In this paper we present a tutorial overview of some of the issues that arise in the design of switched linear control systems. Particular emphasis is given to issues relating to stability and control system realisation. A benchmark regulation problem is then presented. This problem is most naturally solved by means of a switched control design. The challenge to the community is to design a control system that meets the required performance specifications and permits the application of rigorous analysis techniques. A simple design solution is presented and the limitations of currently available analysis techniques are illustrated with reference to this example.

/pdf/issues-in-the-design-of-switched-linear-control-systems-a-51pc7aikg1.pdf

Issues in the design of switched linear control systems: A benchmark study

Gaussian process (GP) regression is a Bayesian nonparametric model showing good performance in various applications. However, its hyperparameter-estimating procedure may contain numerous matrix manipulations of O(N3) arithmetic operations, in addition to the O(N2)-level storage. Motivated by handling the real-world large dataset of 24000 wind-turbine data, we propose in this paper an efficient and economical Toeplitz-computation scheme for time-series Gaussian process regression. The scheme is of O(N2) operations and O(N)-level memory requirement. Numerical experiments substantiate the effectiveness and possibility of using this Toeplitz computation for very large datasets regression (such as, containing 10000~100000 data points).

Time-series Gaussian Process Regression Based on Toeplitz Computation of O(N 2 ) Operations and O(N)-level Storage

Gaussian process (GP) is a Bayesian nonparametric regression model, showing good performance in various applications. However, during its model-tuning procedure, the GP implementation suffers from numerous covariance-matrix inversions of expensive O(N3) operations, where N is the matrix dimension. In this article, we propose using the quasi-Newton BFGS O(N2)-operation formula to approximate/replace recursively the inverse of covariance matrix at every iteration. The implementation accuracy is guaranteed carefully by a matrix-trace criterion and by the restarts technique to generate good initial guesses. A number of numerical tests are then performed based on the sinusoidal regression example and the Wiener–Hammerstein identification example. It is shown that by using the proposed implementation, more than 80% O(N3) operations could be eliminated, and a typical speedup of 5–9 could be achieved as compared to the standard maximum-likelihood-estimation (MLE) implementation commonly used in Gaussian process r...

O(N2)-Operation approximation of covariance matrix inverse in Gaussian process regression based on quasi-Newton BFGS method

Maximum likelihood estimation of hyperparameters in Gaussian processes (GPs) as well as other spatial regression models usually requires the evaluation of the logarithm of the matrix determinant, in short, log det. When using matrix decomposition techniques, the exact implementation of log det is of O(N 3) operations, where N is the matrix dimension. In this paper, a power-series expansion-based framework is presented for approximating the log det of general positive-definite matrices. Three novel compensation schemes are proposed to further improve the approximation accuracy and computational efficiency. The proposed log det approximation requires only 50N 2 operations. The theoretical analysis is substantiated by a large number of numerical experiments, including tests on randomly generated positive-definite matrices, randomly generated covariance matrices, and sequences of covariance matrices generated online in two GP regression examples. The average approximation error is ∼9%.

Approximate implementation of logarithm of the matrix determinant in Gaussian process regression

This paper describes the simulation model of a controller that enables an active-stall wind turbine to ride through transient faults. The simulated wind turbine is connected to a simple model of a power system. Certain fault scenarios are specified and the turbine shall be able to sustain operation in case of such faults. The design of the controller is described and its performance assessed by simulations. The control strategies are explained and the behaviour of the turbine discussed.

/pdf/stability-and-control-of-wind-farms-in-power-systems-4lkvo8tai8.pdf

Stability and control of wind farms in power systems

It is shown that the nonlinear rotor aerodynamics of typical medium and large-scale variable speed wind turbines exhibit a separability property similar to that previously established for constant speed wind turbines. The importance of this result is that it establishes that from a control viewpoint a variable speed wind turbine can be viewed as a nonlinear system with static nonlinearity, h, subject to the external wind disturbance. It is emphasised that the function h is independent of the wind speed. This immediately suggests that the aerodynamic nonlinearity of the rotor can be accommodated by incorporating the inverse function h -1 within the controller. With the plant dynamics globally linearised in this way, the rest of the controller

https://www.hamilton.ie/publications/ewec99-2.pdf

Global gain-scheduling control for variable speed wind turbines

This poster presentation was shown at the European Wind Energy Conference and Exhibition in Madrid, Spain 16-19 June 2003.

Identification of aerodynamics and drive-train dynamics for a variable speed wind turbine

In above rated wind speed the pitch control system of a pitch regulated variable speed wind turbine
aims to maintain the rotor speed within a permitted range. However, this requirement can be difficult to satisfy
during extreme gusts with conventional controllers, particularly for large-scale machines where the pitch actuation
capability may be quite limited. This paper investigates the design of a pitch controller for 1 MW variable speed
turbine which directly responds to a strong gust by pitching the rotor blades at the maximum permissible rate,
thereby exploiting the maximum capability of the actuation system. The performance assessed and compared to
that of a conventional pitch controller by simulation studies.

/pdf/direct-regulation-of-large-speed-excursions-for-variable-3jgvl2zypz.pdf

F. Hardan

Papers

Global gain-scheduling control for variable speed wind turbines

Identification of aerodynamics and drive-train dynamics for a variable speed wind turbine

Direct regulation of large speed excursions for variable speed wind turbines