Rje Roel Merry

Using a Walking Piezo Actuator to Drive and Control a High-Precision Stage

Piezoelectric actuators are commonly used for micropositioning systems at nanometer resolution. Increasing demands regarding the speed and accuracy are inducing the need for new actuators and new drive principles. A nonresonant piezoelectric actuator is used to drive a stage with 1-DOF through four piezoelectric drive legs. In order to improve the positioning accuracy of the stage, a new drive principle and control strategy for the walking piezomotor are proposed in this paper. The proposed drive principle results in overlapping tip trajectories of the drive legs, resulting in a continuous and smooth drive movement. Gain scheduling feedback in combination with feedforward control further improves the performance of the stage. With the developed drive principle and control strategy, the piezomotor is able to drive the stage at constant velocities between 100 nm/s and 1 mum/s with a tracking error below the encoder resolution of 5 nm. Constant velocities up to 2 mm/s are performed with tracking errors below 400 nm. Point-to-point movements between 5 nm and the complete stroke of the stage are performed with a final static error below the encoder resolution.

Modeling and Waveform Optimization of a Nano-motion Piezo Stage

Piezo actuators are used in high-precision systems that require nanometer accuracy. In this paper, we consider a nano-motion stage driven by a walking piezo actuator, which contains four bimorph piezo legs. We propose a (model-based) optimization method to derive waveforms that result in optimal driving properties of the walking piezo motor. A model of the stage and motor is developed incorporating the switching behavior of the drive legs, the contact deformation, and stick-slip effects between the legs and the stage. The friction-based driving principle of the motor is modeled using a set-valued friction model, resulting in a model in terms of differential-algebraic inclusions. For this model, we developed a dedicated numerical time-stepping solver. Experiments show a good model accuracy in both the drive direction and the perpendicular direction. The validated model is used in an optimization, resulting in waveforms with optimal driving properties of the stage at constant velocity. Besides the model-based optimization, also a direct experimental data-based waveform optimization is performed. Experiments with the optimized waveforms show that compared to existing sinusoidal and asymmetric waveforms in literature the driving properties can be significantly improved by the model-based waveforms and even further by the data-based waveforms.

The influence of disturbances in iterative learning control

For systems that perform repetitive tasks, a high performance feedforward signal can be derived using iterative learning control (ELC). The feedforward signal is updated through successive iterations. Disturbances present in the control scheme, such as load and measurement disturbances, are also present in the learning process and deteriorate the performance of ILC. This paper presents an expression for the tracking error of an arbitrary iteration which shows the influence of measurement and load disturbances of the present and previous iterations. The expression is validated by means of simulations and experiments on a motion system. The disturbances of the last two iterations prove to have the largest influence on the tracking error

Removing non-repetitive disturbances in iterative learning control by wavelet filtering

The tracking performance of systems that perform repetitive tasks can be significantly improved using iterative learning control (ILC). During successive iterations, ILC learns a high performance feedforward signal from the measured tracking error. In practice, the tracking error consists of both a repetitive part which is equal every iteration and a non-repetitive part which varies every iteration. ILC can only compensate for the repetitive part, the non-repetitive part limits the achievable performance of ILC. In this paper, a wavelet based filtering method is presented which identifies and removes the non-repetitive part of the tracking error by a comparison of two error realizations for each iteration of ILC. The filtered error signal is used as input for the learning scheme of ILC. Simulations and experiments show that the wavelet filtering method improves the performance of ILC, resulting in a smaller tracking error and in a learned feedforward signal that contains significantly less non-repetitive disturbances

Directional Repetitive Control of a Metrological AFM

Atomic force microscopes (AFMs) are used for sample imaging and characterization at nanometer scale. In this work, we consider a metrological AFM, which is used for the calibration of transfer standards for commercial AFMs. The metrological AFM uses a three-degree-of-freedom (DOF) stage to move the sample with respect to the probe of the AFM. The repetitive sample topography introduces repetitive disturbances in the system. To suppress these disturbances, repetitive control (RC) is applied to the imaging axis. A rotated sample orientation with respect to the actuation axes introduces a nonrepetitiveness in the originally fully repetitive errors and yields a deteriorated performance of RC. Directional repetitive control (DRC) is introduced to align the axes of the scanning movement with the sample orientation under the microscope. Experiments show that the proposed directional repetitive controller significantly reduces the tracking error as compared to standard repetitive control.

Alternative Frequency-Domain Stability Criteria for Discrete-Time Networked Systems with Multiple Delays

Abstract In this paper alternative frequency-domain criteria are provided for the stability of discrete-time networked control systems with time-varying delays. These criteria are in various situations less conservative than the existing frequency-domain conditions as is demonstrated by means of an example. In addition, new stability conditions are presented that allow for multiple sensor-to-controller and controller-to-actuator channels exhibiting different delay characteristics. The stability conditions are formulated in terms of the H ∞ norm and the structured singular value. As a result, the obtained results can be used directly for controller synthesis via standard robust control techniques.