Continuous-Time Identification of SISO Systems using Laguerre Functions

This paper looks at the problem of estimating the coefficients of a continuous-time transfer function given samples of its input and output data. We first prove that any nth-order continuous-time transfer function can be written as a fraction of the form /spl Sigma//sub k=0//sup n/b~/sub k/L/sub k/(s)//spl Sigma//sub k=0//sup n/a~/sub k/L/sub k/(s), where L/sub k/(s) denotes the continuous-time Laguerre basis functions. Based on this model, we derive an asymptotically consistent parameter estimation scheme that consists of the following two steps: (1) filter both the input and output data by L/sub k/(s), and (2) estimate {a~/sub k/, b~/sub k/} and relate them to the coefficients of the transfer function. For practical implementation, we require the discrete-time approximation of L/sub k/(s) since only sampled data is available. We propose a scheme that is based on higher order Pade approximations, and we prove that this scheme produces discrete-time filters that are approximately orthogonal and, consequently, a well-conditioned numerical problem. Some other features of this new algorithm include the possibility to implement it as either an off-line or a quasi-on-line algorithm and the incorporation of constraints on the transfer function coefficients. A simple example is given to illustrate the properties of the proposed algorithm

Fractional-Order Discrete-Time Laguerre Filters: A New Tool for Modeling and Stability Analysis of Fractional-Order LTI SISO Systems

This paper presents new results on modeling and analysis of dynamics of fractional-order discrete-time linear time-invariant single-input single-output (LTI SISO) systems by means of new, two-layer, “fractional-order discrete-time Laguerre filters.” It is interesting that the fractionality of the filters at the upper system dynamics layer is directly projected from the lower Laguerre-based approximation layer for the Grünwald-Letnikov difference. A new stability criterion for discrete-time fractional-order Laguerre-based LTI SISO systems is introduced and supplemented with a stability preservation analysis. Both the stability criterion and the stability preservation analysis bring up rather surprising results, which is illustrated with simulation examples

Convex Optimization In Identification Of Stable Non-Linear State Space Models

A new framework for nonlinear system identification is presented in terms of optimal fitting of stable nonlinear state space equations to input/output/state data, with a performance objective defined as a measure of robustness of the simulation error with respect to equation errors. Basic definitions and analytical results are presented. The utility of the method is illustrated on a simple simulation example as well as experimental recordings from a live neuron.Comment: 9 pages, 2 figure, elaboration of same-title paper in 49th IEEE Conference on Decision and Contro

Continuous time state-space model identification with application to magnetic bearing systems

This thesis presents the identification of continuous time linear multi-variable systems using state-space models. A data-driven approach in realization by the subspace methods is carried out in developing the models. In this thesis, the approach by subspace methods is considered for both open-loop and closed-loop continuous time system identification. The Laguerre filter network, the instrumental variables and the frequency sampling filters are adopted in the framework of subspace model identification. More specifically, the Laguerre filters play a role in avoiding problems with differentiation in the Laplace operator, which leads to a simple algebraic relation. It also has the ability to cope with noise at high frequency region due to its orthogonality functions. The instrumental variables help to eliminate the process and measurement noise that may occur in the systems. The frequency sampling filters are used to compress the raw data, eliminate measurement noise so to obtain a set of clean and unbiased step response data. The combination of these techniques allows for the estimation of high quality models, in which, it leads to successful performance of the continuous time system identification overall. The application based on a magnetic bearing system apparatus is used to demonstrate the efficacy of the proposed techniques