Input Design for Continuous Time Output Error Models

Abstract

In this paper, the problem of input design for identification of continuous time output error models is considered. The input design problem is formulated as maximization of a measure of the Fisher information matrix, which defines the accuracy with which the system parameters can be estimated. The optimization problem involving the Fisher information matrix depends on the true system parameters, which are unknown. Existing methods use an iterative approach to tackle this circular dependency. In this paper, the system transfer function is represented using generalized orthonormal basis functions which makes the Fisher Information matrix independent of the true system parameters. Therefore, the input design problem reduces to solving a single optimization problem instead of a series of optimizations that are performed in existing methods. Further, in existing approaches, the computational complexity of the optimization grows with the length of the input vector to be identified. In the current paper, the input is also represented using smooth basis functions, thereby making the complexity independent of the length of the input vector. A least-squares approach for parameter estimation is given and it is shown that the estimates are unbiased for the optimal inputs. The accuracy of the proposed method is demonstrated with the help of two examples. Further, input design for a continuous stirred tank reactor model and a quadruple tank experimental set up is considered to demonstrate the practical applicability of the new method.