Flatness based ADRC Control of Lagrangian Systems: A moving crane.

A procedure is described for direct tangent linearization, around a given equilibrium point, of non-linear multivariable Lagrangian systems, in terms of second order variational expansions of the Lagrangian function. When the linearized model is controllable (i.e., it exhibits the flatness property), we present an Active Disturbance Rejection Control (ADRC) scheme, valid for stabilization and flat output reference trajectory tracking tasks designed on the basis of the incremental system. The linear approach requires only generalized incremental position measurements, with no explicit need for incremental velocity observers. The ADRC controller is cast in terms of equivalent classical linear compensation networks. A moving crane example is presented which illustrates, through digital computer simulations, the effectiveness of the proposed control scheme.