A new scanning method for fast atomic force microscopy

In recent years, the atomic force microscope (AFM) has become an important tool in nanotechnology research. It was first conceived to generate 3-D images of conducting as well as nonconducting surfaces with a high degree of accuracy. Presently, it is also being used in applications that involve manipulation of material surfaces at a nanoscale. In this paper, we describe a new scanning method for fast atomic force microscopy. In this technique, the sample is scanned in a spiral pattern instead of the well-established raster pattern. A constant angular velocity spiral scan can be produced by applying single frequency cosine and sine signals with slowly varying amplitudes to the x-axis and y -axis of AFM nanopositioner, respectively. The use of single-frequency input signals allows the scanner to move at high speeds without exciting the mechanical resonance of the device. Alternatively, the frequency of the sinusoidal set points can be varied to maintain a constant linear velocity (CLV) while a spiral trajectory is being traced. Thus, producing a CLV spiral. These scan methods can be incorporated into most modern AFMs with minimal effort since they can be implemented in software using the existing hardware. Experimental results obtained by implementing the method on a commercial AFM indicate that high-quality images can be generated at scan frequencies well beyond the raster scans

Precise tip positioning of a flexible manipulator using resonant control

A single-link flexible manipulator is fabricated to represent a typical flexible robotic arm. This flexible manipulator is modeled as a SIMO system with the motor-torque as the input and the hub angle and the tip position as the outputs. The two transfer functions are identified using a frequency-domain system identification method. A feedback loop around the hub angle response with a resonant controller is designed to damp the resonant modes. A high gain integral controller is also designed to achieve zero steady-state error in the tip position response. Experiments are performed to demonstrate the effectiveness of the proposed control scheme

Precise tip positioning of a flexible manipulator using resonant control

A single-link flexible manipulator is fabricated to represent a typical flexible robotic arm. This flexible manipulator is modeled as an SIMO system with the motor torque as the input and the hub angle and the tip position as the outputs. The two transfer functions are identified using a frequency-domain system identification method, and the resonant modes are determined. A feedback loop around the hub angle response with a resonant controller is designed to damp the resonant modes. A high-gain integral controller is also implemented to achieve zero steady-state error in the tip position response. Experiments are performed to demonstrate the effectiveness of the proposed control scheme

Model Reduction and Parameter Estimation for Diffusion Systems

Diffusion is a phenomenon in which particles move from regions of higher density to regions of lower density. Many physical systems, in fields as diverse as plant biology and finance, are known to involve diffusion phenomena. Typically, diffusion systems are modeled by partial differential equations (PDEs), which include certain parameters. These parameters characterize a given diffusion system. Therefore, for both modeling and simulation of a diffusion system, one has to either know or determine these parameters. Moreover, as PDEs are infinite order dynamic systems, for computational purposes one has to approximate them by a finite order model. In this thesis, we investigate these two issues of model reduction and parameter estimation by considering certain specific cases of heat diffusion systems. We first address model reduction by considering two specific cases of heat diffusion systems. The first case is a one-dimensional heat diffusion across a homogeneous wall, and the second case is a two-dimensional heat diffusion across a homogeneous rectangular plate. In the one-dimensional case we construct finite order approximations by using some well known PDE solvers and evaluate their effectiveness in approximating the true system. We also construct certain other alternative approximations for the one-dimensional diffusion system by exploiting the different modal structures inherently present in it. For the two-dimensional heat diffusion system, we construct finite order approximations first using the standard finite difference approximation (FD) scheme, and then refine the FD approximation by using its asymptotic limit. As for parameter estimation, we consider the same one-dimensional heat diffusion system, as in model reduction. We estimate the parameters involved, first using the standard batch estimation technique. The convergence of the estimates are investigated both numerically and theoretically. We also estimate the parameters of the one-dimensional heat diffusion system recursively, initially by adopting the standard recursive prediction error method (RPEM), and later by using two different recursive algorithms devised in the frequency domain. The convergence of the frequency domain recursive estimates is also investigated

Reduced order models for diffusion systems

Mathematical models for diffusion processes like heat propagation, dispersion of pollutants etc., are normally partial differential equations which involve certain unknown parameters. To use these mathematical models as the substitutes of the true system, one has to determine these parameters. Partial differential equations (PDE) of the form beapartial u(x,t)/partial t = L u(x,t)  (eq1.1)eea where L is a linear differential (spatial) operator, describe infinite dimensional dynamical systems. To compute a numerical solution for such partial differential equations, one has to approximate the underlying system by a finite order one. By using this finite order approximation, one then computes an approximate numerical solution for the PDE. We consider a simple case of heat propagation in a homogeneous wall. The resulting partial differential equation, which is of the form (eq1.1), is approximated by finite order models by using certain existing numerical techniques like Galerkin and Collocation etc. These reduced order models are used to estimate the unknown parameters involved in the PDE, by using the well developed tools of system identification. In this paper we concentrate more on the model reduction aspects of the problem. In particular, we examine the model order reduction capabilities of the Chebyshev polynomial methods used for solving partial differential equation