Extracting Second Order Systems from State Space Representations

MI Friswell (University of Wales Swansea), SD Garvey & JET Penny (Aston University)

AIAA Journal, Vol. 37, No. 1, January 1999, pp. 132-135


It is established that every linear dynamic system that can be modelled using a finite number of degrees of freedom can be cast in state space form. The so-called modern control literature has adopted this form almost globally and to good effect. Systems of second order differential equations are transformed into first order (state space) form at the instant that the characteristic roots are required or when any active control is envisaged. Occasionally, however, the reverse transformation is useful. It would appear that little attention has been given in the literature to this transformation. The primary purpose of this note is to provide a simple method to generate the transformation to second order form. Furthermore a condition is given on the original input and output matrices that is required if a transformation exists to the 'standard' second order form, where the outputs are a subset of the degrees of freedom, and the derivative of the input is not applied as a force.

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