408785 Robust Adaptive Model Predictive Control of Chemical and Biological Systems

Sunday, November 8, 2015
Exhibit Hall 1 (Salt Palace Convention Center)
Davood Babaei Pourkargar, Chemical Engineering, The Pennsylvania State University, University Park, PA

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.

Regarding my future research efforts, I intend to extend my computational work to modeling, estimation, control and optimization of advanced chemical and biological systems with specific applications to catalytic chemical processes, advanced biofuels production and continuous pharmaceutical processes. Specifically, the intellectual objective of my future research is to develop a systematic control and optimization framework tailored for chemical and biological systems with unknown transport-reaction mechanisms when the systems uncertainty plays a vital role. For example, the source of parametric uncertainties and unmeasurable unknown parameters in chemical and biological systems, which necessitates applying such novel control and optimization approaches, is reaction rates, activation energies, fouling factors and microbial growth rates which are only approximately known via complex experiments.

The presence of uncertainty in the form of additive disturbances, state estimation and modeling errors, and the associated topic of robustness are still major challenges in control theory and specifically in model predictive control (MPC) designs. The reason for such challenges is that to solve the optimal control problem in the presence of uncertainty we require feedback from the system; solving an open-loop optimal control problem to determine a control law, as is done in nominal MPC, is not optimal. The natural extension of MPC to address the control problem of uncertain systems would be to optimize over a sequence of control laws not over a sequence of control actions. However this dynamic programming approach may be unacceptable in practical situations. One of the practical methods to cope with such uncertainty in the system model is via robust MPC (RMPC) where the required estimation upper bound of the time-varying uncertainty can be improved as time evolves. Generally, the performance of robust controllers is restricted by the quality of the model and its uncertainty description due to the disability of the control approach in learning the system changes during process evolution. To circumvent such limitation we can employ adaptive MPC (AMPC) to improve closed-loop system performance by updating the model through unknown parameters’ estimation based on measurement outputs.

While linear AMPC designs have reached a certain maturity, very few AMPC schemes have been developed for nonlinear systems and only for unconstrained processes. The nonlinear AMPC problem is highly challenging because the robustness to the model uncertainty must be addressed in the presence of constraints while the adaptive estimator is evolving without assuming the separation principle which is only valid for linear systems. I plan to investigate the nonlinear AMPC problem by introducing extra degrees of conservativeness considering robust performance and closed-loop stability. The proposed research in this theoretical subject will introduce systematic computationally efficient process identification methods to estimate system parameters required by MPC to compute the optimal control action subject to a continuous decrease in the identification error. It will also resolve fundamental theoretical and computational issues associated with system identification techniques in control and optimization policies for a wide range of chemical and biological systems.

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