Bharath Bhikkaji

A transfer-function is said to be negative imaginary if the corresponding frequency response function has a negative definite imaginary part (on the positively increasing imaginary axis). Negative imaginary transfer-functions can be stabilized using negative imaginary feedback controllers. Flexible structures with compatible collocated sensor/actuator pairs have transfer-functions that are negative imaginary. In this paper a model structure that typically represents a collocated structure is considered. An identification algorithm which enforces the negative imaginary constraint is proposed for estimating the model parameters. A feedback control technique, known as integral resonant control (IRC), is proposed for damping vibrations in collocated flexible structures. Conditions for the stability of the proposed controller are derived, and shown that the set of stabilizing IRCs is convex. Finally, a flexible beam with two pairs of collocated piezoelectric actuators/sensors is considered. The proposed identification scheme is used determining the transfer-function and an IRC is designed for damping the vibrations. The experimental results obtained are reported. © 1996-2012 IEEE.

Controller design to compensate vibration, hysteresis and time delay in a high-speed serial-kinematic X-Y nanopositioner is presented in this paper. A high-speed serial-kinematic X-Y nanopositioner, designed in-house, is installed in a commercial AFM and its scanning performance is studied. The impediments to fast scanning are (i) the presence of mechanical resonances in the nanopositioning stage, (ii) nonlinearities due to the piezoelectric actuators and (iii) time delay introduced by finite clock speeds of the signal conditioning circuitry associated with displacement sensors. In this paper an integral resonant controller is designed to mitigate the effect of the resonance along the X axis (fast axis). The control design accommodates for the time delay, thereby ensuring robust stability. A high gain integral controller is wrapped around the damped nanopositioner to ensure sufficient linearity near the region of operation. For actuation along the Y axis (slow axis), where the bandwidth requirement is less demanding, a notch filter is used to increase the gain margin and the nonlinearity is compensated using a high gain feedback controller. Enhancement in the scanning speed up to 200 Hz is observed. Imaging and tracking performance for open loop and closed loop scans up to 200 Hz line rate is compared and presented. Limitations and future work are discussed. © 2014 IOP Publishing Ltd.

An XYZ nanopositioner is designed for fast the atomic force microscopy. The first resonant modes of the device are measured at 8.8, 8.9, and 48.4 kHz along the X-, Y-, and Z-axes, respectively, which are in close agreement to the finite-element simulations. The measured travel ranges of the lateral and vertical axes are 6.5 μm × 6.6 μm and 4.2 μm, respectively. Actuating the nanopositioner at frequencies beyond 1% of the first resonance of the lateral axes causes mechanical vibrations that result in degradation of the images generated. In order to improve the lateral scanning bandwidth, controllers are designed using the integral resonant control methodology to damp the resonant modes of the nanopositioner and to enable fast actuation. Due to the large bandwidth of the designed nanopositioner, a field programmable analog array is used for analog implementation of the controllers. High-resolution images are successfully generated at 200-Hz line rate with 200×200 pixel resolution in closed loop. © 1996-2012 IEEE.