Modelling and Control of Batch Processes

Abstract

<p>This thesis considers the problems of modelling and control of batch processes, a class of finite duration chemical processes characterized by their absence of equilibrium conditions and nonlinear, time-varying dynamics over a wide range of operating conditions. In contrast to continuous processes, the control objective in batch processes is to achieve a non-equilibrium desired end-point or product quality by the batch termination time. However, the distinguishing features of batch processes complicate their control problem and call for dedicated modelling and control tools. In the initial phase of this research, a predictive controller based on the novel concept of reverse-time reachability regions (RTRRs) is developed. Defined as the set of states from where the process can be steered inside a desired end-point neighbourhood by batch termination subject to input constraints and model uncertainties, an algorithm is developed to characterize these sets at each sampling instance offline; these characterizations subsequently play an integral role in the control design. A key feature of the resultant controller is that it requires the online computation of only the immediate control action while guaranteeing reachability to the desired end-point neighbourhood, rendering the control problem efficiently solvable even when using the nonlinear process model. Moreover, the use of RTRRs and one-step ahead type control policy embeds important fault-tolerant characteristics into the controller. Next, we address the problem of the unavailability of reliable and computationally manageable first-principles-based process models by developing a new data-based modelling approach. In this approach, local linear models (identified via latent variable regression techniques) are combined with weights (arising from fuzzy c-means clustering) to describe global nonlinear process dynamics. Nonlinearities are captured through the appropriate combination of the different models while the linearity of the individual models prevents against a computationally expensive predictive controller. This modelling approach is also generalized to account for time-varying dynamics by incorporating online learning ability into the model, making it adaptive. This is accomplished by developing a probabilistic recursive least squares (PRLS) algorithm for updating a subset of the model parameters. The data-based modelling approach is first used to generate data-based reverse-time reachability regions (RTRRs), which are subsequently incorporated in a new predictive controller. Next, the modelling approach is applied on a complex nylon-6,6 batch polymerization process in order to design a trajectory tracking predictive controller for the key process outputs. Through simulations, the modelling approach is shown to capture the major process nonlinearities and closed-loop results demonstrate the advantages of the proposed controller over existing options. Through further simulation studies, model adaptation (via the PRLS algorithm) is shown to be crucial for achieving acceptable control performance when encountering large disturbances in the initial conditions. Finally, we consider the problem of direct quality control even when there are limited quality-related measurements available from the process; this situation typically calls for indirectly pursuing the control objective through trajectory tracking control. To address the problem of unavailability of online quality measurements, an inferential quality model, which relates the process conditions over the entire batch duration to the final quality, is required. The accuracy of this type of quality model, however, is sensitive to the prediction of the future batch behaviour until batch termination. This "missing data" problem is handled by integrating the previously developed data-based modelling approach with the inferential model in a predictive control framework. The key feature of this approach is that the causality and nonlinear relationships between the future inputs and outputs are accounted for in predicting the final quality and computing the manipulated input trajectory. The efficacy of the proposed predictive control design is illustrated via simulations of the nylon-6,6 batch polymerization process with a different control objective than considered previously.</p>