Adaptive control of a nanopositioning device

Abstract

Abstract-High-bandwidth tracking control is desirable in many nanopositioning applications, including scanning probe microscopy. Typical nanopositioner designs have several sources of uncertainty which can degrade control performance, and even induce instability. Salient uncertainties are in the control gain and the resonant frequencies of the mechanical structure. The control gain varies due to hysteresis and creep which result in a control gain that is dependent on the offset, range, and form of the driving signal, as well as actuator temperature and age. The resonant frequencies change due to payload mass. In order to maintain performance in the presence of moderately changing dynamic response, a model reference adaptive control (MRAC) scheme is proposed and implemented. The details of implementing a working MRAC will be discussed. Most notably, a novel augmentation of the parameter identification scheme in the form of a special pre-filter, will be shown to be necessary to obtain parameter convergence, and thus also stability in the case of the MRAC scheme. Experimental results are presented to assess the performance. I. INTRODUCTIONNanopositioning is typically associated with scanning probe microscopy (SPM), and its many applications. Some application task typically require general reference trajectory tracking, i.e., for manipulation, fabrication, and lithography. In order to improve throughput in such settings, high bandwidth control is required [1]- [3]. As the dynamic response of typical positioning systems employed has a fair amount of uncertainty, both inherently and due to the specific application, the control laws used also need to have sufficient robustness. Although the dynamic response is uncertain, it is dominantly linear and can be well described by linear ordinary differential equations for specific operating points. These systems should therefore be amenable to adaptive control schemes, which in principle can provide higher and more consistent performance than standard robust static control schemes.The standard indirect model reference adaptive control (MRAC) framework [4] is used in this work in order to develop a complete adaptive control scheme for a nanopositioning device of common design. As will be demonstrated, there are some important considerations to be made with regards to how to choose the plant model, how to tune the control law, and how to obtain parameter convergence for the adaptive law. The resulting control scheme is believed to be a well performing MRAC. The experimental results should therefore be indicative of the performance that can be expected applying MRAC to this particular type of system.The main novelty presented is a special pre-filter needed in order to obtain parameter convergence.