Dual-Extended State Observer-Based Feedback Linearizing Control for a Nonlinear System with Mismatched Disturbances and Uncertainties

This research article presents the nonlinear control framework to estimate and reject the mismatched lumped disturbances acting on the nonlinear uncertain system. It is an unfortunate fact that the conventional extended state observer (ESO) is not capable of simultaneously estimating the mismatched lumped disturbance and its derivative for the systems. Moreover, the basic ESO is only suitable for systems with integral chain form (ICF) structures. Similarly, the conventional feedback linearizing control (FLC) approach is not robust enough to stabilize systems in the presence of disturbances and uncertainties. Hence, the nonlinear control framework is proposed to overcome the above issues, which are composed of (a) a dual-extended state observer (DESO), and (b) a DESO-based FLC. The DESO provides information on the unmeasured state, mismatched disturbance, and its derivatives. The DESO-FLC utilizes the information from the DESO to counter the effects of such disturbances and to stabilize the nonlinear systems around the reference point. The detailed closed-loop analysis is presented for the proposed control framework in the presence of lumped disturbances. The performance robustness of the presented design was validated for the third-order, nonlinear, unstable, and disturbed magnetic levitation system (MLS). The results of the DESO-FLC approach are compared with the most popular linear quadratic regulator (LQR) and nonlinear FLC approaches based on the integral error criterion and the average electrical energy consumption.