Mario A. Rotea

Mixed H/sub 2//H/sub infinity / filtering

The authors consider the problem of finding a filter or estimator that minimizes a mixed H/sub 2//H/sub infinity / filtering cost on the transfer matrix from a given noise input to the filtering error subject to a H/sub infinity / constraint on the transfer matrix from a second noise input to the filtering error. This problem can be interpreted and motivated in many different ways-for instance, as a problem of optimal filtering in the presence of noise with fixed and known spectral characteristics subject to a bound on the filtering error due to a second noise source whose spectral characteristics are unknown. It is shown that one can come arbitrarily close to the optimal mixed H/sub 2//H/sub infinity / filtering cost using a standard Luenberger estimator. The problem of finding a suitable Leunberger estimator gain can be converted into a convex optimization problem over a subset of real matrices of dimension n*(n+1)/2+n*p, where n is the state dimension and p the number of measurements.<<ETX>>

Microfluidic device incorporating closed loop feedback control for uniform and tunable production of micro-droplets

Both micro- and nanofluidics are finding increasing use in the growing toolbox of nanotechnology; for the production of nanoparticles, and as micro-reactors for carefully controlled chemical reactions. These laboratories-on-a-chip hold vast potential for industrial application, however, only the most simple are truly starting to emerge as commercially viable, particularly in the area of droplet formation and emulsion creation. In order to automate droplet production with a desired size and dispersity, we have designed a microfluidic-based technology utilizing elementary microchannel geometries in combination with a closed loop feedback system to control the continuous- and dispersed-phase flow rates. Both the device geometry and control system have been optimized to allow for the production of a tunable emulsion. By utilizing discrete linear control theory, the device is able to produce the desired results with little to no prior knowledge of the fluid material properties to be used in either phase. We present our results from initial development using flow-focusing microfluidic geometry for droplet formation, computer-tethered syringe pumps to individually control the continuous and dispersed phase flow rates, a high-speed camera, and a controller and driver system for the optical measurements and pumps, respectively. We will show the efficacy of this technique for Newtonian and viscoelastic liquids, with and without the presence of surfactants. It can be envisioned that through careful control optimization, such a system can be developed to a point that will allow the production of designer emulsions with droplets eventually reaching the nanoscale.

Suboptimal control of rigid body motion with a quadratic cost

In this paper we consider the problem of controlling the rotational motion of a rigid body using three independent control torques. Given a quadratic cost we seek stabilizing state feedback controllers which guarantee that all motions starting within a specified bounded set have cost less than a given number; i.e., we seek suboptimal stabilizing controllers. For a special class of cost functions, we present explicit expressions for suboptimal stabilizing controllers yielding a cost arbitrarily close to the infimal cost. For the general case, we present sufficient conditions which guarantee the existence of linear, suboptimal, stabilizing controllers.

An /spl Lscr//sub 2/ disturbance attenuation approach to the nonlinear benchmark problem

Uses the theory of /spl Lscr//sub 2/ disturbance attenuation for linear (/spl Hscr//sub /spl infin//) and nonlinear systems to obtain solutions to the nonlinear benchmark problem (NLBP) proposed in the companion paper by Bupp et al. (1995). By considering a series expansion solution to the Hamilton-Jacobi-Isaacs equation associated with the nonlinear disturbance attenuation problem, the authors obtain a series expansion solution for a nonlinear controller. Numerical simulations compare the performance of the third order approximation of the nonlinear controller with its first order approximation (which is the same as a linear /spl Hscr//sub /spl infin// controller obtained from the linearized problem.).

Dynamic Programming Framework for Wind Power Maximization

Abstract The contribution of this paper is the formulation of the wind farm power maximization problem as a multi-stage dynamic programming problem. This formulation is made possible by introducing a state-space model to describe the evolution of the wind velocity profile as a function of the free-stream wind velocity and the wind turbine control variables. This state-space model is coupled with a multi-stage utility function that quantifies the power to be maximized. The benefits of this approach include: a simple algorithm to determine the turbine optimal controls, as a feedback function of the wind farm state, and a rigorous, yet simple, method to calculate the limit of performance for wind farm power maximization. A one-dimensional cascade of wind turbines is used to illustrate the approach. Also given is an analytical expression for the maximum power that can be extracted from the one-dimensional cascade, which parallels the well-known Betz limit for a single turbine.

Data-driven Reduced Order Model for prediction of wind turbine wakes

In this paper a new paradigm for prediction of wind turbine wakes is proposed, which is based on a reduced order model (ROM) embedded in a Kalman filter. The ROM is evaluated by means of dynamic mode decomposition performed on high fidelity LES numerical simulations of wind turbines operating under different operational regimes. The ROM enables to capture the main physical processes underpinning the downstream evolution and dynamics of wind turbine wakes. The ROM is then embedded within a Kalman filter in order to produce a time-marching algorithm for prediction of wind turbine wake flows. This data-driven algorithm enables data assimilation of new measurements simultaneously to the wake prediction, which leads to an improved accuracy and a dynamic update of the ROM in presence of emerging coherent wake dynamics observed from new available data. Thanks to its low computational cost, this numerical tool is particularly suitable for real-time applications, control and optimization of large wind farms.

Large Eddy Simulation for an array of turbines with Extremum Seeking Control

Large Eddy Simulations of the flow past an array of three aligned turbines have been performed using two different control strategies: constant torque gain and the Extremum Seeking Control. An off-design tip speed ratio has been chosen as initial condition for each turbine. It is shown that the turbines controlled with constant torque gain do not reach their optimum tip speed ratio. On the other hand, turbines controlled with ESC reach, to a close approximation, the tip speed ratio which maximizes their power production. The power produced by the array controlled with ESC is about 10% larger than that obtained with constant torque gain. Power spectral densities of the wind velocity in the wake of the turbines are presented to discuss how to select the proper dithering frequency.

Development of a high fidelity CFD code for wind farm control

In this paper we describe an effort recently completed at UT Dallas to develop a high-fidelity computational fluid dynamics code to test and develop control algorithms aimed at maximizing power production and load mitigation. Preliminary results of three aligned turbines operating at different tip speed ratios (TSRs) are discussed to show the wealth of details available from the present code. The finer solution of the flow physics allows to gain a better understanding of how control algorithms should be designed and implemented in practical configurations. The paper includes a detailed analysis of the power and loads for optimal TSRs obtained by applying dynamic programming to a low-fidelity analytical model.

Robots looking for interesting things: Extremum seeking control on saliency maps

This paper presents a novel approach to increase the amount of visual stimuli in sensor measurements using saliency maps. A saliency map is a combination of normalized feature maps in different channels (i.e. color, intensity) to represent the relative strength of visual stimuli in an image. The total saliency is higher when the camera is looking at a scene with more interesting things in the field of view and vise versa. We employ methods of extremum seeking control to find a camera position that corresponds to local maximum saliency value. We combine the global properties of simplex optimization methods with the local search properties and dynamic response of extremum seeking control to create a novel algorithm that is more likely to find a global maximum than conventional extremum seeking control. Simulations and experiments are presented to show the strength of this approach.

Sensors searching for interesting things: Extremum seeking control on entropy maps

This paper presents a novel approach to increasing the information content in sensor measurements, with special applications in images or video. The entropy of a signal gives a measurement of the information content. In the case of images, entropy is low when large parts of an image are uniformly colored or shaded. This can occur due to poor camera settings, poor lighting conditions, or the camera is facing a scene with little interest or activity. Minor camera motions can often alleviate these problems. We employ methods of extremum seeking control to find a local maximum in the entropy map surrounding the camera. Entropy maps often have local maxima that do not correspond to a global maximum. Therefore we combine the global properties of simplex optimization methods with the local search properties and dynamic response of extremum seeking control to create a novel algorithm that is more likely to find a global maximum than conventional extremum seeking control. Simulations and experiments are presented to show the strength of this approach.