Bryn Ll. Jones

Brief paper: When is the discretization of a spatially distributed system good enough for control?

This paper describes a new and straightforward method for controlling spatially distributed plants based on low-order models obtained from spatial discretization techniques. A suitable level of discretization is determined by computing the sequence of @n-gaps between weighted models of successively finer spatial resolution, and bounding this by another sequence with an analytic series. It is proved that such a series forms an upper bound on the @n-gap between a weighted model in the initial sequence and the spatially distributed weighted plant. This enables the synthesis, on low-order models, of robust controllers that are guaranteed to stabilize the actual plant, a feature not shared by most model reduction methods where the gap between the high-order model and plant is often not known, and where the gap between high-order and reduced models may be too expensive to compute. Since the calculation of the current bound is based on weighted models of small state-dimension, the new method avoids the numerical problems inherent in large-scale model reduction based approaches. The ideas presented in this paper are demonstrated on a disturbance rejection problem for a 1D heat equation.

An efficient algorithm for the solution of a coupled Sylvester equation appearing in descriptor systems

Descriptor systems consisting of a large number of differential-algebraic equations (DAEs) usually arise from the discretization of partial differential-algebraic equations. This paper presents an efficient algorithm for solving the coupled Sylvester equation that arises in converting a system of linear DAEs to ordinary differential equations. A significant computational advantage is obtained by exploiting the structure of the involved matrices. The proposed algorithm removes the need to solve a standard Sylvester equation or to invert a matrix. The improved performance of this new method over existing techniques is demonstrated by comparing the number of floating-point operations and via numerical examples.

Fundamental performance similarities between individual pitch control strategies for wind turbines

ABSTRACT The use of blade individual pitch control (IPC) offers a means of reducing the harmful turbine structural loads that arise from the uneven and unsteady forcing from the oncoming wind. In recent years, two different and competing IPC techniques have emerged that are characterised by the specific loads that they are primarily designed to attenuate. In the first instance, methodologies, such as single-blade control and Clarke transform-based control, have been developed to reduce the unsteady loads on the rotating blades, whilst tilt-yaw control and its many variants instead target load reductions in the non-rotating turbine structures, such as the tower and main bearing. Given the seeming disparities between these controllers, the aim of this paper is to show the fundamental performance similarities that exist between them and hence unify research in this area. Specifically, we show that single-blade controllers are equivalent to a particular class of tilt-yaw controller, which itself is equivalent to Clarke transform-based control. This means that three architecturally dissimilar IPC controllers exist that yield exactly the same performance in terms of load reductions on fixed and rotating turbine structures. We further demonstrate this outcome by presenting results obtained from high-fidelity closed-loop turbine simulations.

Flow estimation of boundary layers using DNS-based wall shear information

This article investigates the problem of obtaining a state-space model of the disturbance evolution that precedes turbulent flow across aerodynamic surfaces. This problem is challenging since the flow is governed by nonlinear, partial differential-algebraic equations for which there currently exists no efficient controller/estimator synthesis techniques. A sequence of model approximations is employed to yield a linear, low-order state-space model, to which standard tools of control theory can be applied. One of the novelties of this article is the application of an algorithm that converts a system of differential-algebraic equations into one of ordinary differential equations. This enables straightforward satisfaction of boundary conditions whilst dispensing with the need for parallel flow approximations and velocity–vorticity transformations. The efficacy of the model is demonstrated by the synthesis of a Kalman filter that clearly reconstructs the characteristic features of the flow, using only wall velocity gradient information obtained from a high-fidelity nonlinear simulation.

Modelling for robust feedback control of fluid flows

This paper addresses the problem of obtaining low-order models of fluid flows for the purpose of designing robust feedback controllers. This is challenging since whilst many flows are governed by a set of nonlinear, partial differential-algebraic equations (the Navier-Stokes equations), the majority of established control theory assumes models of much greater simplicity, in that they are firstly: linear, secondly: described by ordinary differential equations, and thirdly: finite-dimensional. Linearisation, where appropriate, overcomes the first disparity, but attempts to reconcile the remaining two have proved difficult. This paper addresses these two problems as follows. Firstly, a numerical approach is used to project the governing equations onto a divergence-free basis, thus converting a system of differential-algebraic equations into one of ordinary differential equations. This dispenses with the need for analytical velocity-vorticity transformations, and thus simplifies the modelling of boundary sensing and actuation. Secondly, this paper presents a novel and straightforward approach for obtaining suitable low-order models of fluid flows, from which robust feedback controllers can be synthesised that provide a priori guarantees of robust performance when connected to the (infinite-dimensional) linearised flow system. This approach overcomes many of the problems inherent in approaches that rely upon model-reduction. To illustrate these methods, a perturbation shear stress controller is designed and applied to plane channel flow, assuming arrays of wall mounted shear-stress sensors and transpiration actuators. DNS results demonstrate robust attenuation of the perturbation shear-stresses across a wide range of Reynolds numbers with a single, linear controller.

A review on applications of model predictive control to wind turbines

This paper aims to give an overview of the recent development and benefits of model predictive control in wind turbines and its future potential. For a modern large wind turbine, the main objective of control is to maximise the power production while maintaining the fatigue loads to be minimal. With such multiple objectives, a multivariable system and actuators constraints the popular PI controller may become ineffective or hard to tune whereas MPC provides a systematic approach for designing a multivariable controller incorporating the knowledge of actuator constraints. This paper reviews the wind turbine control problem and in particular gives a survey of the use of model predictive control on wind turbines.

When is the discretization of a PDE good enough for control

Many systems of engineering importance are governed by partial differential equations (PDEs) in one or more spatial dimensions, and are therefore infinite dimensional. Controlling such spatially distributed plants is non-trivial, given that the bulk of established control theory and practice assumes plant models of finite and low state dimension. In order to obtain such a model it is necessary to approximate the plant dynamics, trading off a reduction in state dimension for an increase in plant/model mismatch. This paper describes a new technique for selecting a low order model that is a suitable approximation in a closed-loop sense to the spatially distributed plant we seek to control. Unlike model reduction, the new procedure starts from a coarse spatial discretization of the plant dynamics and increases in fidelity until a suitable control model is obtained, thus avoiding the numerical difficulties inherent in large-scale model reduction. We argue, through use of H∞ loop-shaping and the ν-gap metric, that it is primarily the closed-loop design specifications and the method of spatial discretization that determine a suitable level of approximation. The main theoretical contribution of this work is a proof that, for plant models of successively finer spatial discretization, the order of convergence in the ν-gap metric is bounded by the order of convergence of their differences in the H∞ norm. We also show how to easily compute reasonably tight upper bounds on the ν-gap between a finite dimensional model and an infinite dimensional plant. The ideas presented in the first part of this paper are demonstrated on a disturbance rejection problem for a 1D heat equation.

Wind turbine gust estimation using remote sensing data

The offshore wind energy industry is experiencing sustained growth as governments around the world look to secure low-carbon sources of energy. In order to capture more energy from the wind, larger turbines are being designed, leading to the structures becoming increasingly vulnerable to damage caused by violent gusts of wind. Advance knowledge of such gusts will enable turbine control systems to take preventative action, reducing the cost of turbine maintenance. Therefore, in this paper we present a methodology to estimate the velocity profile of an oncoming wind field, given only limited spatio-temporal measurements from typical light detection and ranging (LiDAR) instruments, mounted on the turbine nacelle. The main contribution of this paper lies in the derivation of a simplified deterministic model of atmospheric boundary-layer flows, based on the Navier-Stokes equations, that enables subsequent implementation of an unscented Kalman Filter. Results are presented that compare the accuracy of the estimated wind field to actual wind-data produced from large eddy simulations of the atmospheric boundary layer.

Passivity-based feedback control of a channel flow for drag reduction

A new active-closed-loop linear time-invariant robust control strategy for reducing drag in a channel flow is presented. Using the theory of passive systems, controllers were designed so as to make the closed-loop system as close to passive as is possible. Physically, this means minimising the maximum bound on perturbation energy production within the system. Although the resulting controllers are linear, the nonlinearity, inherent in all fluidic systems, is accounted for and included as an exogenous feedback forcing. Passivity-based controllers were generated for a Re = 2230 channel flow for a range of spatial wavenumber pairs and then analysed. They were shown to be capable of greatly restricting transient energy growth.

A survey of good practice in control education

ABSTRACT This paper gives a focussed summary of good practice taken primarily from engineers who are responsible for teaching topics related to systems and control. This engineering specialisation allows the paper to give some degree of focus in the discussions around laboratories, software and assessment, although naturally many of the conclusions are generic. A key intention is to provide a summary document or survey paper which can be used by academics as a start point in studies of what is effective in the discipline. It is also hoped that such a summary will be useful to engineering institutions in drawing together and disseminating open access resources that are freely available to the community at large.