System identification open-loop

The identification of plant models has traditionally been done in the open-loop mode. The desire to minimize the production of the off-spec product during an open-loop identification test and to avoid the unstable open-loop dynamics of certain systems has increased the need to develop methodologies suitable for the system identification. Open-loop identification techniques are not directly applicable to closed-loop data due to correlation between process input (i.e., controller output) and unmeasured disturbances. Based on Prediction Error Method (PEM), several closed-loop identification methods have been presented Direct, Indirect, Joint Input-Output, and Two-Step Methods. 

The PBL reactor considered in the present study is a typical batch process and the open-loop test is inadequate to identify the process. We employed a closed-loop subspace identification method. This method identifies the linear state-space model using high order ARX model. To apply the linear system identification method to the PBL reactor, we first divide a single batch into several sections according to the injection time of initiators, changes of the reactant temperature and changes of the setpoint profile, etc. Each section is assumed to be linear. The initial state values for each section should be computed in advance. The linear state models obtained for each section were evaluated through numerical simulations. 

The primary objective is to perform system identification, that is, obtain a plant model, especially that of the process, in order to design a controller. Two different situations can be considered open-loop system identification and closed-loop system identification. 

In open-loop system identification, it is assumed that the controller and reference signal are not present, that is, the control loop has not been closed. In such a case. Fig. 6.1 reduces to Fig. 6.2. The relationship between the input and output can then be written as... 

This section will examine the principles and key results for modelling an open-loop process modelled using the general prediction error model given by Eq. (6.4). The foundation for such modelling is the prediction error method, which uses the fact that most models in system identification are used for predicting future values of the process. 

An automated pilot-scale 1-litre experimental polymer reactor system with facilities for on-line measurement of flow rate, temperature and density has been set up by Chien and Penlidis (1994a, b). These authors describe a set of open-loop process identification experiments and closed-loop control experiments performed on this system where monomer conversion is controlled in the presence of reactive impurities using the initiator flow rate as the manipulated variable. 

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