(6it) Robust Adaptive Model Predictive Control of Chemical and Biological Systems

My doctoral research work has contributed to the synthesis of advanced control structures for processes where complex transport phenomena and chemical reactions take place in the chemical and advanced material industries. These processes, called distributed parameter systems (DPSs), can be mathematically modeled by a set of nonlinear partial differential equations (PDEs) and are exemplified by packed and fluidized bed reactors in chemical plants; reactive distillation in petrochemical industries; lithographic processes; chemical vapor deposition,  etching processes and plasma discharge reactors in microelectronics manufacturing and complex materials production; crystallization and polymerization processes; and tin float bath processes in glass production industry. In our research, we circumvent the restrictions of the current control approaches tailored for PDE systems via model order reduction by designing low-dimensional output feedback controllers on the basis of reduced order models (ROMs) of the governing PDEs. The successful implementation of the model reduction based approaches depends heavily on the basis functions that are required to construct the ROMs using weighted residual methods. A limitation is that analytical methods to derive a consistent basis function set are not applicable in the presence of unknown parameters, nonlinear spatial derivatives or when the process operates over complex spatial domains. On the other hand statistical methods, such as variants of widely popular proper orthogonal decomposition (POD) method, guarantee basis identification only under strict assumptions that cannot be verified in practice.

Motivated by the above limitations my research focused on

1. Deriving a control-tailored and computationally efficient robust algorithm to recursively compute the optimal set of empirical basis functions required by weighted residual methods to discretize the governing PDEs and construct locally accurate ROMs in the form of ODEs. The algorithm, known as adaptive proper orthogonal decomposition (APOD), circumvents the limitations of online statistical techniques and leads to a three-fold increase in computational speed.
2. Synthesizing advanced nonlinear output feedback control structures that can guarantee closed-loop stability. A wide range of nonlinear Lyapunov-based robust and adaptive controllers and nonlinear dynamic observers were synthesized to address the regulation and tracking problem of nonlinear DPSs as most effective as possible in the presence of time-varying unknown parameters and system uncertainty.
3. Designing a supervisory structure which monitors the controller performance in stabilization and tracking the desired spatiotemporal dynamics, (a) to retune the controller parameters and (b) to revise the ROMs as needed via APOD. Taking advantage of such supervisory control structure, the ROM revisions are minimized which leads to reduction in the required information from spatially distributed sensors to recursively update the empirical basis functions by APOD.