A variational integrators approach to second order modeling and identification of linear mechanical systems

The identification of linear second order models of mechanical systems has been object of intensive research and of several papers in the last decades. In this thesis the interest is focused on mechanical systems which can be described by a second order vector model of the following form: Mq̈ +Dq̇ +Kq = f (1) where M and K are symmetric positive definite while D is only symmetric positive semidefinite. All current identification techniques operate in discrete time. Noisy data obtained by sampling the system must be used to estimate the continuous time physical parameters M,K and D. Since identification operates in discrete time one needs to convert the discrete time identified system into a continuous time one. There are structural constraints that need to be imposed to obtain the second order structure (2). In short, the procedure is composed of three main steps: 1. Discrete-time Identification, mostly using subspace methods, from sampled input-output data; 2. Implementation of a set of constraints which force the identified system to the form (2); 3. Conversion from the discrete to a continuous model and conversion of the relative system parameters. The usual procedure assumes that the discrete time identified system is a Zero-Order-Hold (ZOH) discretization of the underlying continuous time system.