Identification of linear and nonlinear systems using multisine signals : with a gas turbine application

Modern system identification techniques allow dynamic models to be directly estimated from measured data and the design of the data gathering experiment is a key step in any identification procedure. This thesis deals with the design of test signals for both linear and nonlinear modelling and their application to an engineering problem. It is motivated by a desire to fully exploit the recent advances in computer technology, which make the design and application of complex multisine test signals a practical possibility. The thesis can be divided into two parts, the first dealing with test signal design and the second presenting a detailed study of the testing and modelling of an aircraft gas turbine. The main contributions of the first part deal with the influence of noise and nonlinearities on multisine test signals and the design of new types of multisines for testing nonlinear systems. The test times associated with single sine, multisine and maximum length binary signals are studied, with the aim of reducing test times while maintaining accuracy in the presence of noise. A novel methodology is presented for analysing the influence of system nonlinearities on multisines, with the aim of designing signals which are robust to nonlinear effects. This leads to the design of signals which can be used to identify the best linear approximation of block-oriented nonlinear systems of the Wiener-Hammerstein type. The design of signals which minimise the nonlinear distortion at the test frequencies is also studied, with the aim of identifying the underlying linear dynamics of the system. A scheme is proposed for the identification of linear systems in the presence of nonlinear distortions. The designs are then further developed to allow the direct measurement of points on the frequency-domain Volterra kernels (higher-order frequency response functions) of a nonlinear system. The second part of the thesis deals with gas turbine modelling, with the aim of estimating models which can be used to verify the linearised thermodynamic models derived from the engine physics. The design of appropriate test signals is discussed, a detailed analysis of the measured data is presented and engine models are identified. The influence of noise and nonlinearities on the estimated models is studied. It is shown that the use of multisine signals and frequency-domain techniques is particularly suited to this problem, since the continuous-time s-domain models needed to validate the thermodynamic models can be directly estimated. The problem of estimating discrete-time models which do not have a continuous-time counterpart is also discussed and some possible causes of this effect are investigated. This thesis is a contribution to the further application of multisine signals to the measurement and identification of linear and nonlinear systems. It also illustrates the potential of frequency-domain techniques for modelling gas turbine dynamics, where a physical interpretation of the model parameters is to be made. Table of