On the ADRC of Non-Differentially Flat, Underactuated, Nonlinear Systems: An Experimental Case Study

In this article, the output reference trajectory tracking control of a non-differentially flat, underactuated, system is approached from the perspective of Active Disturbance Rejection Control (ADRC) including a suitable Extended State Observer (ESO). The class of underactuated systems, which are non-differentially flat, constitutes the most challenging area for testing the effectiveness of robust feedback control algorithms, specially under output trajectory tracking requirements. The problem, however, is substantially alleviated and feasibly approached provided the tangent linearization of the system is found to be controllable around an arbitrary equilibrium point. The flatness of the tangent system is taken advantage of for the design of an observer-based feedback controller taking the tangent system operation substantially far from the operating point. The ADRC scheme robustly takes efficient care of the excited (endogenous) nonlinearities, which were neglected in the linearization process, as well as any other external (exogenous) disturbances. Here, we take the gantry crane and its closely associated system: the inverted pendulum on a cart, as working laboratory examples to illustrate the effectiveness of the proposed approach.