A parametric study of positive-feedback pole-placement damping controllers for second-order resonant systems

A vast number of technological systems exhibit dynamics similar to a second-order system with a lightly damped resonance mode. A number of closed-loop control strategies have been proposed in the past to damp this resonance mode. Positive-feedback controllers based on the pole-placement technique have emerged as a group of well-performing, and hence, popular damping controllers in a multitude of applications. Yet, their design is based mostly on trial-and-error, where closed-loop poles are arbitrarily placed away from the $j\omega$ axis and further into the left-half complex plane resulting in increased damping. In this paper, a full parametric study of the Positive Position and Velocity Feedback (PVPF) is carried out. This leads to two distinct design strategies pertaining to applications in which only damping is required, and those which require both damping and tracking. One axis of a serial-kinematic nanopositioner is used as a representative second-order system with a lightly damped resonance mode to test the performance of the proposed PVPF controllers.