3,582 research outputs found
Feedback control of unstable steady states of flow past a flat plate using reduced-order estimators
We present an estimator-based control design procedure for flow control,
using reduced-order models of the governing equations, linearized about a
possibly unstable steady state. The reduced models are obtained using an
approximate balanced truncation method that retains the most controllable and
observable modes of the system. The original method is valid only for stable
linear systems, and we present an extension to unstable linear systems. The
dynamics on the unstable subspace are represented by projecting the original
equations onto the global unstable eigenmodes, assumed to be small in number. A
snapshot-based algorithm is developed, using approximate balanced truncation,
for obtaining a reduced-order model of the dynamics on the stable subspace. The
proposed algorithm is used to study feedback control of 2-D flow over a flat
plate at a low Reynolds number and at large angles of attack, where the natural
flow is vortex shedding, though there also exists an unstable steady state. For
control design, we derive reduced-order models valid in the neighborhood of
this unstable steady state. The actuation is modeled as a localized body force
near the leading edge of the flat plate, and the sensors are two velocity
measurements in the near-wake of the plate. A reduced-order Kalman filter is
developed based on these models and is shown to accurately reconstruct the flow
field from the sensor measurements, and the resulting estimator-based control
is shown to stabilize the unstable steady state. For small perturbations of the
steady state, the model accurately predicts the response of the full
simulation. Furthermore, the resulting controller is even able to suppress the
stable periodic vortex shedding, where the nonlinear effects are strong, thus
implying a large domain of attraction of the stabilized steady state.Comment: 36 pages, 17 figure
Application of non-linear system identification approaches to modelling, analysis, and control of fluid flows.
Flow control has become a topic of great importance for several applications, ranging from commercial aircraft, to intercontinental pipes and skyscrapers. In these applications, and many more, the interaction with a fluid flow can have a significant influence on the performance of the system. In many cases the fluids encountered are turbulent and detrimental to the latter.
Several attempts have been made to solve this problem. However, due to the non-linearity and infinite dimensionality of fluid flows and their governing equations, a complete understanding of turbulent behaviour and a feasible control approach has not been obtained.
In this thesis, model reduction approaches that exploit non-linear system identification are applied using data obtained from numerical simulations of turbulent three-dimensional channel flow, and two-dimensional flow over the backward facing step. A multiple-input multiple-output model, consisting of 27 sub-structures, is obtained for the fluctuations of the velocity components of the channel flow. A single-input single-output model for fluctuations of the pressure coefficient, and two multiple-input single-output models for fluctuations of the velocity magnitude are obtained in flow over the BFS.
A non-linear model predictive control strategy is designed using identified one- and multi-step ahead predictors, with the inclusion of integral action for robustness. The proposed control approach incorporates a non-linear model without the need for expensive non-linear optimizations.
Finally, a frequency domain analysis of unmanipulated turbulent flow is perfumed using five systems. Higher order generalized frequency response functions (GFRF) are computed to study the non-linear energy transfer phenomena. A more detailed investigation is performed using the output FRF (OFRF), which can elucidate the contribution of the n-th order frequency response to the output frequency response
Robust feedback control of Rayleigh-Bénard convection
We investigate the application of linear-quadratic-Gaussian (LQG) feedback control, or, in modern terms, H2 control, to the stabilization of the no-motion state against the onset of Rayleigh-Bénard convection in an infinite layer of Boussinesq fluid. We use two sensing and actuating methods: The planar sensor model (Tang & Bau 1993, 1994), and the shadowgraph model (Howle 1997a). By extending the planar sensor model to the multi-sensor case, it is shown that a LQG controller is capable of stabilizing the no-motion state up to 14.5 times the critical Rayleigh number. We characterize the robustness of the controller with respect to parameter uncertainties, unmodelled dynamics. Results indicate that the LQG controller provides robust performances even at high Rayleigh numbers
Control of fluid flows and other systems governed by partial differential-algebraic equations
The motion of fluids, such as air or water, is central to many engineering systems of significant
economic and environmental importance. Examples range from air/fuel mixing in combustion engines
to turbulence induced noise and fatigue on aircraft. Recent advances in novel sensor/actuator
technologies have raised the intriguing prospect of actively sensing and manipulating the motion
of the fluid within these systems, making them ripe for feedback control, provided a suitable control
model exists. Unfortunately, the models for many of these systems are described by nonlinear,
partial differential-algebraic equations for which few, if any, controller synthesis techniques exist.
In stark contrast, the majority of established control theory assumes plant models of finite (and
typically small) state dimension, expressed as a linear system of ordinary differential equations.
Therefore, this thesis explores the problem of how to apply the mainstream tools of control theory
to the class of systems described by partial differential-algebraic equations, that are either linear,
or for which a linear approximation is valid.
The problems of control system design for infinite-dimensional and algebraically constrained
systems are treated separately in this thesis. With respect to the former, a new method is presented
that enables the computation of a bound on the n-gap between a discretisation of a spatially distributed
plant, and the plant itself, by exploiting the convergence rate of the v-gap metric between
low-order models of successively finer spatial resolution. This bound informs the design, on loworder
models, of H[infinity] loop-shaping controllers that are guaranteed to robustly stabilise the actual
plant. An example is presented on a one-dimensional heat equation.
Controller/estimator synthesis is then discussed for finite-dimensional systems containing algebraic,
as well as differential equations. In the case of fluid flows, algebraic constraints typically
arise from incompressibility and the application of boundary conditions. A numerical algorithm is
presented, suitable for the semi-discrete linearised Navier-Stokes equations, that decouples the differential
and algebraic parts of the system, enabling application of standard control theory without
the need for velocity-vorticity type methods. This algorithm is demonstrated firstly on a simple
electrical circuit, and secondly on the highly non-trivial problem of flow-field estimation in the
transient growth region of a flat-plate boundary layer, using only wall shear measurements.
These separate strands are woven together in the penultimate chapter, where a transient energy
controller is designed for a channel-flow system, using wall mounted sensors and actuators
Optimal and adaptive control of chaotic convection — Theory and experiments
In theory and experiments, optimal and adaptive control strategies are employed to suppress chaotic convection in a thermal convection loop. The thermal convection loop is a relatively simple experimental paradigm that exhibits complex dynamic behavior and provides a convenient platform for evaluating and comparing various control strategies. The objective of this study is to evaluate the feasibility of employing optimal control and nonlinear estimator to alter naturally occurring flow patterns and to compare the performance of the optimal controller with that of other controllers such as neural network controllers. It is demonstrated that when the system\u27s model is not known, experimental data alone can be utilized for the construction of a proportional controller
Passivity-Based Output-Feedback Control of Turbulent Channel Flow
This paper describes a robust linear time-invariant output-feedback control strategy to reduce turbulent fluctuations, and therefore skin-friction drag, in wall-bounded turbulent fluid flows, that nonetheless gives performance guarantees in the nonlinear turbulent regime. The novel strategy is effective in reducing the supply of available energy to feed the turbulent fluctuations, expressed as reducing a bound on the supply rate to a quadratic storage function. The nonlinearity present in the equations that govern the dynamics of the flow is known to be passive and can be considered as a feedback forcing to the linearised dynamics (a Lur’e decomposition). Therefore, one is only required to control the linear dynamics in order to make the system close to passive. The ten most energy-producing spatial modes of a turbulent channel flow were identified. Passivity-based controllers were then generated to control these modes. The controllers require measurements of streamwise and spanwise wall-shear stress, and they actuate via wall transpiration. Nonlinear direct numerical simulations demonstrated that these controllers were capable of significantly reducing the turbulent energy and skin-friction drag of the flow
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