From data to diagnosis and control using generalized orthonormal basis filters. Part I: Development of state observers

This work is aimed at the development of a state observer (steady state Kalman filter) for a multivariable system with unknown time delays, which is subjected to unmeasured disturbances. To design such a filter, we explore the feasibility of capturing system dynamics using generalized orthonormal basis filters (GOBF). A two step identification procedure is proposed by exploiting the fact that the GOBF based models have output error structure. The deterministic component of the model is identified in the first step and used to compute a residual signal. In the second step, a filter that whitens the residuals is estimated using GOBF and combined with the deterministic component. A minimal order state realization of the innovation form of the state model is then generated from this high order model using realization based sub-space based state space (4SID) identification algorithm. When time delays are not known a-priori, the similarity between GOBF and Pade approximation is used to estimates time delay matrix directly from multivariate data. The efficacy of the proposed modeling technique is demonstrated by carrying out simulation studies on the benchmark Shell control problem and experimental evaluation on a stirred tank heater (STH) system. From the analysis of simulation and experimental results, it can be inferred that the proposed approach produces fairly accurate estimates of the time delay matrix and the deterministic and stochastic components of the dynamic model.