Some New Transformation Algorithms in the Identification of Continuous-Time Multivariable Systems Using Discrete Identification Methods

Abstract

A procedure for the identification of linear continuous multivariable systems is shown which is based on a discrete identification method and suitable transformation algorithms. Both, the structural and the parametric identification are performed from samples of input and output data, and are based on the discrete input-output model. A new method for the deduction of a state-space model from the identified input-output model is proposed. The method is based on a recursive formula by which construction and inversion of the auxiliary matrix is avoided. The discrete state-space model is transformed into the continuous state-space model using methods based on the fundamental matrix logarithm and its approximations. Four different algorithms for computation of the matrix logarithm function are proposed. For the derivation of the control matrix and the transmission matrix, also four different approaches are shown: the step-invariant, the rampinvariant, the bilinear and the combined approach. The proposed procedure is very efficient when sequences of steps or rectangular pulses can be used as test functions in the identification procedure. If normal operating records of the plant are used, the method is less efficient. The applicability of the proposed procedure for systems simplification is also discussed. Finally, an application of this procedure to a simulated continuous process, using different transformation methods is given.