MIMO H_∞ control of a parallel kinematic XYZ nano-positioner

This paper presents the design, model identification and control of a parallel-kinematics XYZ nano positioning stage for general nano-manipulation and nano-manufacturing applications. The stage features a low degree of freedom monolithic parallel kinematic mechanism with flexure joints. The stage is driven by piezoelectric actuators and its displacement is detected by capacitance gauges. The control loop is closed at the end-effector instead of the each joint, so as to avoid calibration difficulties and guarantee high positioning accuracy. Instead of a single input and single output (SISO) system with joint space control configuration, this design has strongly coupled dynamics with each actuator input producing along multiple axes. The nano-positioner is modeled as a multiple input and multiple output (MIMO) system, where the control design forms an important constituent that accounts for the strongly coupled dynamics. The dynamics that model the MIMO plant is identified by time-domain identification method. A pseudo-random binary signal is used to excite the system while avoiding violent vibrations at resonant frequencies, which comes from the low damping feature of flexure based structure. The order of the model is reduced to make controller efficient and implementable. The control design based on modern robust control theory that gives a high bandwidth closed loop nanopositioning system which is robust to physical model uncertainties arising from flexure-based mechanisms is presented. The nonlinear effects from piezoelectric actuators, such as hysteresis and creep, are compensated effectively by closed loop robust controller. The bandwidth, resolution and repeatability are characterized experimentally, which demonstrate the effectiveness of the robust control approach.