Feedback control and optimization using adaptive reduced order models
Open Access
- Author:
- Pitchaiah, Sivakumar
- Graduate Program:
- Chemical Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- June 16, 2011
- Committee Members:
- Antonios Armaou, Dissertation Advisor/Co-Advisor
Antonios Armaou, Committee Chair/Co-Chair
Ali Borhan, Committee Member
Costas D Maranas, Committee Member
Jacob Willem Langelaan, Committee Member - Keywords:
- Nonlinear control
Process control
Proper orthogonal decomposition
Partial differential equation
Model reduction - Abstract:
- The development of efficient control and optimization schemes for processes described by nonlinear parabolic partial differential (PDE) equations is a fundamental problem with a variety of industrially important applications. Typical examples of such processes range from reactive distillation in petroleum processing to plasma enhanced chemical vapor deposition, etching and metallorganic vapor phase epitaxy (MOVPE) in semiconductor manufacturing. The key difficulty in designing control schemes for such PDE systems arises from the ``infinite-dimensional' nature of the distributed process model. Consequently, ideas for reducing the complexity of these models are considered through the formulation of the reduced order models (ROMs). A properly formulated ROM can replace the existing complex model thus greatly facilitating in the further design of control and optimization schemes for the above PDE processes. One of the widely used methodologies for developing ROMs is the proper orthogonal decomposition (POD). Initially, one collects the experimental data or data from detailed numerical simulations (snapshots) in a ``dataset'. POD then extracts the characteristic basis (shape) functions from the collected data set. The computed basis functions are subsequently used in the framework of "method of weighted residuals" to compute the low-dimensional ROMs. The effectiveness of the POD methodology, however, is dependent on the quality of the collected dataset. Consequently, the ROMs are sufficiently accurate only in a restricted neighborhood around the state space where they are constructed. On the other hand, no well defined methodology exists for constructing ROMs with a larger region of validity as this requires a ``representative' dataset which contains all the possible spatial modes (including those that might appear during closed-loop evolution of the PDE system). Thus there arises a need for the development of efficient methodologies for the systematic update of these ROMs during the closed-loop process evolution. Thus this doctoral thesis attempts to resolve fundamental computational issue associated with the formulation of the ROMs, specifically tailored for controller design, by developing a computationally efficient methodology called the adaptive proper orthogonal decomposition (APOD) that utilizes the closed-loop process information for ROM updates. The updated ROMs are utilized for synthesis of high-performance nonlinear & optimal feedback controllers using Lyapunov and geometric control techniques. The effect of the developed methodology on the closed-loop system is analyzed by a study of stability and other performance properties of the closed-loop system (distributed PDE process model along with the controller). The developed adaptive data-reduction methodology would also have applications in varies other fields such as efficient process monitoring and fault diagnosis of chemical processes.