Ram V. Iyer

Approximate inversion of the Preisach hysteresis operator with application to control of smart actuators

Hysteresis poses a challenge for control of smart actuators. A fundamental approach to hysteresis control is inverse compensation. For practical implementation, it is desirable for the input function generated via inversion to have regularity properties stronger than continuity. In this paper, we consider the problem of constructing right inverses for the Preisach model for hysteresis. Under mild conditions on the density function, we show the existence and weak-star continuity of the right-inverse, when the Preisach operator is considered to act on Holder continuous functions. Next, we introduce the concept of regularization to study the properties of approximate inverse schemes for the Preisach operator. Then, we present the fixed point and closest-match algorithms for approximately inverting the Preisach operator. The convergence and continuity properties of these two numerical schemes are studied. Finally, we present the results of an open-loop trajectory tracking experiment for a magnetostrictive actuator.

Control of hysteretic systems through inverse compensation

Inverse compensation is a fundamental technique in the control of systems with hysteresis. In this expository article, we present algorithms for constructing the inverse of the Preisach operator, a hysteresis model with application to magnetics, smart materials, terrestrial hydrology, and economics. Adaptive inverse control is discussed for cases where hysteresis parameters are not known precisely. To meet the demand of highly dynamic applications, an embedded inversion approach is presented that exploits the parallelism offered by FPGAs.

Tour Planning for an Unmanned Air Vehicle Under Wind Conditions

Abstract : A very important sub-problem in the task assignment problem for unmanned air vehicles (UAVs) is the evaluation of costs for the state transitions of a directed graph. Usually a Dubins vehicle flying in the absence of wind is considered in the computation of costs. However, when a prevailing wind vector field is considered, the costs take on very different values and the task assignment problem can have very different solutions. In this paper, we consider the problem of constructing minimum time trajectories for a Dubins vehicle in the presence of a time varying wind vector field. We present results on the existence and uniqueness of minimum-time solutions for a Dubins vehicle flying in a general time-varying wind vector field under some technical conditions. These results extend the conclusions of the well-known Dubins theorem. We also propose an algorithm for obtaining the minimum-time solution for an UAV and prove its convergence. We also present the results of numerical experiments that show that the importance of considering wind vector fields while planning the tour for an UAV.

Vision-based UAV flight control and obstacle avoidance

In this work, we explore various ideas and approaches to deal with the inherent uncertainty and image noise in motion analysis, and develop a low-complexity, accurate and reliable scheme to estimate the motion fields from UAV navigation videos. The motion field information allows us to accurately estimate ego-motion parameters of the UAV and refine (or correct) the motion measurements from other sensors. Based on the motion field information, we also compute the range map for objects in the scene. Once we have accurate knowledge about the vehicle motion and its navigation environment (range map), control and guidance laws can be designed to navigate the UAV between way points and avoid obstacles

Modeling and control of hysteresis

The five articles in this special issue focus on the modeling and control of hysteresis. Hysteresis is a nonlinear effect that arises in diverse disciplines ranging from physics to biology, from material science to mechanics, and from electronics to economics.

On the computation of the ego-motion and distance to obstacles for a micro air vehicle

In this paper, we have considered the problem of velocity and range estimation for an UAV using a camera and the knowledge of linear speed through a GPS device. In our earlier work (2006), a method for decomposition of a scene into structure blocks, and finding correspondences between such blocks in successive frames was developed. The result of this low-level image processing is (a) a set of structure blocks; (b) the motion of each structure block; and (c) a reliability index between zero and one denoting the confidence of the solution in (b). Here, we show that by solving a constrained optimization problem set up using the results of the image processing, one can obtain the linear and angular velocity of the camera motion, provided the speed of the linear motion is known. Once the velocity parameters is computed, we show how the range to objects in the field of view can be computed

A new method for the computation of motion from image sequences

The object of this paper is to introduce a new method for computing the linear velocity and angular velocity of an unmanned air vehicle (UAV) using only the information obtained from image sequences. In UAV applications, computational resources are limited due to payload constraints and the real-time computation requirement. Therefore, computationally intensive techniques employing feature extraction cannot be used. The alternative, in existing literature, is the computation of optical flow and the subsequent computation of motion. Both of these problems are ill-posed due to the correspondence and aperture problems. In this paper, we consider a different approach for motion estimation that is based on the spatial differentiation of an image function. We show that the solution is a well-posed problem that involves a least squares problem and nonlinear filtering. We also discuss the implementation of such a scheme on a UAV, and discuss the existence of such schemes in insects and crustaceans.

Wide Band Modeling and Parameter Identification for Magnetostrictive Actuators

Smart materials, such as magnetostrictive and piezoelectric materials and shape memory alloys, display certain coupling phenomena between applied electromagnetic or thermal fields and their mechanical properties. This leads to complicated constitutive behaviors of actuators built from these materials and limits their effective use. In this paper, we introduce a model for magnetostrictive actuators that effectively captures phenomenological behavior over the frequency range 0-800 Hz. The model includes rate-independent hysteresis, classical eddy current losses, excess losses, magneto-elastic coupling and inertial effects. In related work, we had shown the existence, uniqueness and stability of weak solutions to this model for voltage inputs in the space L2(0,T) cap Linfin (0,T) and external mechanical forces in the space L2(0,T). In this paper, we also propose a method for identifying parameters related to the eddy current and excess losses. Our method holds the hysteresis loss per cycle at a constant value as the frequency of the input voltage is changed, which then allows the identification of the parameters related to eddy and excess losses using linear programming. Our theoretical analysis indicates that the lead resistance cannot be assumed to have a constant value at frequencies higher than 800 Hz, which means that the skin effect becomes important at higher frequencies.

Macroscopic theory for capillary-pressure hysteresis.

In this article, we present a theory of macroscopic contact angle hysteresis by considering the minimization of the Helmholtz free energy of a solid-liquid-gas system over a convex set, subject to a constant volume constraint. The liquid and solid surfaces in contact are assumed to adhere weakly to each other, causing the interfacial energy to be set-valued. A simple calculus of variations argument for the minimization of the Helmholtz energy leads to the Young-Laplace equation for the drop surface in contact with the gas and a variational inequality that yields contact angle hysteresis for advancing/receding flow. We also show that the Young-Laplace equation with a Dirichlet boundary condition together with the variational inequality yields a basic hysteresis operator that describes the relationship between capillary pressure and volume. We validate the theory using results from the experiment for a sessile macroscopic drop. Although the capillary effect is a complex phenomenon even for a droplet as various points along the contact line might be pinned, the capillary pressure and volume of the drop are scalar variables that encapsulate the global quasistatic energy information for the entire droplet. Studying the capillary pressure versus volume relationship greatly simplifies the understanding and modeling of the phenomenon just as scalar magnetic hysteresis graphs greatly aided the modeling of devices with magnetic materials.

On the solution of operator equation problems with application to Preisach density estimation

In this paper, we study the numerical solution of a linear, compact, integral operator equation with linear inequality constraints on the solution space. The operator equation is approximated by a linear matrix equation via discretization, which may be then solved using a linear least squares L2 approach. Three methods, including two new methods, for the regularization of the discretized equation without constraints were presented. We compare the sensitivity of the solutions from these methods for perturbations in the data; we also compare the time taken for solution. Next, we present a new algorithm to solve the linear inequality constrained, minimum norm, least squares problem by adapting the solution methods presented for the unconstrained problem. Then we compare it with the MatLab© function quadprog with respect to residual error and speed. Finally, we apply the new method to identify the density of a Preisach operator for two electro-active polymers and a magnetostrictive actuator and again show that the new method performs as well or better than quadprog.