### Browsing by Author "Krishnaprasad, Perinkulam S."

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Item Adaptive Friction Compensation for Bi-Directional Low-Velocity Position Tracking(1992) Leonard, Naomi E.; Krishnaprasad, Perinkulam S.; ISRThis paper presents a comparative investigation of friction- compensating control strategies designed to improve low-velocity position tracking performance in the presence of velocity reversals for servomechanisms. The methods considered include adaptive control and estimation-based control. Additionally, the various controller designs incorporate different friction models ranging from classical friction and Stribeck friction to the less popular Dahl friction model. This investigation of friction models is motivated by the fact that there is little consensus in the literature on how best to model friction for dynamic friction compensation. the control strategies are compared in an extensive test program involving sinusoidal position trajectory tracking experiments on a direct-drive dc motor. We focus attention on comparative experimental results of friction compensation especially with repeated velocity reversals. The results show that the adaptive experiments also yield insight into the appropriateness of the different friction models under the tested operating conditions. In particular, the Dahl model, typically ignored in the literature proves to be significant for the firction-compensating control problem with repeated zero- velocity crossings.Item Adaptive Wavefront Control using a Nonlinear Zernike Filter(2001) Justh, Eric W.; Vorontsov, Mikhail A.; Carhart, Gary W.; Beresnev, Leonid A.; Krishnaprasad, Perinkulam S.; ISR; CDCSSA conventional Zernike filter measures wavefront phase by superimposing the aberrated input beam with a phase-shifted version of its zero-orderspectral component. The Fourier-domain phase-shifting is performed by afixed phase-shifting dot on a glass slide in the focal plane of a Fourier-transforming lens.Using an optically-controlled phase spatiallight modulator (SLM) instead of the fixed phase-shifting dot, we havesimulated and experimentally demonstrated a nonlinear Zernike filterrobust to wavefront tilt misalignments. In the experiments, a liquid-crystal light valve (LCLV) was used as the phase SLM. The terminology "nonlinear" Zernike filter refers to the nonlinear filteringoperation that takes place in the Fourier domain due to the phase changefor field spectral components being proportional to the spectral componentintensities.

Because the Zernike filter output intensity is directlyrelated to input wavefront phase, a parallel, distributed feedback systemcan replace the wavefront reconstruction calculations normally requiredin adaptive-optic phase correction systems. Applications include high-resolution phase distortion suppression for atmospheric turbulence,optical phase microscopy, and compensation of aberrations in optical system components.

A factor of eight improvement in Strehl ratio wasobtained experimentally, and simulation results suggest that even betterperformance could be obtained by replacing the LCLV with a more sophisticated optically-controlled phase SLM.

*SPIE Proc., High-Resolution Wavefront Control:Methods, Devices, and Applications II, Vol. 4124, pp. 198-200, 2000.*Item Affine Frames of Rational Wavelets in H2 (II+)(1992) Pati, Y.C.; Krishnaprasad, Perinkulam S.; ISRIn this paper we investigate frame decompositions of H2(II+) as a method of constructing rational approximations to nonrational transfer functions in H2(II+). The frames of interest are generated from a single analyzing wavelet. We consider the case in which the analyzing wavelet is rational and show that by appropriate grouping of terms in a wavelet expansion, H2(II+) can be decomposed as an infinite sum of a rational transfer functions which are related to one another by dilation and translation. Criteria for selecting a finite number of terms from such an infinite expansion are developed using time-frequency localization properties of wavelets.Item Almost Poisson Integration of Rigid Body Systems(1991) Austin, Mark; Krishnaprasad, Perinkulam S.; Wang, L.S.; ISRIn this paper we discuss the numerical integration of Lie-Poisson Systems using the mid-point rule. Since such systems result from the reduction of hamiltonian systems with symmetry by Lie Group actions, we also present examples of reconstruction rules for the full dynamics. A primary motivation is to preserve in the integration process, various conserved quantities of the original dynamics. A main result of this paper is a third order error estimate for the Lie-Poisson structure where h is the integration step-size. We note that Lie-Poisson systems appear naturally in many areas of physical science and engineering, including theoretical mechanics of fluids and plasmas, satellite dynamics, and polarization dynamics. In the present paper we consider a series of progressively complicated examples related to rigid body systems. We also consider a dissipative example associated to a Lie-Poisson system. The behavior of the mid-point rule and an associated reconstruction rule is numerically explored.Item Analysis and Synthesis of Feedforward Neural Networks Using Discrete Affine Wavelet Transformations(1990) Pati, Y.C.; Krishnaprasad, Perinkulam S.; ISRIn this paper we develop a theoretical description of standard feedfoward neural networks in terms of discrete affine wavelet transforms. This description aids in establishing a rigorous understanding of the behavior of feedforward neural networks based upon the properties of wavelet transforms. Time-frequency localization properties of wavelet transforms are shown to be crucial to our formulation. In addition to providing a solid mathematical foundation for feedforward neural networks, this theory may prove useful in explaining some of the empirically obtained results in the field of neural networks. Among the more practical implications of this work are the following: (1) Simple analysis of training data provides complete topological definition for a feedforward neural network. (2) Faster and more efficient learning algorithms are obtained by reducing the dimension of the parameter space in which interconnection weights are searched for. This reduction of the weight space is obtained via the same analysis used to configure the network. Global convergence of the iterative training procedure discussed here is assured. Moreover, it is possible to arrive at a non-iterative training procedure which involves solving a system of linear equations. (3) Every feedforward neural network constructed using our wavelet formulation is equivalent to a 'standard feedforward network.' Hence properties of neural networks, which have prompted the study of VLSI implementation of such networks are retained.Item Analysis of a complex activator-inhibitor equation(1999) Justh, Eric W.; Krishnaprasad, Perinkulam S.; ISR; CDCSSBasic properties of solutions and a Lyapunov functionalare presented for a complex activator-inhibitor equation witha cubic nonlinearity.Potential applications include control of coupled-oscillator arrays(for quasi-optical power combining and phased-array antennas),and control of MEMS actuator arrays (for micro-positioning small items).(

*This work to appear in Proc. 1999 American Control Conference.*)Item Analysis of a high-resolution optical wave-front control system(2002) Justh, Eric W.; Krishnaprasad, Perinkulam S.; ISR; CDCSSWe consider the formulation and analysis of a problem of automaticcontrol: correcting for the distortion induced in an optical wave frontdue to propagation through a turbulent atmosphere. It has recentlybeen demonstrated that high-resolution optical wave-front distortionsuppression can be achieved using feedback systems based on high-resolution spatial light modulators and phase-contrast techniques.We examine the modeling and analysis of such systems for the purposeof refining their design. The approach taken here might also beapplicable to other problems involving feedback controlof physical fields, particularly if the field sensing is performedoptically. (In Proc. Conf. on Information Sciences and Systems, Vol. 2, pp. 718-723, 2001.)Item Approximate Nonlinear Filtering and Its Applications for GPS(2001) Azimi-Sadjadi, Babak; Krishnaprasad, Perinkulam S.; ISRIn this paper we address the problem of nonlinear filtering in the presence of integer uncertainty. In the simulation results we show that Particle Filtering is capable of resolving integer ambiguity in the given nonlinear setup. Motivated by these results, we introduce a new Particle Filtering algorithm that can reducethe computational complexity for a certain class of problems. In this class, it isassumed that the conditional density of the state of the system given the observations is close to a known exponential family of densities. The proof of convergence of the approximated density to the actual density is given, and the application for GPS positioning is stated.Item Averaging and Motion Control On Lie Groups(1993) Leonard, Naomi E.; Krishnaprasad, Perinkulam S.; ISRThe deeper investigation of problems of feedback stabilization and constructive controllability has drawn increased attention to the question of structuring control systems. Thus, for instance, it is interesting to know how to combine periodic open loop controls with intermittent feedback corrections to achieve prescribed behavior in robotic motion planning systems. As a first step towards understanding this type of question, it would be useful to obtain some insight into the average behavior of a periodically forced system. In the present paper we are primarily interested in periodic forcing of left-invariant systems on Lie groups such as would arise in spacecraft attitude control. We prove averaging theorems applicable to systems evolving on general matrix Lie groups with particular focus on the attitude control problem. The results of this paper also yield useful formulae for motion planning of a variety of other systems such as an underwater vehicle which can be modeled as a control system evolving on the Lie group SE (3).Item The Berry-Hannay Phase of the Equal-Sided Spring-Jointed Four-Bar Mechanism(2001) Andersson, Sean B.; Krishnaprasad, Perinkulam S.; Krishnaprasad, Perinkulam S.; ISRIn this work we apply the moving systems approach developed by Marsden, Montgomery, and Ratiu to a free-floating, equal-sided, spring-jointed, four-bar mechanism that is being slowly rotated about its central axis and derive a formula for the induced geometric phase.Item The Berry-Hannay Phase of the Equal-Sided, Spring-Jointed, Four-Bar Mechanism: A Detailed Story(2002) Andersson, Sean B.; Krishnaprasad, Perinkulam S.; Krishnaprasad, Perinkulam S.; ISRIn this work we apply the moving systems approach developed by Marsden, Montgomery, and Ratiu to a free-floating, equal-sided, spring-jointed, four-bar mechanism that is being slowly rotated about its central axis and derive a formula for the induced geometric phase. We investigate the phase for a few specific systems using both analytic analysis and simulation.Item Cayley Transforms in Micromagnetics(2001) Krishnaprasad, Perinkulam S.; Tan, Xiaobo; ISR; CDCSSMethods of numerical integration of ordinary differential equations exploiting the Cayley transform arise in a variety of contexts, ranging from the classical mid-point rule to symplectic and (almost) Poisson integrators, to numerical methods on Lie Groups. In earlier work, the first author investigated the interplay between the Cayley transform and the Jacobi identity in establishing certain error formulas for the mid-point rule (with applications to coupled rigid bodies). In this paper, we use the Cayley transform to lift the Landau-Lifshitz-Gilbert equation of micromagnetics to the Lie algebra of the group of currents (on a compact magnetic body) with values in the 3-dimensional rotation group. This follows an idea of Arieh Iserles and, we use the lift to numerically integrate the Landau-Lifshitz-Gilbert equation conserving automatically the norm of the magnetization everywhere.Item Characterization of an ETREMA MP 50/6 Magnetostrictive Actuator(1998) Venkataraman, R.; Rameau, J.; Krishnaprasad, Perinkulam S.; ISR; CDCSSThis report presents the Displacement (Strain)-Current characteristic of an ETREMA MP 50/6 magnetostrictive actuator. This actuator is made of TERFENOL-D and displays giant magnetostriction. The displacement-current characteristic shows significant hysteresis behavior that depends on the rate at which the input is applied. Another important property of ferromagnetic hysteresis - the wiping out property, was also observed in the experiments.Item Comparative Study of Friction-Compensating Control Strategies for Servomechanisms(1991) Leonard, Naomi E.; Krishnaprasad, Perinkulam S.; ISRThis paper describes a comparative investigation of friction- compensating control strategies designed to improve low-velocity position tracking performance for servomechanisms. Several control methods are considered including adaptive control and estimation-based control. Additionally, the various controller designs incorporate different friction models ranging from classical friction and Stribeck friction to the less popular Dahl friction model. This investigation of friction models is motivated by the fact that there is little consensus in the literature on how best to model friction for dynamic friction compensation. The control strategies are compared in an extensive test program involving position tracking experiments on a direct- drive de motor. This effort addresses the current lack of comparative experimental results on friction compensation. The results show that the adaptive and estimation-based controllers outperform more traditional linear controllers. The experiments also yield insight into the appropriateness of the different friction models under the tested operating conditions. In particular, the Dahl model is observed to provide a reliable representation of friction behavior near zero velocity.Item Computation for Nonlinear Balancing(1998) Newman, Andrew J.; Krishnaprasad, Perinkulam S.; Krishnaprasad, Perinkulam S.; ISR; CDCSSWe illustrate a computational approach to practicalnonlinear balancing via the forced damped pendulum example.Item Computational Micromagnetics for Magnetostrictive Actuators(2000) Tan, X.; Baras, John S.; Krishnaprasad, Perinkulam S.; Baras, John S.; Krishnaprasad, Perinkulam S.; ISR; CDCSSComputational micromagnetics plays an important role in design and control of magnetostrictive actuators. A systematic approach to calculate magnetic dynamics and magnetostriction is presented. A finite difference method is developed to solve the coupled Landau-Lifshitz-Gilbert(LLG) equation for dynamics of magnetization and a one dimensional elastic motion equation. The effective field in the LLG equation consists of the external field, the demagnetizing field, the exchange field, and the anisotropy field.A hierarchical algorithm using multipole approximation speeds up the evaluation of the demagnetizing field, reducing computational cost from O(N^2) to O(NlogN). A hybrid 3D/1D rod model is adopted to compute the magnetostriction: a 3D model is used in solving the LLG equation for the dynamics of magnetization; then assuming that the rod is along z-direction, we take all cells with same z-cordinate as a new cell. The values of the magnetization and the effective field of the new cell are obtained from averaging those of the original cells that the new cell contains. Each new cell is represented as a mass-spring in solving the motion equation.

Numerical results include: 1. domain wall dynamics, including domain wall formation and motion; 2. effects of physical parameters, grid geometry, grid refinement and field step on H-M hysteresis curves; 3. magnetostriction curve.

Item Computing Balanced Realizations for Nonlinear Systems(2000) Newman, Andrew J.; Krishnaprasad, Perinkulam S.; Krishnaprasad, Perinkulam S.; ISR; CDCSSThis paper addresses the problem of computability pertaining to the Scherpen(1994) theory and procedure for balancing of nonlinear systems. In contrastto Moore's (1981) balancing method for linear systems, the Scherpen procedurefor nonlinear balancing is not immediately amenable to computationalimplementation. For example, the controllability energy function correspondsto the value function for a nonlinear optimal control problem. Also, theMorse-Palais lemma guarantees the existence of a local coordinatetransformation under which the controllability energy function takes acanonical quadratic form, but provides no constructive procedure for obtainingit. Thus, tools have not yet appeared for computing balanced realizations fornonlinear systems, and the procedure has not yet been applied as a tool formodel reduction.First, we consider the problem of computing the controllability energyfunction without numerically solving the family of optimal control problems,or the associated Hamilton-Jacobi-Bellman equation, implied in its definition.Stochastically excited systems play a major role in our methodology. Wepresent a stochastic method for computing an estimate of the controllabilityfunction, and show that in certain situations the method provides an exactsolution. The procedure is tested on applications via Monte-Carlo experiments.

Then, we address the problem of numerically determining a Morse transformationfor a function with non-degenerate critical point at 0. We develop analgorithm for computing the desired nonlinear transformation and estimatingthe neighborhood on which the transformed controllability function isquadratic.

In the literature, examples of applied nonlinear balancing have been limited topseudo-balancing of 2-dimensional gradient systems and noting that in the caseof linear systems the energy functions approach reduces to the usual setting ofgramians. We apply our approach to numerically derive, for the first time,balanced representations of nonlinear state-space models. In particular, wepresent applications to a forced damped pendulum system and a forced dampeddouble pendulum system.

*The research and scientific content in this material has been published in theProceedings of the 14th International Symposium on Mathematical Theory of Networks and Systems, Perpignan, France, June 19-23, 2000.*Item Control of Hysteresis in Smart Actuators with Application to Micro-Positioning(2003) Tan, Xiaobo; Baras, John S.; Krishnaprasad, Perinkulam S.; ISR; CDCSSHysteresis in smart material actuators makes the effective use of these actuators quite challenging. The Preisach operator has been widely used to model smart material hysteresis. Motivated by positioning applications of smart actuators, this paper addresses the value inversion problem for a class of discretized Preisach operators, i.e., to find an optimal input trajectory given a desired output value. This problem is solved through optimal state transition of a finite state machine (FSM) that corresponds to the discretized Preisach operator. A state-space reduction scheme for the FSM is developed, which significantly saves the memory and the computation time. As an example, micro-positioning control of a magnetostrictive actuator is investigated. Experimental results are presented to demonstrate the effectiveness of the proposed approach.Item Control of Hysteresis: Theory and Experimental Results(2001) Tan, Xiaobo; Venkataraman, Ram; Krishnaprasad, Perinkulam S.; ISRHysteresis in smart materials hinders the wider applicability ofsuch materials in actuators. In this paper, a systematic approachfor coping with hysteresis is presented. The method is illustratedthrough the example of controlling a commercially available magnetostrictive actuator.We utilize the low-dimensional model for the magnetostrictive actuator that was developed in earlier work. For low frequency inputs, the model approximates to a rate-independent hysteresis operator, with current as its input and magnetization as its output. Magnetostrictive strain is proportional to the square of the magnetization. In this paper, we use a classical Preisach operator for the rate-independent hysteresis operator.

We present the results of experiments conducted on a commercial magnetostrictive actuator, the purpose of which was the control of the displacement/strain output. A constrained least-squares algorithm is employedto identify a discrete approximation to the Preisach measure. We then discussa nonlinear inversion algorithm for the resulting Preisach operator, basedon the theory of strictly-increasing operators. This algorithm yields a control input signal to produce a desired magnetostrictive response.

The effectiveness of the inversion scheme is demonstrated via an open-looptrajectory tracking experiment.

Item Control of Small Formations Using Shape Coordinates(2003) Zhang, Fumin; Goldgeier, Michael; Krishnaprasad, Perinkulam S.; Krishnaprasad, Perinkulam S.; ISR; CDCSSFormations that contain a small number of robots are modeled as controlled Lagrangian systems on Jacobi shape space. This allows a block-structured control of position, orientation and shape of the formation. Feedback control laws are derived using control Lyapunov functions. The controlled dynamics converges to the invariant set where desired shape is achieved. Controllers are implemented in a layered fashion via the extended motion description language(MDLe) system. Group MDLe plans are constructed to allow structured controller design for formations.