• MPC Monitoring
• Process Control
• Process Identification

Process optimization represents an important task in the management of industrial plants. It is strictly related to plant economics, so there is a high interest in the definition of reliable optimization schemes. At the moment, one of the most successful optimization algorithm is represented by MPC. This is an acronym standing for ``Model Predictive Controller''. MPC optimizes the process to which it is applied by ``predicting'' the state of the system over a future time window, using a process model as a part of its internal structure. MPC has been used since the last two decades, and at the moment it represents a proven optimization scheme, with thousands of applications in chemical and petrochemical industry. It is important to check regularly for MPC performances in order to guarantee optimal operation in spite of unknown disturbances and/or changes in the process dynamics. Such an operation is named “Performance Monitoring” or simply “Monitoring”. Despite its importance, at the moment there has not been an extensive analysis of this task in the literature, which is relatively poor compared to other fields related to MPC. A monitoring technique should be able to discern the cases in which the optimization scheme is working in optimal or sub-optimal conditions, and, in this latter case, it should recognize the causes of performance degradation. In the literature, the causes of performance degradation are usually two, i.e. inadequate estimation of unknown disturbances and a mismatch between the internal model and the real process. In the first case, the operations that are needed to correct the mistake consist in a better definition of the noise level of the system and in the calculation of a new estimator using the correct disturbance information. In the second case, the only way to improve the performances of the system is the definition of a new process model. This is a complex task, which takes a long time and requires a particular attention, and it is named “Identification”. Several different identification techniques were presented in the literature. They use input and output data sets coming from the system to compute a process model In this thesis, identification techniques for systems which can present difficulties have been introduced, i.e. unstable systems and ill-conditioned systems, and a monitoring technique for optimization schemes, tailored on MPC structure, has been discussed. Unstable systems cannot be usually identified with a class of identification schemes that perform a particular regression on data, because numerical problems arise due to the presence of high powers of the ``unstable'' system dynamic matrix. This work introduces an extension of the structure of this class of identification schemes which permits to handle data coming from an unstable system. Ill-conditioned processes give problems because data coming from this kind of processes are aligned in a particular direction, called “strong direction”. For this reason, a high level of information is present in the data set over that direction, but a low information level is present over other directions, resulting in models which cannot describe the system adequately in all directions. This work presents the guidelines of a successful identification method in which data are collected in closed-loop. Finally, the problem of MPC monitoring in this work is addressed analyzing the difference between the value of the real outputs coming from the system and the value of outputs predicted by the internal MPC model, which is usually indicated as ``Prediction error''. This analysis takes into account the statistical properties of the previously mentioned prediction error, in order to define if the optimization scheme works in sub-optimal conditions. Then, if this analysis shows the presence of some issues, the cause that generates these issues is determined by checking the rank of a particular matrix obtained from data, that is the observability matrix of an extended closed-loop system.