Arnfinn Aas Eielsen

Damping and Tracking Control Schemes for Nanopositioning

Fast and accurate tracking of reference trajectories is highly desirable in many nanopositioning applications, including scanning probe microscopy. Performance in common positioning stage designs is limited by the presence of lightly damped resonances and actuator nonlinearities such as hysteresis and creep. To improve the tracking performance in such systems, several damping and tracking control schemes have been presented in the literature. In this paper, six different control schemes are presented and applied to a nanopositioning system for experimental comparison. They include schemes applying damping control in the form of positive position feedback, integral resonant control, integral force feedback, and passive shunt-damping. Also, general pole placement in the form of model reference control, as well as a control scheme requiring only a combination of a low-pass filter and an integrator, is presented. The control schemes are fixed-structure, low-order control laws, for which few results exist in the literature with regard to optimal tuning. A practical tuning procedure for obtaining good tracking performance for five of the control schemes is, therefore, presented. Experimental results show that the schemes provide similar performance, and the main differences are due to the specific implementation of each scheme.

Adaptive feed-forward hysteresis compensation for piezoelectric actuators

Piezoelectric actuators are often employed for high-resolution positioning tasks. Hysteresis and creep nonlinearities inherent in such actuators deteriorate positioning accuracy. An online adaptive nonlinear hysteresis compensation scheme for the case of symmetric hysteretic responses and certain periodic reference trajectories is presented. The method has low complexity and is well suited for real-time implementation. Experimental results are presented in order to verify the method, and it is seen that the error due to hysteresis is reduced by more than 90% compared to when assuming a linear response.

Passive shunt damping of a piezoelectric stack nanopositioner

The speed and accuracy of nanopositioning systems is heavily influenced by the presence of lightly damped mechanical resonances. In this work, an electrical impedance is connected in series with the driving piezoelectric stack actuator to damp the first mechanical resonance. The electrical shunt is shown to act equivalently to an output feedback controller except that no sensor is required. A simple inductor-resistor shunt circuit is demonstrated to damp the first mechanical resonance of a high-speed nanopositioner by 19.6 dB. The technique of shunt damping is low-cost, simple, guaranteed to be stable, and significantly improves the system response.

PI2-Controller Applied to a Piezoelectric Nanopositioner Using Conditional Integrators and Optimal Tuning

Abstract For tracking control of nanopositioning stages using piezoelectric actuators, controllers with integral action can be employed to robustly track a reference in the presence of hysteresis, creep, and plant parametric uncertainties. In any practical configuration of instrumentation for this application, saturations will be present. Thus, a controller with integral action is prone to windup, which typically cause large transients and long settling times, and will in general degrade performance and potentially damage equipment. In this paper it is demonstrated that conditional integrators provides a very accessible and convenient framework for introducing anti-windup for any order integral controller, and the effectiveness is verified experimentally. Also, the influence reconstruction and anti-aliasing filters have on the stability limits for PI and PI 2 controllers is investigated, and a novel tuning procedure is proposed in order to obtain the best performance for the overall system. It is demonstrated experimentally that optimal tuning can damp resonances and increase bandwidth.

Moving Horizon Observer for vibration dynamics with plant uncertainties in nanopositioning system estimation

This paper considers the estimation of states and parameters of a Single-Degree-of-Freedom (SDOF) vibration model in nanopositioning system based on a nonlinear Moving Horizon Observer (MHO). The MHO is experimentally tested and verified on measured data. The information about the displacement and speed together with the system parameters and unmodeled force disturbance is estimated through the Sequential Quadratic Programming (SQP) optimization procedure. The MHO provided superior performance in comparison with the benchmark method Extended Kalman Filter (EKF) in terms of faster convergence.

Discrete-time repetitive control with model-less FIR filter inversion for high performance nanopositioning

Repetitive control (RC) is used to track and reject periodic exogenous signals. RC achieves tracking by incorporating a model of a periodic signal in the feedback path, which provides infinite loop-gain at the harmonic frequencies of the periodic signal. To improve robustness, the periodic signal model is bandwidth limited, and to improve the performance, an inverse plant response filter is used. This filter can either be an infinite impulse response (IIR) filter or a finite impulse response (FIR) filter. The accuracy of the filter typically determines the allowable bandwidth of the periodic signal model, and it is therefore desirable to obtain the most accurate inverse possible. In this paper a model-less method for synthesizing an FIR filter for the inverse response is presented, and it is compared to the common approach of using an inverse model-based IIR filter. An experimental comparison of the two approaches is presented, and it is demonstrated that the two methods produce identical results, but where the model-less FIR filter approach has the added benefit of avoiding the modeling effort needed to obtain the IIR filter.

Robust damping PI repetitive control for nanopositioning

In many applications of nanopositioning, such as scanning probe microscopy, tracking fast periodic reference trajectories with high accuracy is highly desirable. Repetitive control (RC) is a simple and effective scheme to obtain good tracking of such reference trajectories. However, the highly resonant dynamics of the positioning stage combined with hysteresis and creep behavior in the piezoelectric actuator can degrade performance and even make creating a stable RC system difficult. In this paper, a damping proportional-integral (PI) controller is combined with a repetitive controller for robustness and high performance. Compared to a regular PI controller, the modified PI controller introduces damping, increases the bandwidth, and reduces the overall noise level due to feedback. Also, due to the integral action, the hysteresis and creep nonlinearities inherent in the piezoelectric actuator is minimized. A novel method for tuning the PI controller is proposed. The control approach is applied to a custom-design flexure-guided nanopositioning system with a dominant resonance of approximately 725 Hz. Experimental results demonstrate the effectiveness of the overall control scheme, and the maximum tracking error for scanning at 100 Hz and 400 Hz is measured at 0.27% and 2.7%, respectively, of the total positioning range.

Adaptive Model Estimation of Vibration Motion for a Nanopositioner With Moving Horizon Optimized Extended Kalman Filter

Fast, reliable online estimation and model adaptation is the first step towards high-performance model-based nanopositioning control and monitoring systems. This paper considers the identification of parameters and the estimation of states of a nanopositioner with a variable payload based on the novel moving horizon optimized extended Kalman filter (MHEKF). The MHEKF is experimentally tested and verified with measured data from the capacitive displacement sensor. The payload, attached to the nanopositioners sample platform, suddenly changes during the experiment triggering the transient motion of the vibration signal. The transient is observed through the load dependent parameters of a single-degree-of-freedom vibration model, such as spring, damping, and actuator gain constants. The platform, before and after the payload change, is driven by the excitation signal applied to the piezoelectric actuator. The information regarding displacement and velocity, together with the system parameters and a modeled force disturbance, is estimated through the algorithm involving the iterative sequential quadratic programming (SQP) optimization procedure defined on a moving horizon window. The MHEKF provided superior performance in comparison with the benchmark method, extended Kalman filter (EKF), in terms of faster convergence.

Topography and force imaging in atomic force microscopy by state and parameter estimation

A novel imaging method for atomic force microscopy based on estimation of state and parameters is presented. The cantilever dynamics is modeled as a linear system augmented by the tip-sample interaction force. The states of this augmented system are observed. The tip-sample force function is based on the Lennard-Jones potential with a nonlinearly parameterized unknown topography parameter. By estimating this parameter together with the tip-sample force using a nonlinear observer approach, the topography of the sample can be found. The observer and parameter estimator is shown to be exponentially stable. Simulation results are presented and compared to a more conventional extended Kalman filter.

Experimental comparison of online parameter identification schemes for a nanopositioning stage with variable mass

An experimental comparison of two common parameter identification schemes is presented. The recursive least-squares method and the extended Kalman filter are applied to identify three parameters of a second-order linear mass-spring-damper model, using data obtained from a nanopositioning stage with a highly resonant dynamic response.