Dynamic differentiation and smoothing of noisy signals specifying the trajectory of an unmanned aerial vehicle

The problem of developing a complex approach to filtering and smoothing of reference trajectories, which are signal reference actions, and to recovery of their derivatives is considered on the example of an unmanned aircraft of the airplane type. To solve this problem, methods of design and algorithms for setting up a dynamic generator of acceptable trajectories are developed. The system of differential equations, which describes the generator of tasks, corresponds to the canonical model of the control plant "input - output". The output variables of the generator track the reference noisy and non-smooth vector signal of the reference actions. Thus, the generator is a tracking differentiator. To design its local links and corrective actions, smooth and bounded sigmoidal functions with bounded derivatives are used. This approach allows considering the restrictions on the speed and acceleration of a particular aircraft, so the output variables of the tracking differentiator generate a naturally smoothed spatial curve and its derivatives, which are used in the plant control system as a realizable reference trajectory. Numerical simulation results demonstrated the efficiency of the developed approach to dynamic differentiation and smoothing of vector signals both in the deterministic case and in the presence of noise. A comparative analysis of dynamic generators with different variants of additional low-pass filters is performed. The application of the developed approach is possible for processing the reference actions of various control plants, it is only necessary that their dynamic model be reduced to the canonical form.