Two-degrees-of-freedom controller delivering zero-error tracking of ramp-like trajectories for nanopositioning systems

Piezoelectrically actuated nanopositioning systems (tube or platform type) are widely employed in applications where fine mechanical displacements with resolution down to atomic scale are required. This paper presents the design, analysis, and validation of a new control scheme based on the structure of the traditional Two-Degrees-of-Freedom (2DOF) PID controller. The proposed controller is established based on a linear continuous input-output nominal model, and presents a simple structure composed by two second order transfer functions. Despite its simplicity, the controller studied in this paper is able to achieve zero error in the tracking of ramp input signals and, therefore, in the slopes of triangular signals, typically used in nanopositioning applications to trace a raster pattern. The controller also suppresses the unmodeled nonlinearities of the piezoelectric actuated nanopositioning systems without the need of an hysteresis model or a state observer. Moreover, the stability of the control system is proved, and its effectiveness is validated through experimental chattering-free control on a piezoelectric stack-actuated nanopositioning platform. Results demonstrate that the proposed controller is superior to the conventional polynomial-based, proportional-integral, and resonant controllers proposed in literature for motion-tracking tasks in nanopositioning systems.