Reconstruction of Linear and Nonlinear Continuous Time Models from Discrete Time Sampled-Data Systems

A new approach for identifying continuous time models from discrete time sampled-data records is presented. The proposed method involves estimating and validating a discrete time model, linear or nonlinear, based on sampled data records, evaluating the discrete time linear and nonlinear frequency response functions and then curve fitting to the frequency response data to yield a continuous time model. No numerical differentiation and integration is involved and hence higher derivatives of input and output data records are avoided. Errors which would be introduced by the numerical approximation of differentiation and integration are therefore eliminated. The orthogonal estimator which is introduced to curve fit to the complex frequency response functions, provides information on the model structure and the unknown parameter values for linear and nonlinear continuous time models. The advantage of this approach is that nonlinear differential equation models which can be related to the physical behaviour of the system can be readily computed from discrete time data.