Robust trajectory following without availability of the reference time-derivatives in the control scheme with active disturbance rejection

The conventional application of the active disturbance rejection control (ADRC) scheme leads to robust feedback-linearization of the original system dynamics which is followed next by a design of the outer-loop state-feedback with feedforward controller designed for the resultant chain of integrators. The latter design stage assumes perfect knowledge (availability) of the consecutive reference time-derivatives up to the order of the linearized dynamics. In the paper, such assumption will be removed by showing how to modify the ADRC design for SISO systems to obtain practical following of sufficiently smooth reference trajectories which are not known in advance. The key idea results from expressing of a control task in the error domain, treating simultaneously the reference trajectory as a source of an additional external disturbance which has to be actively rejected. By embedding the prescribed closed-loop error dynamics into a structure of an extended-state observer it will be shown that the outer-loop controller can be limited in this case to a proportional static output-feedback regardless of the order of system dynamics. Simple tuning rules of the original ADRC have been preserved in the modified scheme requiring only two design parameters to be selected by a user. Simulation and experimental examples illustrate efficiency of the proposed control law.