Design of ADRC for Second-Order Mechanical Systems without Time-Derivatives in the Tracking Controller

In this article, the problem of designing Active Disturbance Rejection Control (ADRC) for a class of second-order mechanical systems, expressed with Euler-Lagrange equations, is studied. A specific and practically motivated case is considered here, namely trajectory tracking task without the use of signal time-derivatives in the tracking controller. A general solution is proposed showing how to synthesize and tune the observer and the controller parts of the ADRC scheme. A special Extended State Observer is used in the design and here it takes the form of a Generalized Proportional Integral Observer (GPIO), which uses a Taylor series approximation of the total disturbance. A set of experimental results, obtained using a two degree-of-freedom robotic manipulator, shows the effectiveness of the proposed governing scheme in terms of trajectory realization and disturbance rejection without the use of signal time-derivatives in the controller.