The challenge to increase range without loss of bandwidth is a common problem in nanopositioning systems. The proposed research will address this challenge by developing inchworm positioners that achieve high-resolution positioning within each step of the inchworm while allowing large range with multiple steps. Towards this, the research will develop novel vibration mitigation tools for systems with switched dynamics. The research will: (1) develop optimal output transitions without vibrations which improve on current state transition approaches; (2) invert switched dynamic systems that arise due to the changing of boundary conditions in the inchworm; (3) account for hysteresis input nonlinearities using inversion methods; and (4) develop preview-based techniques for the integrated tracking/resetting problem. The resulting optimal approach will be used to mitigate transitional vibrations caused by each inchworm step. Thereby, the proposed work will achieve large-range, high-bandwidth positioning without loss of resolution due to movement induced vibrations during transitions. The vibration-mitigation strategy for the inchworm will be evaluated during nanoscale positioning. In summary, the proposed research will: (1) develop new tools for vibration mitigation in systems with switched dynamics; and (2) increase the bandwidth without loss of range in nanopositioning systems.
The proposed research will have broad impact on nanotechnology since it improves nanopositioning in scanning probe microscopes, which are key enabling tools in nanoscience and nanotechnology. The proposed research will provide training and education in nanotechnologies through novel senior-level capstone design projects in nanopositioning and vibration mitigation. Additionally, the proposed work will offer research and educational experience to undergraduate students and promote the involvement of minority students in research. Thus, the proposed work will help to build the research and human resource infrastructure needed in emerging nanotechnologies.
The goal of the project was to develop inchworm nanopositioners, for SPMs, which have both large range and high bandwidth. We designed an experimental (inchworm-type) nano-stepper that overcomes this fundamental limit — i.e., the need to tradeoff between large-range and high-bandwidth. By making multiple steps, nanosteppers can achieve infinite range without sacrificing bandwidth. However, precision could be lost during each stepping motion. To enable precision during the stepping process, we have modeled the dynamics of such systems and developed dynamics-based methods to improve the positioning precision. These dynamics-based input and trajectory design methods were implemented and tested on an experimental system to demonstrate large-range positioning with nanopositioners. The research of one graduate student (Scott M. Wilcox) was supported by the grant. Additionally, two undergraduate students (Kurt J. Stalsberg and Alex Ching) participated in the research through a research experience for undergraduates (REU) supplement. Research in nanotechnology is critical to US competitiveness in high-tech industries such as the development and manufacturing of future electronics and optical applications. Additionally, the study of chemistry, physics and biology at the nano-scale has applications in human health (National Nanotechnology Initiative: Leading to the Next Industrial Revolution, a Report by the Interagency Working Group on Nanoscience, Engineering and Technology, 2000). Therefore, the proposed work to improve nanopositioners used in SPMs (a key enabling tool in nanoscience and nanotechnology) will have broad impact on the economy and on health. The main research outcomes are briefly summarized below. I. INVERSION OF PIEZO DYNAMICS Models of the piezo dynamics could be developed that can be used for vibration suppression. Current efforts to model and suppress vibrations, using inversion of the system dynamics, were reviewed and compared with other feedforward methods in Ref 1. This article reviewed approaches to model dynamics effects such as creep, hysteresis and vibrations to enable precision positioning. Additionally, the article showed the optimal inverse leads to a generalization of robust control by allowing non-causal inputs. Additional details are provided in Ref 1. II. OPTIMAL OUTPUT TRANSITION FOR NONLINEAR SYSTEMS Considering pre- and post-actuation can lead to substantial improvements in the switching performance. In particular the time needed for switching could be reduced. We studied the optimal (minimum time) transition between operating points of general nonlinear system in Ref 2. The minimum-time state transition problem with bounds on the input magnitude leads to the classical bang-bang-type input for the fastest state transition. However, the transition time can be reduced further if only the system output needs to be transitioned from one value to another rather than the entire system state. It was shown that the flexibility in the choice of the boundary values of the internal state in the optimal output transition (with pre- and post-actuation) can reduce the transition time further when compared to the standard state transition (without pre- and post-actuation) for invertible systems. Additional details are provided in Ref 2. III. OPTIMAL OUTPUT TRANSITION FOR ACTUATOR REDUNDANT SYSTEMS Actuator redundancy can be exploited to improve vibrations suppression in high speed positioning as studied in Ref 3. This article considers the output transition problem to change the system output, from an initial value to a final value for dual-stage systems. The main contribution of the article is to show that the use of pre- and post-actuation input outside the transition interval (without changing the output) can reduce the transition time beyond the standard bang-bang-type inputs for optimal state transition. Additional details are provided in Ref 3. IV. MODELING AND CONTROL OF LARGE-RANGE NANOSTEPPER Nano-steppers enable nanoscale precision over relatively large range — by making multiple nanoscale steps. The main contribution of this work (Ref 4) was to show that model-based feedforward input can improve the performance of piezo-based nano-steppers by accounting the dynamics-caused vibrations and thereby enabling operation at higher frequencies. Towards this, a model of the nano-stepper was developed and inverted to find feedforward inputs that correct for the vibrational effects. Additional details are provided in Ref 4. REFERENCES [1] G. M. Clayton, S. Tien, K. K. Leang, Q. Zou, and S. Devasia. A Review of Feedforward Control Approaches in Nanopositioning for High Speed SPM. ASME Journal of Dynamic Systems, Measurement and Control, Special Issue on Dynamic Modeling, Control and Manipulation at the Nanoscale, 131(6):# 061001, 1–19, Nov. 2009. [2] S. Devasia. Nonlinear Minimum-Time Control With Pre- and Post-Actuation. Automatica, 47(7), 1379–1387, July 2011. [3] S. Devasia. Time-Optimal, Dual Stage, Output Transition: with PrePost Actuation. IEEE Transactions on Control Systems Technology, 20(2), 323–334, March 2012. [4] S. Wilcox, and S. Devasia. Modeling and Feedforward Control of a Large-Range, Piezo Nano-Stepper. American Control Conference, San Francisco, CA, June 29 - July 1, 2011.
