W.E. Leithead

Survey of Gain-Scheduling Analysis & Design

The gain-scheduling approach is perhaps one of the most popular non-linear control design approaches which has been widely and successfully applied in fields ranging from aerospace to process control. Despite the wide application of gainscheduling controllers and a diverse academic literature relating to gain-scheduling extending back nearly thirty years, there is a notable lack of a formal review of the literature. Moreover, whilst much of the classical gain-scheduling theory originates from the 1960s, there has recently been a considerable increase in interest in gain-scheduling in the literature with many new results obtained. An extended review of the gain-scheduling literature therefore seems both timely and appropriate. The scope of this paper includes the main theoretical results and design procedures relating to continuous gain-scheduling (in the sense of decomposition of non-linear design into linear sub-problems) control with the aim of providing both a critical overview and a useful entry point into the relevant literature.

Control of variable speed wind turbines: Design task

Owing to concern over the environment, there is much interest in renewable sources of electrical power generation, of which one of the most promising is wind power. There are essentially two types of wind turbines, namely constant speed and variable speed machines. In comparison to constant speed wind turbines, variable speed wind turbines are perceived to have several potential advantages which outweigh the considerable cost of the power electronics required to realize variable speed operation. The two frequently mentioned ones are: additional energy capture below rated wind speed and additional power-train compliance and associated load alleviation above rated wind speed. The purpose of this paper is to investigate the design of the control system (as opposed to the synthesis of the controller) for variable speed wind turbines. The choice of control strategy is investigated and appropriate realizations of the controller, to cater for the implementation issues of accommodation of variation in the plant dynamics over the operational envelope and switching transients, are identified. A thorough investigation of the dynamics and control of both stall regulated and pitch regulated variable speed machines is undertaken.

Appropriate realization of gain-scheduled controllers with application to wind turbine regulation

Power regulation of horizontal-axis grid-connected up-wind constant-speed pitch-regulated wind turbines presents a demanding control problem with the plant, actuation system and control objectives all strongly nonlinear. In this paper, a novel nonlinear control strategy is devised which, in some sense, optimizes performance across the operating envelope. In comparison with linear control, the nonlinear strategy achieves a substantial improvement in performance. The realization adopted is crucial in attaining the required performance. An extended local linear equivalence condition is introduced which provides a basis for the selection of an appropriate realization. This is an important, and general, issue in the design of gain-scheduled systems and generic realizations, which satisfy the extended local linear equivalence condition, are derived for SISO systems scheduled upon an internal plant or controller variable. For the wind turbine nonlinear controller, realizations which satisfy the extended local li...

Control of variable speed wind turbines: Dynamic models

Owing to concern over the environment, there is much interest in renewable sources of electrical power generation, of which one of the most promising is wind power. Wind turbines exploit this energy source to directly generate electrical power. There are essentially two types of windturbines, namely constant speed and variable speed machines. The purpose of this paper is to investigate the dynamics of variable speed wind turbines and determine suitable models to support the control design task. A basic but widely used dynamic representation of variable speed wind turbines and the corresponding models of the control plant dynamics are initially discussed. More detailed, yet still simple models, are derived separately for the rotor aerodynamics, the drive-train dynamics and the power generation unit dynamics before being combined to form the complete model of the wind turbine dynamics. The resulting combined model, in addition to supporting the control design task, enables the extent, to which the basic models adequate represent the wind turbine, to be assessed. It is concluded that the basic models of variable speed wind turbines are not adequate and do not exhibit all the relevant aspects of the dynamics necessary to support the control design.

Multivariable control by individual channel design

Abstract A new approach—individual channel design (ICD)—to an enduring problem— multivariable feedback control—is presented. The approach is applications-oriented: it starts from the engineering premise that feedback control design is interactive; it involves an interplay between customer specification, uncertain plant characteristics, and the multivariable feedback design process itself. It is shown that individual signal transmission channels arise naturally from customer specification on selected plant outputs with no loss of structural (loop interaction) information. By invoking customer performance specification on different channels, highly successful single-input single-output classical (Nyquist-Bode) design is made possible. ICD is not a design method per se per se; rather it is a global structural framework wherein the possibilities and limitations for local-loop-shaping design (e.g. Bode or Nichols) of a particular plant are made apparent from the outset. Also, the conditions are established whe...

Enhanced Power System Stability by Coordinated PSS Design

A step-by-step coordinated design procedure for power system stabilisers (PSSs) and automatic voltage regulators (AVRs) in a strongly coupled system is described in this paper. It is shown that it is possible to separate the design of individual PSSs and separate the design of individual AVRs. Thereby, the designs of AVR and PSS devices at a given machine can be coordinated to achieve near-optimal overall power system stability performance, including oscillation stability performance and transient stability performance. The proposed coordinated PSS/AVR design procedure is established within a frequency-domain framework and serves as a most useful small-signal complement to established large-signal transient simulation studies.

Gain-scheduled and nonlinear systems: Dynamic analysis by velocity-based linearization families

A family of velocity-based linearizations is proposed for a nonlinear system. In contrast to the conventional series expansion linearization, a member of the family of velocity-based linearizations is valid in the vicinity of any operating point, not just an equilibrium operating point. The velocity-based linearizations facilitate dynamic analysis far from the equilibrium operating points and enable the transient behaviour of the nonlinear system to be investigated. Using velocity-based linearizations, stability conditions are derived for both smooth and non-smooth nonlinear systems which avoid the restrictions to trajectories lying within an unnecessarily (perhaps excessively) small neighbourhood about the equilibrium operating points inherent in existing frozen-input theory. For systems where there is no restriction on the rate of variation the velocity-based linearization analysis is global in nature. The analysis techniques developed, although quite general, are motivated by the gain-scheduling design...

Implementation of wind turbine controllers

Three of the important generic implementation issues encountered when developing controllers for pitch-regulated constant-speed wind turbines are considered; namely, accommodation of the strongly nonlinear rotor aerodynamics, automatic controller start-up-shut-down and accommodation of velocity and acceleration constraints within the actuator. Both direct linearization and feedback linearization methods for accommodating the nonlinear aerodynamics are investigated and compared. A widely employed technique for accommodating the nonlinear aerodynamics, originally developed on the basis of physical insight, is rigorously derived and extended to cater for all wind turbine configurations. A rigorous stability analysis of controller start-up is presented for the first time, and novel design guidelines are proposed which can significantly reduce the power transients at controller start-up. The relation to anti-wind-up is noted and several aspects of an existing wind-turbine controller start-up strategy are obser...

Dynamics of distribution networks with distributed generation

This paper discusses the results of case studies which assess transient and small-signal stability of distributed generators connected to utility distribution networks. It also presents an investigation of the interaction between the controllers of individual generators. Case studies are based on different levels of generation penetration and a variety of operating conditions of both the networks and the generators. Transient stability and small-signal stability were assessed using commercially available power system simulation software. The interaction between the controllers is initially examined using eigenanalysis. A novel approach, i.e., individual channel analysis and design (ICAD), is then utilised to obtain an insight into the dynamics of the multivariable control problem.

Analytic framework for blended multiple model systems using linear local models

In this paper it is shown that the dynamics of a conventional type of blended multiple model system are only weakly related to the local models from which it is formed. A novel class of velocity-based blended multiple model systems is proposed for which the dynamics are directly related to the local models. Indeed, the solution to the blended multiple model system, locally to a specific operating point, is approximated by the weighted linear combination of the solutions to the local models. Moreover, in contrast to conventional blended multiple model systems, the velocity-based blended multiple model systems employs linear local models, thereby providing a degree of continuity with established linear methods and, consequently, facilitating analysis and design.