A Snapshot Algorithm for Linear Feedback Flow Control Design

The control of fluid flows has many applications. For micro air vehicles, integrated flow control designs could enhance flight stability by mitigating the effect of destabilizing air flows in their low Reynolds number regimes. However, computing model based feedback control designs can be challenging due to high dimensional discretized flow models. In this work, we investigate the use of a snapshot algorithm proposed in Ref. 1 to approximate the feedback gain operator for a linear incompressible unsteady flow problem on a bounded domain. The main component of the algorithm is obtaining solution snapshots of certain linear flow problems. Numerical results for the example flow problem show convergence of the feedback gains

A low-rank solution method for Riccati equations with indefinite quadratic terms

Algebraic Riccati equations with indefinite quadratic terms play an important role in applications related to robust controller design. While there are many established approaches to solve these in case of small-scale dense coefficients, there is no approach available to compute solutions in the large-scale sparse setting. In this paper, we develop an iterative method to compute low-rank approximations of stabilizing solutions of large-scale sparse continuous-time algebraic Riccati equations with indefinite quadratic terms. We test the developed approach for dense examples in comparison to other established matrix equation solvers, and investigate the applicability and performance in large-scale sparse examples.Comment: 19 pages, 2 figures, 5 table

A numerical comparison of solvers for large-scale, continuous-time algebraic Riccati equations and LQR problems

In this paper, we discuss numerical methods for solving large-scale continuous-time algebraic Riccati equations. These methods have been the focus of intensive research in recent years, and significant progress has been made in both the theoretical understanding and efficient implementation of various competing algorithms. There are several goals of this manuscript: first, to gather in one place an overview of different approaches for solving large-scale Riccati equations, and to point to the recent advances in each of them. Second, to analyze and compare the main computational ingredients of these algorithms, to detect their strong points and their potential bottlenecks. And finally, to compare the effective implementations of all methods on a set of relevant benchmark examples, giving an indication of their relative performance

Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis and computer science

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, and computer science during the period April l, 1988 through September 30, 1988

Detecting fluid flows with bioinspired hair sensors

Many animals detect prey or enhance their locomotion with information from hair-like receptors that are activated by local fluid flows. The utility of biological hair receptors has motivated the design of artificial hair sensors (AHS) for flow control applications where aerodynamic or hydrodynamic forces play a significant role in the dynamics of a body. Among the potential applications for AHS are low-Reynolds number flyers for enhanced maneuverability and underwater vehicles for greater efficiency while navigating. For such applications, how flow phenomena related to aerodynamically or hydrodynamically important forces can be detected through the mechanical response of AHS must be understood. In this collection of manuscripts, we investigate the utility of AHS for detecting flow phenomena pertinent to these applications. One aerodynamically adverse phenomena of low-Reynolds number flight is boundary layer separation. By modeling each hair as a viscoelastic beam coupled to its local flow environment, the dynamic and mechanical response of a hair sensor array was simulated in unsteady flow separation. We show that the resultant moment at the base of each hair sensor in the array provides a space and time accurate representation of the onset and span of reversed flow, the location of the point of zero wall shear-stress, the formation and relative position of near wall vortices, and the spatial development and evolution of boundary layer flows. The shape of a boundary layer flow is another means of detecting flow separation and is also related to the local wall shear-stress. Here, we determine the hair lengths relative to a general measure of boundary layer thickness that maximizes output sensitivity to changes in boundary layer shape. The range of computed optimal hair lengths is in close agreement with the range of hair receptor lengths measured on three bat species. A tapered hair profile is shown to provide larger sensitivities over a wider range of flow conditions compared to hairs of uniform cross section. The feedback of surface mounted AHS measurements for accurate flow state estimation away from the wall is important for effective flow control design. A linear quadratic Gaussian observer is designed for an unsteady viscous incompressible flow with hair sensor arrays. Here, the Riccati equation was numerically solved using the modified Kleinman-Newton method combined with a snapshot procedure for solving Lyapunov equations. We show that measurements provided by two patches of hair sensor arrays significantly contributes to the estimation of a nearby region of the flow velocity field. The results herein support artificial hair sensors as an effective means of detecting flow phenomena important to the dynamics of bodies in fluid flows. Within the following manuscripts, contributions are also made to biology, artificial hair sensor design and application, and linear control theory

Path planning, flow estimation, and dynamic control for underwater vehicles

Underwater vehicles such as robotic fish and long-endurance ocean-sampling platforms operate in challenging fluid environments. This dissertation incorporates models of the fluid environment in the vehicles' guidance, navigation, and control strategies while addressing uncertainties associated with estimates of the environment's state. Coherent flow structures may be on the same spatial scale as the vehicle or substantially larger than the vehicle. This dissertation argues that estimation and control tasks across widely varying spatial scales, from vehicle-scale to long-range, may be addressed using common tools of empirical observability analysis, nonlinear/non-Gaussian estimation, and output-feedback control. As an application in vehicle-scale flow estimation and control, this dissertation details the design, fabrication, and testing of a robotic fish with an artificial lateral-line inspired by the lateral-line flow-sensing organ present in fish. The robotic fish is capable of estimating the flow speed and relative angle of the oncoming flow. Using symmetric and asymmetric sensor configurations, the robot achieves the primitive fish behavior called rheotaxis, which describes a fish's tendency to orient upstream. For long-range flow estimation and control, path planning may be accomplished using observability-based path planning, which evaluates a finite set of candidate control inputs using a measure related to flow-field observability and selects an optimizer over the set. To incorporate prior information, this dissertation derives an augmented observability Gramian using an optimal estimation strategy known as Incremental 4D-Var. Examination of the minimum eigenvalue of an empirical version of this Gramian yields a novel measure for path planning, called the empirical augmented unobservability index. Numerical experiments show that this measure correctly selects the most informative paths given the prior information. As an application in long-range flow estimation and control, this dissertation considers estimation of an idealized pair of ocean eddies by an adaptive Lagrangian sensor (i.e., a platform that uses its position data as measurements of the fluid transport, after accounting for its own control action). The adaptive sampling is accomplished using the empirical augmented unobservability index, which is extended to non-Gaussian posterior densities using an approximate expected-cost calculation. Output feedback recursively improves estimates of the vehicle position and flow-field states