replace every state that appears in the controller or observer with its estimate from a HGO.
The main result is a control law that lets the quadrotor follow its path even when both internal and external disturbances act on it. Every sub-model is allowed its own type of disturbance, so the design stays realistic. We introduce a new state transformation and, with Lyapunov arguments, build a backstepping controller that includes a first-order filter; the filter keeps the design from suffering the usual “explosion of complexity.” A HGO then reconstructs the unmeasured states and their rates, yielding an output feedback implementation. In parallel, the nonlinear DO attenuates constant and nonlinear disturbances and band-limited white noise.
The method reduces reliance on high-precision sensors and mitigates the impact of wind, model error and rotor noise during flight.
Previous studies typically address either disturbance rejection or partial sensing, rarely both. Our design brings the filter, DO and HGO together, so it tackles disturbances, limited sensors and the well-known complexity spike in backstepping all at once.
