Sensitivity-based feedforward and feedback control using algorithmic differentiation

The computation of tracking controllers is one of the most important tasks in control engineering. For differentially flat systems, this task can be solved analytically if the initial conditions of all system states are consistent with the desired output trajectories. However, exact analytical solutions are not possible if the initial conditions are contradictory with desired output profiles or if non-flat outputs are specified for systems with complex nonlinearities in the state equations and the systems' input characteristics. For that reason, strategies based on the computation of differential sensitivities are investigated in this contribution to find approximate solutions for the tracking control problem. In contrast to classical output feedback structures, the proposed algorithm is capable of both providing dynamic feedforward and feedback control strategies. Selected application scenarios are presented to highlight the applicability of the suggested procedure which is based on the computation of the required partial derivatives online with the help of operator overloading techniques provided by algorithmic differentiation.