Analysis and design of process dynamics using spectral methods

Walsh, Ashley Michael. (1999). Analysis and design of process dynamics using spectral methods PhD Thesis, School of Engineering, The University of Queensland.

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Author Walsh, Ashley Michael.
Thesis Title Analysis and design of process dynamics using spectral methods
School, Centre or Institute School of Engineering
Institution The University of Queensland
Publication date 1999
Thesis type PhD Thesis
Total pages 357
Language eng
Subjects 230116 Numerical Analysis
240502 Fluid Physics
Formatted abstract The traditional approach to process design views the design of steady-state and dynamic performance as separate tasks which are performed sequentially. Steady-state performance is first determined by the process design, and then dynamic performance is determined by the design of the control system. The problem with this method is that the performance of any control system, no matter how advanced, is ultimately limited by the process. The limits imposed by a plant's controllability can have a significant economic impact. For this reason dynamic performance should be considered during process design. The goal of this thesis is therefore to develop a systematic methodology for the simultaneous design of the steady-state and dynamic performance of process systems.

The methodology developed is based on spectral association, or the association of model states and components with the system's fundamental dynamic modes, or eigenvalues. The dynamic structure identified by this procedure provides valuable insight into the dynamic performance of a system. Retaining the physical significance of the model states also retains that significance within the measures of dynamic structure, which can then be directly related to the structure of the process units and the connections between then. System performance and constraints are presented to the designer in a more natural framework, and the sources of performance limitations can be identified with respect to specific process units.

Two methods of spectral association are developed in this work. Eigenvalue tracking is a continuation method which determines associations by transforming a system with known eigenvalue-to-state associations into the system whose associations are to be determined. Improvements were made to the eigenvalue tracking algorithm, but the method is limited by the assumption of one-to-one eigenvalue-to-state associations. The nature in which eigenvalue tracking can fail has been partially explored with the different eigenvalue interaction patterns corresponding to crossings and deflections.

The unit perturbation spectral resolution (UPSR) is a matrix which measures the strength of association between every system state and every eigenvalue. This is a quantitative method of spectral association which is capable of identifying multiple eigenvalue to-state associations. Its development provides a rigorous tool for spectral association that is much more reliable than eigenvalue tracking.

The UPSR is based on the spectral resolution solution to a linear differential equation. The spectral resolution describes the dynamic response of each system state as a sum of the contributions of all the system eigenvalues. A description of the spectral resolution in terms of disturbance source, dynamic pathway, and dynamic response was developed. The UPSR is a specific subset of the entire dynamic structure represented by the spectral resolution.

The structure of the spectral resolution was further exploited by the definition of the state spectral resolution (SSR). The SSR describes a state's dynamics in terms of the impact of all the other system states and the system's dynamic pathways.

A new methodology is proposed for the analysis of the dynamic structure of large systems. The method of incremental component connection (ICC) starts with a detailed analysis of the dynamic structure of the unconnected system components. Inter-component connections are then introduced in a systematic fashion that builds up an understanding of the fully connected system dynamics in terms the unconnected components and the effects of the connections between them.

ICC was used to analyse a forced circulation evaporator system in detail. This case-study demonstrated the usefulness of the ICC methodology in providing valuable insight into the dynamic structure of a process system. It also provided guidance for the development of a number of principles for the application of ICC based on UPSR and eigenvalue properties, and the dynamic structures associated with physical phenomena common to process units.

The design methodology proposed is based on the translation of performance objectives into a required dynamic structure expressed in terms of spectral resolution measures. These measures are then included in a design homotopy which combines steady-state and dynamic criteria. The homotopy formulation allows eigenvalue-to-state associations to be maintained through the solution process by a combination of eigenvalue tracking and the UPSR. Using the design homotopy, an initial design can be driven to a new design which has the desired dynamic structure.

The design case-study showed the ability of the design algorithm to shape a system's dynamic structure as specified. However, the initial failure to achieve the performance objectives showed the importance of analysis for determining the performance limiting structures within a process system. The proposed methodology includes a procedure for determining the sources of dynamic behaviour within a system, and identifying those elements within a design that limit dynamic performance.

This work has addressed the issue of designing the dynamic performance of a processing system. The techniques employed have focused on providing insight into the dynamic structure of systems. The main contributions of this work include:

• Development of the UPSR as a new method for spectral association. The UPSR is a quantitative measure, which is a significant improvement over the use of eigenvalue tracking for spectral association.

• Development of ICC as a systematic procedure for the analysis of large systems based on the selective introduction of inter-component connections. ICC is a new approach, and has potential for application in other areas. The use of partially connected systems in the design case-study showed how the variation of component connections can be used to avoid problems in design optimisation.

• Development of a design methodology based on the exploitation of model structure. The algorithm developed can change the design of a system to achieve a specified dynamic structure, but performance improvements rely on the identification of the elements of a design which limit dynamic performance.

Keyword Fluid dynamics.
Numerical analysis.

Document type: Thesis
Collection: UQ Theses (RHD) - UQ staff and students only
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