Optimal Input Signal Design for Identification of Interactive and Ill-Conditioned Systems

Research paper by Abhishankar Kumar, Sridharakumar Narasimhan

Indexed on: 06 Apr '16Published on: 22 Mar '16Published in: Industrial & Engineering Chemistry


Optimal input design is the process of generating informative inputs that can be used to generate good quality dynamic models using minimal resources. In this work, we propose an optimization-based input design method for identification of ill-conditioned and interactive MIMO systems. The interactions of the inputs, outputs, and ill-conditionality of system are accounted in the formulation. The resulting problem is convex where the decision variables are the input autocorrelation and cross-correlation coefficients. The inputs are realized as white noise filtered through an m-tap FIR filter. The filter coefficients are obtained by the spectral factorization. These proposed ideas are illustrated using simulation of two well-studied problems: (i) heat exchanger system; (ii) high purity distillation column. The system response obtained using conventional D-optimal inputs shows alignment in one particular direction while the system outputs in the proposed formulation show good distribution in the output space. The performance of the inputs signal is also compared based on scattering factor, crest factor, and fit percent of the identified model.

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