A Fast Algebraic Estimator for System Parameter Estimation and Online Controller Tuning—A Nanopositioning Application

Abstract

Parameter uncertainty is a key challenge in the real-time control of nanopositioners employed in Scanning Probe Microscopy. Changes in the sample to be scanned, introduces changes in system resonances; requiring instantaneous online tuning of controller parameters to ensure stable, optimal scanning performance. This paper presents a method based on the frequency-domain algebraic derivative approach for the accurate online identification of the nanopositioner's parameters. The parameter estimates are produced within a fraction of one period of the resonant mode frequency, allowing almost instantaneous tuning of controller parameters. Experimental results show that the proposed method can be utilized to automatically tune an Integral Resonant Control (IRC) scheme, that combines both damping and tracking actions, and consequently deliver positioning performance far superior to that achieved solely due to the scheme's inherent robustness properties. It is further shown that the achieved performance compares favourably with an optimally designed control scheme of the same type.

Global fast non-singular terminal sliding-mode control for high-speed nanopositioning

“…The nanopositioner typically has both linear dynamics due to its mechanical structure and nonlinear hysteresis dynamics due to the piezo-actuator, as shown in our previous work [38,39,40]. Typically, the linear dynamics can be accurately modeled in the frequencydomain via a summation of second-order transfer functions (one for each resonant mode) [41,42,43] while the hysteresis can be modeled via a kind of hysteresis model, such as Bouc-Wen model [44], Prandtl-Islinskii model [45], Preisach model [46].…”