Equivalence between Reduced Order Extended State Observer based Active Disturbance Rejection Control and Disturbance Observers Based control schemes

A frequency domain approach is used to establish an equivalence between Reduced Order Extended State Observer (ROESO) based Active Disturbance Rejection Control (ADRC) and Disturbance Observer Based (DOB) control using nominal (estimated) state feedback. These robust control schemes are traditionally devised to solve automatic control problems for systems with unmeasured states and subject to unknown disturbances. The results are presented in the context of pure integration perturbed systems, which constitute a paradigmatic model of nonlinear, uncertain, SISO differentially flat systems. Application to the control of a non-trivial, nonlinear, mechanical example is presented along with computer simulations.