Sajal K. Das

Damping Controller Design for Nanopositioners: A Mixed Passivity, Negative-Imaginary, and Small-Gain Approach

A design of a damping controller to damp the first resonant mode of a piezoelectric tube scanner (PTS) used in most commercial atomic force microscopes (AFMs) is proposed in this study. The design of the controller is carried out by proposing a novel analytical framework. The analytical framework examines the finite-gain stability for a positive feedback interconnection between two stable linear time-invariant systems, where one system has mixed passivity, negative-imaginary, and small-gain properties and the other system has mixed negative-imaginary, negative-passivity, and small-gain properties. Experimental results are presented to show the effectiveness of the proposed analytical framework to design the proposed controller.

Resonant Controller Design for a Piezoelectric Tube Scanner: A Mixed Negative-Imaginary and Small-Gain Approach

This brief presents the design and implementation of a single-input single-output and a multiple-input multiple-output resonant controller to damp the first resonant mode of a piezoelectric tube scanner of an atomic force microscope. The design of the controller is based on a mixed negative-imaginary and small-gain approach and the controller structure is chosen such that closed-loop stability is guaranteed. Experimental results are presented to demonstrate the effectiveness of the resonant controller.

Resonant controller for fast atomic force microscopy

The imaging performance of the atomic force microscope (AFM) in higher scanning speed is limited to the one percent of the first resonant frequency of its scanning unit i.e., piezoelectric tube scanner (PTS). In order to speed up the functioning of the AFM for high speed imaging, a resonant controller with an integral action has been applied in the both x and y axis of the PTS for damping the resonant mode of the scanner and improve the tracking performance. The overall closed-loop system with this scheme has higher bandwidth with improved gain and phase margin than the existing PI controller. It can reduce the cross coupling of the scanner and allows faster scanning. To measure the performance improvement of the proposed scheme a comparison has been made between the proposed controller scanned image and the existing AFM PI controller scanned image.

Resonant control of atomic force microscope scanner: A “mixed” negative-imaginary and small-gain approach

This paper presents the design and implementation of a resonant controller for the piezoelectric tube scanner (PTS) of an atomic force microscope (AFM) to damp the first resonant mode. The dynamics of the PTS is identified by using the measured data and the “mixed” negative-imaginary and small-gain approach is used to establish the internal stability of the interconnected systems. The experimental results demonstrate the performance improvement achieved by the proposed controller.

Stability analysis for interconnected systems with “mixed” passivity, negative-imaginary and small-gain properties

An analytical framework to examine the finite-gain stability for a positive feedback interconnection between two stable, linear time-invariant systems where one system has “mixed” passivity, negative-imaginary and small-gain properties and the other system has “mixed” negative-imaginary, negative-passivity, and small-gain properties is proposed. A classical Nyquist argument is used to examine the stability of the interconnected systems and the usefulness of the proposed framework is illustrated by a numerical example.

A MIMO Double Resonant Controller Design for Nanopositioners

A design of a double resonant controller to enhance the high-speed nanopositioning performance of a piezoelectric tube scanner (PTS) is presented in this paper. The design of the controller is demonstrated using a multi-input multi-output framework for damping, tracking, and cross coupling control in the PTS. A reference model control technique is applied to design the controller. The controller proposed in this paper achieves a bandwidth near to the first resonance frequency of the PTS. The controller is robust against changes in the resonance frequency of the PTS due to load change on the scanner. Experimental results using open-loop, closed-loop, and the built-in AFM proportional integral controller are presented to show the effectiveness of the proposed controller.

Multivariable Negative-Imaginary Controller Design for Damping and Cross Coupling Reduction of Nanopositioners: A Reference Model Matching Approach

This paper presents the design and experimental implementation of a novel multi-input multi-output (MIMO) control structure using two negative-imaginary damping controllers to damp the first resonant mode and attenuate cross coupling effects between the axes of a piezoelectric tube scanner. The dynamics of the scanner in the lateral and longitudinal axes are identified from measured data and the design of the controller using a MIMO framework is done based on a reference model matching approach. The controller proposed in the paper is able to achieve a bandwidth near to the first resonance frequency of the scanner and the proposed controller is robust against changes in resonance frequencies that are due to load changes on the scanner. Experimental results are presented to show the effectiveness of the proposed controller.

High bandwidth multi-variable combined resonant and integral resonant controller for fast image scanning of atomic force microscope

This paper presents the design and implementation of a multi-variable combined resonant and integral resonant controller for the piezoelectric tube scanner (PTS) of an atomic force microscope (AFM) to damp the resonant mode of the scanner, reduce the cross coupling effect between the axes of the scanner, increase the bandwidth of the overall closed-loop system, and improve the high speed imaging performance of the AFM. The lateral and longitudinal positioning system of the PTS is treated as a two-input two-output system and the system is identified using measured open-loop data. The value of each parameter of the proposed controller is determined by minimizing H2 norm of the difference between the desired and the actual closed-loop transfer function. The performance improvement achieved by the proposed controller is presented by comparing scanned images obtained by implementing the proposed controller and the built-in proportional-integral (PI) controller of the AFM.

Double resonant controller for fast atomic force microscopy

This paper presents the design and implementation of a double resonant controller with an integral controller in the piezoelectric tube scanner (PTS) of an atomic force microscope (AFM) to damp the resonant mode of the scanner, increase the bandwidth of the overall closed-loop system, and improve the high speed imaging performance of the AFM. The X and Y axes of the PTS is treated as an independent single-input singleoutput system and the system is identified by using the measured open-loop data. In order to measure the performance of the proposed controller a comparison of the scanned images have been made by using the proposed controller and the built-in proportional-integral (PI) controller of the AFM. The comparison of the scanned images demonstrate the performance improvement achieved by the proposed controller.

Multi-variable double resonant controller for fast image scanning of atomic force microscope

This paper presents the design and implementation of a multi-variable double resonant controller with a multivariable integral controller on the piezoelectric tube scanner (PTS) of an atomic force microscope (AFM) to damp the resonant mode of the scanner, reduce the cross coupling between the axes of the scanner, increase the bandwidth of the overall closed-loop system, and improve the high speed imaging performance of the AFM. The lateral and longitudinal positioning system of the PTS is treated as a multi-input multi-output system and the system is identified by using the measured open-loop data. The controller parameters are obtained by minimizing the H2 norm of the difference between the desired and the actual closed-loop transfer function and the performance improvement achieved by the proposed controller is shown by comparing the scanned images obtained by implementing the proposed controller and the built-in proportional-integral (PI) controller of the AFM.