Special section system identification tutorial: Correlation methods

Pseudorandom signals have been widely used for system identification. Maximum length binary (MLB) signals are the best known class of pseudorandom signals, because of their ease of generation using feedback shift registers, but it is less well known that there are several other classes of binary and near-binary signals with identical, or nearly identical properties. An overview of these classes of signals is given, and the design of a new MATLAB routine incorporating all these classes of signals is described. The importance of the choice of MLB signal to use in particular applications is illustrated with the identification of a Wiener system having a quadratic nonlinearity and a cubic nonlinearity. Using correlation analysis to estimate the linear system weighting function, errors due to the nonlinearities can be reduced if an appropriate choice is made of feedback connections and of data length used for the estimation.

The generation of binary and near-binary pseudorandom signals: an overview

This paper examines the effects of nonlinearities on frequency response function measurements using periodic multifrequency signals. A class of broadband pilot test signals is proposed, termed sparse odd multisines, which can be used to establish the system bandwidth and detect nonlinearities. Signals are then defined within this class which allow the measurement of the best linear approximation of a nonlinear system. A comparison is made with related work in this area.

Nonlinear distortions and multisine signals. I. Measuring the best linear approximation

The identification of the fuel flow to shaft speed dynamics of a twin-shaft gas turbine is addressed, with the aim of validating thermodynamic engine models. A measured input signal must be used in estimation in order to exclude the fuel feed dynamics from the model. This has been shown to present problems when fitting discrete models to engine data, and this paper examines the direct estimation of s-domain models in the frequency domain. A number of different multisine test signals were applied to the engine for the purposes of model estimation and nonlinear detection. The use of frequency-domain techniques is shown to produce high-quality models, and the tests also yield information on the levels of noise and nonlinearity and the length of the pure time delay. This work illustrates the potential of frequency-domain techniques for modeling systems where a physical interpretation is to be made of the model and where the need for accuracy requires that a measured input signal be used in estimation.

D. J. Moore

Papers

Identification of processes having direction-dependent responses, with gas-turbine engine applications