Infinite dimensional and reduced order observers for Burgers equation

Obtaining a representative model in feedback control system design problems is a key step and is generally a challenge. For spatially continuous systems, it becomes more difficult as the dynamics is infinite dimensional and the well known techniques of systems and control engineering are difficult to apply directly. In this paper, observer design is reported for one-dimensional Burgers equation, which is a non-linear partial differential equation. An infinite dimensional form of the observer is demonstrated to converge asymptotically to the target dynamics, and proper orthogonal decomposition is used to obtain the reduced order observer. When this is done, the corresponding observer is shown to be successful under certain circumstances. The paper unfolds the connections between target dynamics, observer and their finite dimensional counterparts. A set of simulation results has been presented to justify the theoretical claims of the paper. © 2005 Taylor & Francis Group Ltd

Feedback control design for subsonic cavity flows

A benchmark problem in active aerodynamic flow control, suppression of strong pressure oscillations induced by flow over a shallow cavity, is addressed in this paper. Proper orthogonal decomposition and Galerkin projection techniques are used to obtain a reduced-order model of the flow dynamics from experimental data. The model is made amenable to control design by means of a control separation technique, which makes the control input appear explicitly in the equations. A prediction model based on quadratic stochastic estimation correlates flow field data with surface pressure measurements, so that the latter can be used to reconstruct the state of the model in real time. The focus of this paper is on the controller design and implementation. A linear-quadratic optimal controller is designed on the basis of the reduced-order model to suppress the cavity flow resonance. To account for the limitation on the magnitude of the control signal imposed by the actuator, the control action is modified by a scaling factor, which plays the role of a bifurcation parameter for the closed-loop system. Experimental results, in qualitative agreement with the theoretical analysis, show that the controller achieves a significant attenuation of the resonant tone with a redistribution of the energy into other frequencies, and exhibits a certain degree of robustness when operating in off-design conditions

Modeling of subsonic cavity flows by neural networks

Influencing the behavior of a flow field is a core issue as its improvement can yield significant increase of the efficiency and performance of fluidic systems. On the other hand, the tools of classical control systems theory are not directly applicable to processes displaying spatial continuity as in fluid flows. The cavity flow is a good example of this and a recent research focus in aerospace science is its modeling and control. The objective is to develop a finite dimensional representative model for the system with appropriately defined inputs and outputs. Towards the goal of reconstructing the pressure fluctuations measured at the cavity floor, this paper demonstrates that given some history of inputs and outputs, a neural network based feedforward model can be developed such that the response of the neural network matches the measured response. The advantages of using such a model are the representational simplicity of the model, structural flexibility to enable controller design and the ability to store information in an interconnected structure

Flow and Noise Control in High Speed and High Reynolds Number Jets Using Plasma Actuators

The idea of manipulating flow to change its characteristics is over a century old. Manipulating instabilities of a jet to increase its mixing and to reduce its radiated noise started in the 1970s. While the effort has been successful in low-speed and low Reynolds number jets, available actuators capabilities in terms of their amplitude, bandwidth, and phasing have fallen short in control of high-speed and high Reynolds number jets of practical interest. Localized arc filament plasma actuators have recently been developed and extensively used at Gas Dynamics and Turbulence Laboratory (GDTL) for control of highspeed and high Reynolds number jets. While the technique has been quite successful and is very promising, all the work up to this point had been carried out using small high subsonic and low supersonic jets from a 2.54 cm diameter nozzle exit with a Reynolds number of about a million. The preliminary work reported in this paper is a first attempt to evaluate the scalability of the technique. The power supply/plasma generator was designed and built in-house at GDTL to operate 8 actuators simultaneously over a large frequency range (0 to 200 kHz) with independent control over phase and duty cycle of each actuator. This allowed forcing the small jet at GDTL with azimuthal modes m = 0, 1, 2, 3, plus or minus 1, plus or minus 2, and plus or minus 4 over a large range of frequencies. This power supply was taken to and used, with minor modifications, at the NASA Nozzle Acoustic Test Rig (NATR). At NATR, 32 actuators were distributed around the 7.5 in. nozzle (a linear increase with nozzle exit diameter would require 60 actuators). With this arrangement only 8 actuators could operate simultaneously, thus limiting the forcing of the jet at NATR to only three azimuthal modes m = plus or minus 1, 4, and 8. Very preliminary results at NATR indicate that the trends observed in the larger NASA facility in terms of the effects of actuation frequency and azimuthal modes are similar in both small GDTL and larger NASA jets. However, the actuation authority seems to fall short in the larger jet at higher Mach numbers, resulting in decreased amplitude response compared to the small jet, which is attributed at this point to the lack of sufficient number of actuators. The preliminary results seem also to suggest that amplitude of actuation tones is similar in both the small and larger jets

Effects of nozzle trailing edges on acoustic field of a supersonic rectangular jet

Acoustic measurements of a Mach 2, rectangular nozzle with modi ed trailing edges were carried out using three microphones, placed 90 deg apart azimuthally in a plane normal to the jet axis. The measurements were obtained at three streamwise locations, with microphone angles of 90, 60, and 30 deg with respect to the jet centerline. The trailing-edge modi ed nozzles substantially reduced the turbulent mixing and broadband shock associated noise radiation by up to 12 dB for the underexpanded ow regime and up to 7 dB for the overexpanded condition. However, in some symmetric modi cations, the very-high-frequency noise was increased for the overexpanded condition. Screech tones in the overexpanded ow condition were either reduced or eliminated for asymmetric modi cations, but ampli ed for symmetric modi cations. The trailing-edge modi cations were found to not signi cantly alter the noise eld for the ideally expanded ow condition

Seven tuning schemes for an ADALINE model to predict floor pressures in a subsonic cavity flow

This paper presents a simple yet effective one-step-ahead predictor based on an adaptive linear element (ADALINE). Several tuning schemes are studied to see whether the obtained model is consistent. The process under investigation is a subsonic cavity flow system. The experimental data obtained from the system is post-processed to obtain a useful predictor. The contribution of the paper is to demonstrate that despite the spectral richness of the observed data, a simple model with various tuning schemes can help to a satisfactory extent. Seven algorithms are studied, including the least mean squares (LMS), recursive least squares (RLS), modified Kaczmarz's algorithm (MK), stochastic approximation algorithm (SA), gradient descent (GD), Levenbergĝ€ "Marquardt optimization technique (LM) and sliding mode-based tuning (SM). The model and its properties are discussed comparatively. © 2009 The Institute of Measurement and Control

Support vector networks for prediction of floor pressures in shallow cavity flows

During the last decade, Support Vector Machines (SVM) have proved to be very successful tools for classification and regression problems. The representational performance of this type of networks is studied on a cavity flow facility developed to investigate the characteristics of aerodynamic flows at various Mach numbers. Several test conditions have been experimented to collect a set of data, which is in the form of pressure readings from particular points in the test section. The goal is to develop a SVM based model that emulates the one step ahead behavior of the flow measurement at the cavity floor. The SVM based model is built for a very limited amount of training data and the model is tested for an extended set of test conditions. A relative error is defined to measure the reconstruction performance, and the peak value of the FFT magnitude of the error is measured. The results indicate that the SVM based model is capable of matching the experimental data satisfactorily over the conditions that are close to the training data collection conditions, and the performance degrades as the Mach number gets away from the conditions considered during training. ©2006 IEEE

Parallel fuel injection from the base of an extended strut into supersonic flow

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76778/1/AIAA-1994-711-873.pd

Neural network-based modelling of subsonic cavity flows

A fundamental problem in the applications involved with aerodynamic flows is the difficulty in finding a suitable dynamical model containing the most significant information pertaining to the physical system. Especially in the design of feedback control systems, a representative model is a necessary tool constraining the applicable forms of control laws. This article addresses the modelling problem by the use of feedforward neural networks (NNs). Shallow cavity flows at different Mach numbers are considered, and a single NN admitting the Mach number as one of the external inputs is demonstrated to be capable of predicting the floor pressures. Simulations and real time experiments have been presented to support the learning and generalization claims introduced by NN-based models

Control of subsonic cavity flows by neural networks -Analytical models and experimental validation

Flow control is attracting an increasing attention of researchers from a wide spectrum of specialties because of its interdisciplinary nature and the associated challenges. One of the main goals of The Collaborative Center of Control Science at The Ohio State University is to bring together researchers from different disciplines to advance the science and technology of flow control. This paper approaches the control of subsonic cavity flow, a study case we have selected, from a computational intelligence point of view, and offers a solution that displays an interconnected neural architecture. The structures of identification and control, together with the experimental implementation are discussed. The model and the controller have very simple structural configurations indicating that a significant saving on computation is possible. Experimental testing of a neural emulator and of a directly-synthesized neurocontroller indicates that the emulator can accurately reproduce a reference signal measured in the cavity floor under different operating conditions. Based on preliminary results, the neurocontroller appears to be marginally effective and produces spectral peak reductions analogous to those previously observed by the authors using linearcontrol techniques. The current research will continue to improve the capability of the neural emulator and of the neurocontroller