Multiple ARX model based identification for switching/nonlinear systems with EM algorithm

Benefits brought by automatic control systems through increasing the production efficiency, reducing the production cost and environmental footprint have already been seen and experienced by process industry in the past few decades. However, given the rapid increase of the complexity in process itself as well as its interactions with the outside world, it is getting more common to observe that the controlled process exhibits time-varying/switching behaviors due to, for instance, the change of its operating conditions such as grade change in polymer plants or the feedstock change for chemical reactors. In this thesis, systems showing gradually varying dynamics or abrupt changing behaviors will be referred to altogether as switched systems. In real production practice, these switching behaviors may greatly compromise the performance of the most of current control systems owing to the fact that they are not initially designed for process with switching behaviors. Due to the critical role the control systems play in ensuring the safety as well as the profitability of the plant operation, it is desirable to enable the control systems to achieve satisfactory performance for the switched process. Therefore, as a prerequisite for any model-based optimal controllers, modeling of the switched systems is of necessity and it directly determines the performance of the designed controller.In the process industry, process may gradually switch over several local sub-systems. To model the switched systems exhibiting gradual or smooth transition among different local models, in addition to estimating the local sub-systems parameters, a smooth validity (an exponential function) function is introduced to combine all the local models so that throughout the working range of the gradual switched system, the dynamics of the nonlinear process can be appropriately approximated. Scheduling variable(s) is/are defined to represent the conditions under which the process is operated and it is assumed to be measurable. The EM algorithm is applied in estimating the local model parameters as well as the key parameters for the validity functions for each local model. Verification results on a simulated numerical example and an CSTR process confirm the effectiveness of the proposed Linear Parameter Varying (LPV) identification algorithm.Two different types of switching mechanism are considered in this thesis, one is featured with abrupt/sudden switching while the other one shows gradual changing behavior in its dynamics. The Expectation-Maximization (EM) algorithm is employed throughput the thesis in identifying the switched systems. Identification methods with/without considering the modeling of the switching dynamics are proposed and they are tested on various numerical simulation examples as well as a pilot scale tank system. For the identification method without considering the modeling of switching dynamics, its robustness to the data set polluted with outliers is achieved by assuming a contaminated Gaussian distribution as the distribution of noise. It is shown that, through the comparison of the identification results from the proposed method and a benchmark method, the proposed robust identification method can achieve better performance when dealing with the data set mixed with outliers. For the identification method in which the modeling of discrete switching dynamics is considered, the hidden Markov model is employed in describing the evolution of the discrete switching variable. By simultaneously estimating parameters of the discrete dynamics (hidden Markov model) and continuous dynamics (local ARX model), it is found that the performance of the identification method can be effectively increased compared with the methods without considering the switching dynamics.