Andy Kho

Exploiting Nonlinear Dynamics in Novel Measurement Strategies and Devices: From Theory to Experiments and Applications

This paper is focused on the exploitation of intrinsic nonlinear dynamics toward novel measurement systems and readout methodologies. In particular, sensors that can be represented as nonlinear dynamical systems and are often reducible to systems described by a static nonlinearity are considered; the nonlinear behavior therefore reduces to the dynamics of a system characterized by two or more (meta)stable equilibrium states (or attractors) separated by energetic thresholds to be overcome to transition from one attractor to the other. The presence of a weak unknown target signal is assessed via the monitoring of the “residence times” in the attractors. This operational scenario that is based on the monitoring of suitable “events” avoids an “amplitude-based” readout and provides a very simple and sensitive readout-processing scheme. Many noise effects are also mitigated by the intrinsic decoupling between the amplitude domain of the input signal and the event or time domain of the output signal. We present here the general transduction methodology for this class of “residence-times difference” sensors, together with the experimental results obtained from the working versions of these sensors (in particular, a simple fluxgate magnetometer). We then introduce some novel dynamical behavior that occurs when the active nonlinear (in this case, bistable) elements are coupled using well-crafted coupling topologies. Sensors based on these coupling schemes provide several advantages over their single-element counterparts. We discuss the dynamics of the coupled-element device, summarizing recent theoretical and experimental results. Finally, we describe the construction and performance of working devices (magnetic- and electric-field sensors) based on these concepts.

A Bistable Microelectronic Circuit for Sensing Extremely Low Electric Field

Bistable systems are prevalently found in many sensor systems. Recently, we have explored unidirectionally coupled overdamped bistable systems that admit self-sustained oscillations when the coupling parameter is swept through the critical points of bifurcations. Complex behaviors emerge, in addition, from these relatively simple coupled systems when an external signal ac or dc is applied uniformly to all the elements in the array. In particular, we have demonstrated this emergent behavior for a coupled system comprised of mean-field hysteretic elements describing a single-domain ferromagnetic sample. The results are being used to develop extremely sensitive magnetic sensors capable of resolving field changes as low as 150 pT by observing the changes in the oscillation characteristics of the coupled sensors. In this paper, we explore the underlying dynamics of a coupled bistable system realized by coupling microelectronic circuits, which belong to the same class of dynamics as the aforementioned ferromagnetic system, with the nonlinear features and coupling terms modeled by hyperbolic tangent nonlinearities; these nonlinearities stem from the operational transconductance amplifiers used in constructing the microcircuits. The emergent behavior is being applied to develop an extremely sensitive electric-field sensor.

Self-induced oscillations in coupled fluxgate magnetometer: a novel approach to operating the magnetic sensors

A fluxgate magnetometer is one of the numerous devices that belong to a class of nonlinear systems known as the overdamped bistable system. Its dynamics can be described by the generic form x=-/spl nabla/U(x), where U(x) is the potential energy function with two minima that form the bases for the bistability. It is well known that an overdamped system does not oscillate on its own. To switch states, the system is forced by an external periodic signal with large enough amplitude to overcome the potential energy barrier that separates the two minima. However, well-designed coupling schemes, together with the appropriate choice of initial conditions can induce oscillations when a control parameter exceeds a threshold value. The self-induced oscillation, therefore, eliminates the necessity of the forcing function. We demonstrate these concepts numerically and experimentally using three single-domain fluxgate magnetometers that are coupled unidirectionally in a ring.

Advanced dynamic magnetometer for persistent surveillance

We present an overview of the “coupled-core” fluxgate magnetometer and its “single-core” counterpart. The basic theory is briefly discussed and some prototype realizations presented via a set of assorted applications. In particular, the results of sea-tests carried out, in collaboration with FOI-Stockholm, in the Baltic Sea will be presented and discussed together with other experimental results in the area of intrusion detection.

Exploiting nonlinearity in a Coupled-Core Fluxgate Magnetometer

Coupling-induced oscillations are a feature that appears to be universal in coupled systems that are (individually) described by bi-or multi-stable potential energy functions U(x); these properties are being exploited in a new class of dynamical sensors being developed by us. Here, we describe one of these devices, a coupled core fluxgate magnetometer (CCFM), whose operation is underpinned by this dynamic behavior.

Torus Bifurcation in Uni-Directional Coupled Gyroscopes

Nowadays, the global positioning system (GPS) is popularly used by the U.S. Navy in navigation systems to gain precise position, velocity, and time information. One of the biggest issues for using GPS is its susceptibility to jamming and other inferences. The received GPS signal is approximately 20 dB below the thermal noise level from a distance 11,000 miles away. Because of these weakness and vulnerability, many other alternative navigation methods are needed to improve performance and reduce the dependency on GPS. One of the main alternative methods is the Inertial Guidance System (IGS) that can operate wherever GPS signals are jammed or denied. A prototypical IGS is composed of three accelerometers to measure linear movement and three angular rate sensors (gyroscopes) to gauge the rotational movement. The main benefit of IGS is its low cost relatively to other methods. Current MEMS (Micro-Electro-Mechanical Systems) gyroscopes are compact and inexpensive, but their performance does not meet the requirements for an inertial grade guidance system. In this work, a difference approach was examined on the dynamics of coupled gyroscopes to improve performance through synchronization referred as vibratory coupled gyroscopes with drive amplitudes’ coupling. One of the main discoveries from the coupled gyroscopes’ mathematical model is a Torus bifurcation, which leads to synchronized behavior in and array of three gyroscopes uni-directionally coupled.

Coupled-Core Fluxgate Magnetometer

A fluxgate magnetometer is a magnetic field sensor that is used to detect relatively low intensity magnetic fields. It belongs to a class of nonlinear systems known as the overdamped bistable system whose dynamics can be described by the generic form x(t)=-ΔU(x). It is well known that an overdamped system will not oscillate on its own. It is usually driven with a known periodic signal with an amplitude large enough to overcome the potential barrier height. Instead of this approach, we will show how similar oscillations can be generated with a carefully selected coupling scheme, coupling parameters, and initial conditions [1, 2], thus eliminating the need for expensive driving signals. We will show that the coupled-core fluxgate magnetometer can not only detect DC magnetic fields, but it can detect and classify AC magnetic fields as well.

Self‐Induced Oscillations in Electronically‐Coupled Fluxgate Magnetometers

We present theoretical and experimental investigations of the fundamental idea that coupling‐induced oscillations can enhance the sensitivity of an array of magnetic sensors. In particular, we consider arrays made up of fluxgate magnetometers inductively coupled through electronic circuits. The underlying dynamics of the coupled system is more complicated as it shows new spatio‐temporal features that are not observed in a single fluxgate. Among these new features, self‐induced oscillations in the form of a traveling wave pattern are of particular interest because they can lead to higher sensitivity levels at reduced costs. Details of the experiments, a new signal detection mechanism, and results from numerical bifurcation analyzes are described in this work.