Modified ESO based disturbance rejection for dynamical systems: An experimental study

This paper introduces a new approach to designing a disturbance observer called a modified extended state observer (ESO). The existing ESO technique ensures that the trajectories of estimation error dynamics globally asymptotically converge to zero in the absence of time varying disturbances. However, for perturbed systems, where time varying disturbances affect system behavior, these trajectories never reach zero but rather remain bounded around the origin within a constant value. Consequently, this discrepancy leads to challenges in accurately estimating state trajectories and discerning information about disturbances. This, in turn, complicates the precise estimation of state dynamics and disturbances and poses difficulties in designing control laws for stability analysis of the system. Unlike existing ESO methods, the distinguishing characteristic of this modified ESO is its capability to achieve global and asymptotic convergence of observation error in the presence of unknown bounded time varying disturbances. This unique property enables the exact estimation of state trajectories. Information about the bounded time varying disturbances is obtained and significantly attenuate more efficiently compared to existing ESO techniques. Based on the estimated disturbances, any classical controller can be designed for the system to achieve set-point tracking subject to time varying disturbances. To validate the performance of the proposed modified ESO, the model of a coupled-tank setup is simulated for the stabilization problem and its experimental setup is demonstrated for the tracking problem. For carrying out the experiment on a real-time hardware setup, an input of step change at every 60 s with water level variation of $\pm$2 cm from initial set value of 15 cm to achieve the set-point tracking of the water levels in the both the tanks along with good transient performance in the presence of time-varying external disturbances.