Framework for System Identification

Proof Take the limit as oo of the corresponding equations in Theorem 6.1 and Theorem 6.2 to give the above results. Q.E.D. 

The infinite horizon predictor is useful when looking at the predictive properties of a model and how generalisable the model is. Basically, the infinite horizon predictor assumes that the errors are not known and seeks to predict the process solely on the basis of the available input information. 

The system identification framework shown in Fig. 6.3 extends the general regression framework shown in Fig. 3.1 to take into account the specific issues in process system identification. The framework consists of three steps  

Data Collection During the data collection step, the required data are collected and analysed to determine if there are any obvious problems with the data set, such as missing data, faulty sensors, faulty values, or multiple operating modes. The framework presented in Fig. 6.3 assumes that a separate experiment will be designed in order to obtain the data required for system identification. In industry, the ability to perform such experiments can be limited due to various factors, including safety, economic, or reluctance on the part of the plant operators. Instead, historical data from the data historian are extracted and preprocessed to determine their usefulness for the given problem. 

Model Creation and Validation During this step, the data set is used to create the model and obtain parameter estimates. Also, the given model is validated to determine if it could potentially be used. 

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