Lubomir Baramov

H∞ control of nonperiodic two-dimensional channel flow

This paper deals with finite-dimensional boundary control of the two-dimensional (2-D) flow between two infinite parallel planes. Surface transpiration along a few regularly spaced sections of the bottom wall is used to control the flow. Measurements from several discrete, suitably placed shear-stress sensors provide the feedback. Unlike other studies in this area, the flow is not assumed to be periodic, and spatially growing flows are considered. Using spatial discretization in the streamwise direction, frequency responses for a relevant part of the channel are obtained. A low-order model is fitted to these data and the modeling uncertainty is estimated. An H-infinity controller is designed to guarantee stability for the model set and to reduce the wall-shear stress at the channel wall. A nonlinear Navier-Stokes PDE solver was used to test the designs in the loop. The only assumption made in these simulations is that the flow is two dimensional. The results showed that, although the problem was linearized when designing the controller, the controller could significantly reduce fundamental 2-D disturbances in practice.

Robust Control of Linearized Poiseuille Flow

An approach to feedback control of linearized planar Poiseuille flow using H\infty control is developed. Surface transpiration is used to control the flow and point measurements of the wall shear stress are assumed to monitor its state. A high-but-finite dimensional model is obtained via a Galerkin procedure, and this model is approximated by a low dimensional one using Hankel-optimal model reduction. For the purposes of control design the flow is modeled as an interconnection of this low dimensional system and a perturbation, reflecting the uncertainty in the model. The goal of control design is to achieve robust stability (i.e. to stabilize any combination of the nominal plant and a feasible perturbation), and to satisfy certain performance requirements. Two different types of surface actuation are considered -- harmonic transpiration and a model of a pair of suction/blowing panels. It is found that the latter is more efficient in suppressing disturbances in terms of the control effort required.

H/sub /spl infin// control of nonperiodic two-dimensional channel flow

This paper deals with finite-dimensional boundary control of the two-dimensional (2-D) flow between two infinite parallel planes. Surface transpiration along a few regularly spaced sections of the bottom wall is used to control the flow. Measurements from several discrete, suitably placed shear-stress sensors provide the feedback. Unlike other studies in this area, the flow is not assumed to be periodic, and spatially growing flows are considered. Using spatial discretization in the streamwise direction, frequency responses for a relevant part of the channel are obtained. A low-order model is fitted to these data and the modeling uncertainty is estimated. An H-infinity controller is designed to guarantee stability for the model set and to reduce the wall-shear stress at the channel wall. A nonlinear Navier-Stokes PDE solver was used to test the designs in the loop. The only assumption made in these simulations is that the flow is two dimensional. The results showed that, although the problem was linearized when designing the controller, the controller could significantly reduce fundamental 2-D disturbances in practice.

Suboptimal state estimation under communication delays

Abstract We present a suboptimal state estimation method under communication delays. The missing measurements are replaced with model predictions and these predictions are put into memory. When the delayed measurements arrive, the effect of using prediction as fictitious measurements is removed. The optimality is recovered, which this is the key property of the method. The algorithm complexity is low compared to the optimal solution. The method requires the measurements to be time stamped. The plant model must be linear, time invariant.

Model for estimating stress in pressurized boiler components based on interconnections

This paper proposes a method of modeling stress in pressurized boiler components for the use in a boiler life monitoring system and/or in life-extending control. A low- dimensional model of stress components at critical locations is obtained by a suitable approximation of the underlying partial differential equations. A typical boiler component, e.g., a steam header, is spatially large with repeated elements. The proposed method is based on splitting the component into elementary parts, modeled separately as n-port systems and then obtaining the overall model as an interconnected network. The interconnection is done on a finite set of frequencies to avoid the complexity escalation. Transfer function is then fitted on the frequency-domain data. The resulting model is of low order with a good agreement with a finite element model.

H/sub /spl infin// control for non-periodic planar channel flows

This paper deals with finite-dimensional boundary control of the linearized 2D flow between two infinite parallel planes. Surface transpiration along a few regularly spaced sections of the bottom wall is used to control the flow. Measurements from several discrete, suitably placed shear-stress sensors provide the feedback. Unlike other studies in this area, the flow is not assumed to be periodic, and spatially growing flows are considered. An H/sub /spl infin// control scheme is designed to guarantee stability for the model set and to reduce the wall-shear stress at the channel wall. This design is tested by simulations with a nonlinear Navier-Stokes PDE solver in the loop. The simulation results show that the controller is effective in reducing shear disturbances.

Kalman Filter for Systems with Communication Delay

Abstract This paper deals with estimating the process state where measurements are obtained via wireless networks. Transmission between the sensor and the estimator may be subject to random delays and/or data losses. A straightforward approach to address this problem is using a time-varying Kalman filter (KF) for the plant augmented by a delay model, which is computationally extensive. Research effort has recently focused on low complexity approximations of these filters. We revisit the time varying KF and, by exploiting the structure of the augmented process model, propose a new algorithm, which is computationally less extensive than the standard one. Moreover, interesting properties of the variable-delay estimators were obtained that are of independent interest.

Minimum Order Transfer Function: the Interpolation Approach

This paper presents an algorithm for obtaining the minimum order MISO transfer function model for the use in a model-based predictive controller. The source model can be either a non-minimal ARX model, a state-space model or any interconnection of linear models of mixed state-space and transfer function representations. The algorithm is based on polynomial interpolation theory, representing polynomials by their values on a set of points in the complex plane. Using this theory, we can find the minimum order from the dimension of the null space of a particular matrix. Finding the minimum order model is equivalent to finding a specific base of the null space. A novel feature of the presented approach is using a set of complex interpolation nodes obtained by mapping the standard set of real Chebyshev nodes by a bilinear transform.

ENHANCING ARX-MODEL BASED MPC BY KALMAN FILTER AND SMOOTHER

Abstract An approach to enhancing a model-based predictive controller by Kalman filter is proposed. The controller uses an ARX process model and the structure of the controller is assumed fixed; some of its internal variables – past values of controlled variables (output history) are accessible and can be modified to achieve better performance in disturbance attenuation and noise rejection. We present an algorithm of updating the output history using Kalman filter to achieve predictions equivalent to those of the state-space model, thus overcoming the limitations of the ARX predictor. Interesting relations of this algorithm to Kalman interval smoother are given.

Robust Control of Non-Periodic Channel Flow

In this paper we consider the control of disturbances in a channel where surface sensing and actuation (blowing/suction) are used. Unlike in many other studies, the flow is not assumed to be periodic. As a result disturbances are allowed over the full range of unstable wave numbers/frequencies, and spatially growing disturbances can be studied explicitly. However, a major drawback is that, even for two-dimensional flow, the order of the numerical model is extremely large. Model order reduction based on a non-linear least squares fit is used to generate a model plus an uncertainty bound that are suitable for control design purposes. These are used to produce a robustly stable H∞ controller. The behaviour of this controller is compared with those designed assuming periodic flow. It is shown that a non-periodic controller can perform satisfactorily in cases where a periodic one will not.Copyright