Kam K. Leang

Feedback-Linearized Inverse Feedforward for Creep, Hysteresis, and Vibration Compensation in AFM Piezoactuators

In this brief, we study the design of a feedback and feedforward controller to compensate for creep, hysteresis, and vibration effects in an experimental piezoactuator system. First, we linearize the nonlinear dynamics of the piezoactuator by accounting for the hysteresis (as well as creep) using high-gain feedback control. Next, we model the linear vibrational dynamics and then invert the model to find a feedforward input to account vibration - this process is significantly easier than considering the complete nonlinear dynamics (which combines hysteresis and vibration effects). Afterwards, the feedforward input is augmented to the feedback-linearized system to achieve high-precision highspeed positioning. We apply the method to a piezoscanner used in an experimental atomic force microscope to demonstrate the methods effectiveness and we show significant reduction of both the maximum and root-mean-square tracking error. For example, high-gain feedback control compensates for hysteresis and creep effects, and in our case, it reduces the maximum error (compared to the uncompensated case) by over 90%. Then, at relatively high scan rates, the performance of the feedback controlled system can be improved by over 75% (i.e., reduction of maximum error) when the inversion-based feedforward input is integrated with the high-gain feedback controlled system.

High-speed serial-kinematic AFM scanner: Design and drive considerations

In this paper, we describe the design of a flexure guided, two-axis nanopositioner driven by piezoelectric stack actuators. The scanner is specifically designed for high-speed scanning probe microscope (SPM) applications. A high-speed atomic force microscope (AFM) is required to acquire high resolution, three-dimensional, time-lapse images of fast processes such as the rapid movement of cells and the diffusion of DNA molecules. High-speed scanner designs have been proposed, for example, by Ando and co-workers as well as Schitter and coworkers, for AFM imaging. In the proposed design, the slow and fast scanning axes are serially connected and both axes are flexure-guided to minimize runout. The achievable scan range is 10 x 10 mum. The scanners mechanical resonance frequencies were optimized using finite element analysis. Experimental results show a first major resonance, in the slow and fast axis respectively, at approximately 1.5 kHz and 29 kHz. In addition to evaluating the proposed design, this paper also discusses the various tradeoffs between speed, range, and required control hardware. Electrical requirements and scan trajectory design are also considered.

Hysteresis, Creep, and Vibration Compensation for Piezoactuators: Feedback and Feedforward Control 1

Abstract We present an integrated two-step approach, which combines feedback and feedforward control, to compensate for the effects of hysteresis, creep, and vibration in piezoactuators. In this approach, the control of hysteresis and creep is decoupled from the control of vibrational dynamics. First, high-gain feedback control is used to minimize positioning error caused by hysteresis and creep. Second, an inversion-based feedforward approach, which can achieve exact tracking for general output trajectories, is used to compensate for error due to vibration at high scan rates. The feedforward approach is applicable to minimum (collocated sensor and actuator) and nonminimum phase (noncollocated sensor and actuator) positioning systems. The decoupling of hysteresis and creep control from vibration control simplifies the inversion-based approach, and the use of feedback provides robustness. We show significant improvement in positioning precision and scanning rate, and illustrate our results with an experimental piezoactuator scanner that is used in Atomic Force Microscope (AFM) applications.

Iterative feedforward compensation of hysteresis in piezo positioners

In this article, we prove convergence of an iterative control algorithm to find an input that achieves precise positioning in hysteretic systems. In the analysis, the Preisach hysteresis model is used to characterize the nonlinear behavior of the piezo positioner. We quantify the number of iterations required to achieve a prescribed precision. The method is applied to an experimental piezo system to demonstrate its efficacy, and results show that the positioning error can be reduced to the noise level of the sensor measurement.

Optimal Output Transitions for Dual-Stage Systems

This paper solves the minimum-energy output-transition problem for dual-stage systems, such as dual-stage disk-drives, where the second actuator can be used to increase the bandwidth and precision of conventional single-actuator systems. The objective is to find optimal inputs that change the system output from an initial value to a final value during a specified output-transition time interval. The paper shows that, for dual-stage systems, inputs applied outside the output-transition time interval (i.e., pre- and postactuation) can substantially reduce the required input energy. For an experimental dual-stage system, results are presented to show that the input energy can be reduced by 65% with the use of pre- and postactuation inputs when compared to standard methods that do not use such pre- and postactuation.

Evaluation of charge drives for scanning probe microscope positioning stages

Due to hysteresis exhibited by piezoelectric actuators, positioning stages in scanning probe microscopes require sensor-based closed-loop control. Although closed-loop control is effective at eliminating non-linearity at scan speeds below 10 Hz, it also severely limits bandwidth and contributes sensor-induced noise. The need for high-gain feedback is reduced or eliminated if the piezoelectric actuators are driven with charge rather than voltage. Charge drives can reduce hysteresis to less than 1% of the scan range. This results in a corresponding increase in bandwidth and reduction of sensor induced noise. In this work we review the design of charge drives and compare them to voltage amplifiers for driving lateral SPM scanners. The first experimental images using charge drive are presented.

Hysteresis characterization using charge feedback control for a LIPCA device

In this paper, we study the no-load behavior of a lightweight piezo-composite curved actuator (LIPCA) subjected to voltage and charge control. First, we examine the effect of hysteresis and creep when the actuator is voltage controlled at a slow scan speed. The experimental results show that creep increases the displacement hysteresis by over 25% when scanning at 1/60 Hz. Afterwards, we discuss the design and implementation of a charge-feedback circuit to control the displacement of the actuator. The hysteresis curves between voltage- and charge-control modes are compared for the scan frequencies of 1 and 5 Hz. The results show that charge control (compared to voltage control) of a LIPCA device exhibits significantly less hysteresis, over 80% less.

Hysteresis Compensation for High-Precision Positioning of a Shape Memory Alloy Actuator using Integrated Iterative-Feedforward and Feedback Inputs

In this paper, we investigate the design of an iteration-based control algorithm combined with feedback control to address the positioning error caused by hysteresis effect in a shape memory alloy (SMA) actuator. SMA actuators offer relatively large strain (up to 8%) and high strength-to-weight ratio, and as a result, they are being exploited in minimally invasive surgery tools and microrobotics. But unfortunately, SMA actuators exhibit significant hysteresis effect which can lead to loss in positioning precision; it can cause as much as 50% error in positioning. To address the prohibitive effect of hysteresis, we study the application of an iterative-feedforward algorithm specifically designed to account for this behavior. We show that one of the major challenges with iterative- feedforward inputs for SMA actuators is the slope of the hysteresis curve at the phase transition zones (from martensite to austenite and vice versa) can be significantly large, and thus the output response can be highly sensitive to small changes in the input. As a result, iterative-feedforward input provides limited performance because at the transition zones, small changes in the input (due to noise, for example) cause the output to change significantly, thus inducing tracking error. To alleviate this problem, and to help improve the performance of the feedforward method, we consider the addition of a feedback input to add robustness. We show: (1) experimental results that demonstrate the efficacy of the method and (2) the tracking precision can be reduced by over ten times compared to just using iterative-feedforward input. In particular, the ultimate tracking error was reduced to 0.15% of the total displacement range - approximately the sensor noise level.

Hysteresis Inverse Iterative Learning Control of Piezoactuators in AFM

Abstract We consider the application of iterative learning control (ILC) in which the input update law exploits an inverse model of the hysteresis behavior for piezoactuators. Compared to ILC for hysteresis that updates the control input using the measured tracking error scaled by a constant (fixed) learning gain, the proposed ILC algorithm converges more rapidly. The approach is analyzed and experimental results are presented to demonstrate the methods ability for precision output tracking.

A BIAXIAL SHAPE MEMORY ALLOY ACTUATED CELL/TISSUE STRETCHING SYSTEM

In this article, we describe the design of a shape memory alloy-based system to stretch cells cultured on top of a flexible membrane in multi-directions (longitudinal and transverse). Mechanical cues (such as strain and force) can affect the state and behavior of cells, such as, morphology, the differentiation process, and apoptosis. Therefore, a thorough understanding of the effects of mechanical perturbations on cells/tissues will have a deep impact in the biological sciences. The proposed design allows application of anisotropic (multi-axial) strain with high-precision. Certain cells, for example endothelial cells that line the inside of blood vessels, experience multi-axial (circumferential and longitudinal) stresses and strains. A cell stretching device that enables controlled application of biaxial strain will allow for systematic and accurate studies of the effects of externally applied mechanical perturbation throughout the cell, tissue, or organ. A preliminary design is proposed that exploits the strain recovery property of the shape memory alloy (SMA) actuators. We describe the design of the mechanical system and show experimental results to demonstrate stretching of a thin PDMS membrane in the longitudinal and transverse directions. To account for the inherent nonlinearity of the SMA, a feedback controller is implemented to achieve high-precision control of the stretching process. Additionally, the design can be integrated with an atomic force microscope (AFM) for high spatial and temporal resolution studies.Copyright