Optimal nonlinear damping control of second-order systems

Abstract

Novel nonlinear damping control is proposed for second-order systems. The proportional output feedback is combined with the damping term which is quadratic to the output derivative and inverse to the set-point distance. The global asymptotic stability, passivity, convergence time, and accuracy of the controller are demonstrated. Furthermore, the control saturation case is explicitly analyzed. The proposed non-linear damping is said to be optimal because no additional design parameters are required and it ensures faster than exponential convergence, without transient overshoots for a non-saturated and one transient overshoot for a saturated control configuration.