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To improve the performance of the three-way catalytic (TWC) converter, advanced control strategies and onboard diagnostics (OBD) systems are needed. Both rely on a relatively accurate but computationally efficient TWC converter model. This thesis aims to develop a control-oriented model that can be employed to develop the control strategies and OBD systems of the TWC converter. The thesis consists of two parts, i.e., the high-fidelity model development and the model reduction. Firstly, a high-fidelity model is built using the energy and mass conservation principles. In this model, a constant inlet simulation is used to validate the warming-up characteristics, and a driving cycle simulation is used to calibrate the reaction rate parameters. The results of the simulation show that the high-fidelity model has adequate accuracy. Secondly, a reduced-order model is developed based on phase and reaction simplifications of the high-fidelity model. The aim of the development of the reduced-order model is to propose a computationally efficient model for further development of control strategies and state estimators for OBD systems. The accuracy of the reduced-order model is then validated by means of simulations. / Thesis / Master of Science (MSc)

To improve the performance of the three-way catalytic (TWC) converter, advanced control strategies and on-board diagnostics (OBD) systems are needed. Both rely on a relatively accurate but computationally efficient TWC converter model. This thesis aims to develop a control-oriented model that can be employed to develop the control strategies and OBD systems of the TWC converter. The thesis consists of two parts, i.e., the high-fidelity model development and the model reduction. Firstly, a high-fidelity model is built using the energy and mass conservation principles. In this model, a constant inlet simulation is used to validate the warming-up characteristics, and a driving cycle simulation is used to calibrate the reaction rate parameters. The results of the simulation show that the high-fidelity model has adequate accuracy. Secondly, a reduced-order model is developed based on phase and reaction simplifications of the high-fidelity model. The aim of the development of the reduced-order model is to propose a computationally efficient model for further development of control strategies and state estimators for OBD systems. The accuracy of the reduced-order model is then validated by means of simulations. / Thesis / Master of Applied Science (MASc)

Numerical models of PDE systems can involve very large matrix equations, but feedback controllers for these systems must be computable in real time to be implemented on physical systems. Classical control design methods produce controllers of the same order as the numerical models. Therefore, reduced order control design is vital for practical controllers. The main contribution of this research is a method of control order reduction that uses a newly developed low order basis. The low order basis is obtained by applying Proper Orthogonal Decomposition (POD) to a set of functional gains, and is referred to as the functional gain POD basis. Low order controllers resulting from the functional gain POD basis are compared with low order controllers resulting from more commonly used time snapshot POD bases, with the two dimensional heat equation as a test problem. The functional gain POD basis avoids subjective criteria associated with the time snapshot POD basis and provides an equally effective low order controller with larger stability radii. An efficient and effective methodology is introduced for using a low order basis in reduced order compensator design. This method combines "design-then-reduce" and "reduce-then-design" philosophies. The desirable qualities of the resulting reduced order compensator are verified by application to Burgers' equation in numerical experiments. / Ph. D.

Heat transfer systems contain many sources of nonlinearity including temperature dependent material properties, radiation boundary conditions, and internal source terms. Despite progress in numerical simulations, producing accurate models that can predict these complex behaviors are still encumbered by lengthy processing times. Accurate models can be produced quickly by utilizing projection Reduced Order Modeling (ROM) techniques. For discretized systems, the Singular Value Decomposition technique is the preferred approach but has had limited success on treating nonlinearities. In this research, the treatment of nonlinear temperature dependent material properties was incorporated into a ROM. Additional sources of nonlinearities such as radiation boundary conditions, temperature dependent source heating terms, and complex geometry were also integrated. From the results, low conductivity, highly nonlinear material properties were predicted by the ROM within 1% of full order models, and additional nonlinearities were predicted within 8%. A study was then done to identify initial snapshots for use in developing a ROM that can accurately predict results across a wide range of inputs. From this, a step function was identified as being the most accurate and computationally efficient. The ROM was further investigated by a discretization study to assess computational gains in both 1D and 3D models as a function of mesh density. The lower mesh densities in the 1D and 3D ROMs resulted in moderate computational times (up to 40 times faster). However, highly discretized systems such as 5000 nodes in 1D and 125000 nodes in 3D resulted in computational gains on the order of 2000 to 3000 times faster than the full order model. / Ph. D.

This thesis proposes a large eddy simulation reduced order model (LES-ROM) framework for the numerical simulation of realistic flows. In this LES-ROM framework, the proper orthogonal decomposition (POD) is used to define the ROM basis and a POD differential filter is used to define the large ROM structures. An approximate deconvolution (AD) approach is used to solve the ROM closure problem and develop a new AD-ROM. This AD-ROM is tested in the numerical simulation of the one-dimensional Burgers equation with a small diffusion coefficient ( ν= 10⁻³). / Master of Science