Observer-based saturated proportional derivative control of perturbed second-order systems: Prescribed input and velocity constraints

This study introduces a new methodology for controlling second-order nonlinear systems in point-to-point tasks with simultaneous input and velocity saturation constraints. The proposed approach utilizes a robust disturbance observer for compensating for the unknown dynamics and disturbances affecting the system. Then, the disturbance observer is combined with a saturated proportional derivative (PD) controller. The resulting control signal allows solving the regulation problem and generating input values and velocities with some prescribed bounds defined by the user. Based on the Lyapunov-theory, asymptotic stability of the origin of the closed-loop error dynamics is attained, which implies that the position regulation objective is achieved while keeping the input and velocity values within prescribed bounds defined by the user. The new control scheme is assessed through numerical simulations, which corroborate the new saturated controller's feasibility.