Yingfeng Shan

Design and Analysis of Discrete-Time Repetitive Control for Scanning Probe Microscopes

This paper studies repetitive control (RC) with linear phase lead compensation to precisely track periodic trajectories in piezo-based scanning probe microscopes (SPMs). Quite often, the lateral scanning motion in SPMs during imaging or nanofabrication is periodic. Dynamic and hysteresis effects in the piezoactuator cause significant tracking error. To minimize the tracking error, commercial SPMs commonly use proportional-integral-derivative (PID) feedback controllers; however, the residual error of PID control can be excessively large, especially at high scan rates. In addition, the error repeats from one operating cycle to the next. To account for the periodic tracking error, a discrete-time RC is designed, analyzed, and implemented on an atomic force microscope (AFM). The advantages of RC include straightforward digital implementation and it can be plugged into an existing feedback control loop, such as PID, to enhance performance. The proposed RC incorporates two phase lead compensators to ensure robustness and minimize the steady-state tracking error. Simulation and experimental results from an AFM system compare the performance among (1) PID, (2) standard RC, and (3) the modified RC with phase lead compensation. The results show that the latter reduces the steady-state tracking error to less than 2% at 25 Hz scan rate, an over 80% improvement compared with PID control.

Accounting for hysteresis in repetitive control design: Nanopositioning example

This paper deals with designing a repetitive controller (RC) for tracking periodic reference trajectories for systems that exhibit hysteresis, such as piezoelectric actuators used in nanopositioning systems. Hysteresis can drastically limit the performance of an RC designed around a linear dynamics model, and thus the effect of hysteresis on the closed-loop stability of RC is analyzed and the allowable size of the hysteresis nonlinearity for a stable RC is quantified. But when the hysteresis effect exceeds the maximum bound, an inverse-hysteresis feedforward controller based on the Prandtl-Ishlinskii hysteresis model is used to compensate for the nonlinearity. The control method is implemented on a custom-designed nanopositioning stage. Experimental results show that by incorporating hysteresis compensation the stability margin and the rate of error reduction improve. Likewise, the maximum tracking error reduces by 71%, from 13.7% (using industry-standard integral control) to 3.9% (using RC with hysteresis compensation), underscoring the benefits of RC with hysteresis compensation.

Design and Control for High-Speed Nanopositioning: Serial-Kinematic Nanopositioners and Repetitive Control for Nanofabrication

This article focuses on the design and control of nanopo-sitioning systems (nanoposi-tioners) that operate mostly in a repetitive fashion. In addition to accuracy, speed is also a crucial requirement for these systems. Multi-axis nanopositioners are critical in applications such as atomic force microscopy (AFM) [1], fiber optic alignment [2], micro- and nanoma-chining [3], [4], and nanometrology [5], [6]. More specifically, for video-rate scanning probe microscopy (SPM) and high-throughput probe-based nano-fabrication [7], the desired motion trajectory of the nanopositioner repeats from one operating cycle to the next and the motion should be as fast and accurate as possible. However, vibrations caused by mechanical resonance are a major factor limiting the speed. Typically, the bandwidth of these systems is limited by the first mode of vibration [8], [9].

Integrated Sensing for IPMC Actuators Using Strain Gages for Underwater Applications

Ionic polymer-metal composite (IPMC) actuators have many advantages, for instance, they: 1) can be driven with low voltages (<;5 V); 2) are soft, flexible, and easily shaped; and 3) can operate in an aqueous environment (such as water). Important applications for IPMCs include active catheter devices for minimally invasive surgery, artificial muscles, and sensors and actuators for biorobotics. Due to inherent nonlinear behavior, dynamic effects, and external disturbances, sensing and feedback control are required for precision operation. A new method to sense the displacement of an IPMC actuator using resistive strain gages is proposed. The sensing scheme is low cost, practical, effective, and importantly, compact compared to existing methods such as lasers and charge-coupled device (CCD) cameras. The strain-to-displacement relationship is developed and experimental results are presented to demonstrate the effectiveness of the sensing scheme. Furthermore, the sensor signal is used as feedback information in a repetitive controller to improve the tracking of periodic motion. The stability condition for the controller is presented, and the sensing scheme and feedback control approach are applied to a fabricated perfluorinated ion-exchange-membrane-based IPMC actuator with lithium as its counterion. Experimental results show that the tracking error can be reduced by approximately 50% compared to PID control for tracking of periodic signals, including sinusoidal and triangular wave forms.

Low-Cost IR Reflective Sensors for Submicrolevel Position Measurement and Control

This paper investigates the feasibility of using commercially available, low-cost IR reflective sensors for micro- to sub- microscale position measurement and control. These sensors are typically used as optical switches; however, their application for detecting fine motion, such as the movement of a piezoactuator, has not been investigated. Five IR sensors were evaluated to determine their range, resolution, linear distortion, noise characteristics, and bandwidth. Experimental results show that the performance of the IR sensors compares well with a commercial inductive sensor that costs significantly more. For example, the measured resolution was within several hundred nanometers over a plusmn200 mum range and the linear distortion was significantly lower than the inductive sensor. A selected IR sensor was used in the design of a state-feedback control system to compensate for hysteresis and creep in an experimental piezopositioner. Compared to the open-loop system, by using the IR sensor in feedback, the output hysteresis was reduced by over 95 %. These results show the potential of such sensors in the design of low-cost microprecision mechatronic positioning systems.

Frequency-weighted feedforward control for dynamic compensation in ionic polymer–metal composite actuators

Ionic polymer–metal composites (IPMCs) are innovative materials that offer combined sensing and actuating ability in lightweight and flexible package. IPMCs have been exploited in robotics and a wide variety of biomedical devices, for example, as sensors for teleoperation, as actuators for positioning in active endoscopy, as fins for propelling aquatic robots, and as an injector for drug delivery. In the actuation mode, one of the main challenges is precise position control. In particular, IPMC actuators exhibit relaxation behavior and nonlinearities; and at relatively high operating frequencies dynamic effects limit accuracy and positioning bandwidth. A frequency-weighted feedforward controller is designed to account for the IPMCs structural dynamics to enable fast positioning. The control method is applied to a custom-made Nafion-based IPMC actuator. The controller takes into account the magnitude of the control input to avoid generating excessively large voltages which can damage the IPMC actuator. To account for unmodeled effects not captured by the dynamics model, a feedback controller is integrated with the feedforward controller. Experimental results show a significant improvement in the tracking performance when feedforward control is used. For instance, the feedforward controller shows over 75% reduction in the tracking error compared to the case without feedforward compensation. Finally, the integrated feedforward and feedback control system reduces the tracking error to less than 10% for tracking an 18-Hz triangle-like trajectory. Some of the advantages of feedforward control as well as its limitations are also discussed.

Repetitive control with Prandtl-Ishlinskii hysteresis inverse for piezo-based nanopositioning

Repetitive control (RC) is a feedback-based approach useful for tracking periodic reference trajectories, for example in scanning applications. The major challenges with RC include closed-loop stability, robustness, and minimizing the steady-state tracking error. In piezo-based nanopositioning systems, the hysteresis effect can limit the performance of RC designed based on a linear dynamics model. An enhanced discrete-time repetitive controller is combined with an inverse-hysteresis compensator based on the Prandtl-Ishlinskii (P-I) model for hysteresis. The feasibility of the inverse model and the performance of the RC system with the inverse compensator are investigated experimentally. Measured results from a flexure-guided nanopositioner show that hysteresis compensation leads to improvement in the stability margin and rate of convergence of the tracking error for the closed-loop RC system. For scanning at 25 Hz, the maximum tracking error is 1.72%.

Tracking control of oscillatory motion in IPMC actuators for underwater applications

Ionic polymer-metal composite (IPMC) actuators have many advantages; for instance, they (1) can be driven with low voltages (<5 V); (2) are soft, flexible and easily shaped; and (3) can operate in an aqueous environment (such as water). Important applications for IPMCs include active catheter devices for minimally invasive surgery, artificial muscle, and sensors and actuators for biorobotics. For applications such as endoscopy and flapping-based propulsion systems in aquatic robots, the IPMC actuator is required to precisely track a periodic reference trajectory. However, due to dynamic effects, nonlinear behavior, and external disturbances, uncompensated open-loop control yields excessively-large tracking error. This paper focuses on precision tracking of oscillatory motion in IPMC actuators. A feedback controller based on the repetitive control concept is proposed to improve tracking performance from one operating period to the next. The stability of the controller is analyzed in the discrete-time domain, and design considerations are discussed. The method is applied to a newly fabricated Perfluorinated Ion Exchange Membrane based IPMC actuator with lithium as its counterion. The tip displacement of the IPMC actuator is measured by a strain gage sensor. This newly proposed sensing scheme is low cost, practical, effective, and importantly, compact. Experimental results show the combined control and sensing scheme can minimize the tracking error by approximately 50% compared to PID control for tracking of periodic signals including sinusoidal and triangular wave forms.

Discrete-Time Phase Compensated Repetitive Control for Piezoactuators in Scanning Probe Microscopes

This paper studies repetitive control (RC) with linear phase lead compensation to precisely track periodic trajectories in piezo-based scanning probe microscopes (SPMs). Quite often, the lateral scanning motion in SPMs during imaging or fabrication is periodic in time. Because of hysteresis and dynamic effects in the piezoactuator, the tracking error repeats from one scanning period to the next. Commercial SPMs typically employ PID feedback controllers to minimize the tracking error; however, the error repeats from one operating cycle to the next. Furthermore, the residual error can be excessively large, especially at high scan rates. A discrete-time repetitive controller was designed, analyzed, and implemented on an experimental SPM. The design of the RC incorporates two phase lead compensators to provide stability and to minimize the steady-state tracking error. Associated with the lead compensators are two parameters that can be adjusted to control the performance of the repetitive controller. Experimental tracking results are presented that compare the performance of PID, standard RC, and the modified RC with phase lead compensation. The results show that the modified RC reduces the steady-state tracking error to less than 2% at 25 Hz scan rate, an over 80% improvement compared to PID control.Copyright

REPETITIVE CONTROL DESIGN FOR PIEZOELECTRIC ACTUATORS

Piezoactuators exhibit hysteresis and dynamic effects which often cause significant positioning error in a wide variety of motion control applications, especially in applications where the reference trajectory is periodic in time, such as the raster motion in scanning probe microscopy. A feedback-based approach known as repetitive control (RC) is well-suited to track periodic reference trajectories and/or to reject periodic disturbances. However, when an RC is designed with a linear dynamics model and subsequently applied to a system with hysteresis, stability and good tracking performance may not be guaranteed. In this work, the effect of hysteresis on the closed-loop stability of RC is analyzed. In the analysis, the hysteresis effect is represented by the Prandtl-Ishlinskii hysteresis model. Using this model, stability conditions are provided for an RC designed for piezoelectric actuators which commonly exhibit hysteresis. The approach is applied to a custom-designed piezo-driven nanopositioner for tracking periodic trajectories.Copyright