A novel parallel-kinematics mechanism for integrated, multi-axis nanopositioning: Part 2: Dynamics, control and performance analysis

In this paper, we discuss the dynamics, controls and performance of a parallel-kinematics, integrated, multi-axis nanopositioner, the PKXYZNP [Yao Q, Dong J, Ferreira PM. A novel parallel-kinematics mechanisms for integrated, multi-axis nano-positioning. Part 1: Kinematics and design for fabrications]. The paper focuses on computing the workspace of the stage, characterization of its dynamic behavior, synthesis of a controller for it, and the testing of its contour tracking and positioning performance. For this system, because of the coupled nature of the axes, a MIMO control scheme is adopted to directly close the loop around the kinematics of the stage, i.e., the position of the table/end-effector is fed back to control the actuators. This scheme has the added advantage of not requiring complex and fragile kinematic calibration of the stage as the accuracy becomes a function of only the accuracy of the sensing system and the servo performance. To make the MIMO control scheme tractable by reducing its order, the controller design is performed in the modal space of the system. A resolution of 2–4 nm is achieved from this stage. Linear and circular tests were performed to evaluate the contouring performance of the PKXYZ stage. In spite of a relatively heavy load condition (the weight of a solid target), the linear and circular contouring errors are less than 40 and 150 nm, respectively, with contouring speeds ranging up to 40 μm/s.