Perturbed second-order systems: Finite-time control design with disturbance observer

Second-order systems are essential to describe a variety of devices. Also, finite-time control is a vital methodology that allows counteracting the effect of disturbances, providing robustness to the closed-loop system. Based on these two essential topics, this manuscript proposes a new observer-based finite-time scheme that allows controlling second-order systems affected by matched disturbances. The proposed methodology enables the perturbed system to follow a given reference signal in a finite time. In the new proposal, the control signal is split into three parts. In the first part, an observer estimates and compensates for various endogenous or exogenous disturbances. Then, the system error dynamics are transformed into a decoupled system with bounded disturbances through the second control part. Finally, a finite-time controller is designed to accomplish finite-time convergence of the error signal. A formal mathematical development utilizing the Lyapunov theory demonstrates the effectiveness of the new control scheme. Also, the novel controller is compared against two existing observer-based finite-time controllers, and the remarkable performance of the latest proposal and its low power demands are demonstrated via numerical analysis.