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Studies on Controllability Evaluation of Nonminimum Phase Processes

Kuhlmann, Annette; (1998) Studies on Controllability Evaluation of Nonminimum Phase Processes. Doctoral thesis (Ph.D), UCL (University College London). Green open access

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Abstract

In order to prevent a process from failing to meet the required performance specifications due to system inherent characteristics that cannot be overcome by controller design, it is important to analyse the controllability of a process at the design stage where modifications are still possible. In this work the evaluation of the controllability of nonlinear systems with unstable zero dynamics, i.e. with nonminimum phase behaviour, is addressed. Single-input, single-output, stable, time invariant models that are affine in control are considered. For such systems the best achievable move (switch) from one operating point to another is evaluated. A phenomenon that is found frequently in nonlinear nonminimum phase processes is input multiplicity, which is therefore also analysed for its impact on controllability. A number of process examples with nonminimum phase behaviour (and input multiplicity) have been identified during this project and are investigated in order to highlight different aspects of nonminimum phase behaviour. In terms of controllability evaluation the thesis presents two approaches, both based on the idea of factorising the nonlinear dynamic system in an integral square error (ISE) optimal way, analogous to the existing approach for linear systems. This leads to the ISE optimal closed loop response of the nonlinear process. The corresponding value of the ISE can be employed to evaluate the extent of the system's nonminimum phase behaviour. The first approach presented involves analytically solving the factorisation problem. The approach is applicable to two classes of systems, where for each a case study is elaborated. The analysis shows that in a nonlinear system the ISE of the optimal closed-loop response depends on the direction of the step, i.e. the value is either bigger or smaller than the value determined with the corresponding linear analysis. This demonstrates how the nonlinearity of the process is reflected also in its controllability. In order to achieve a more general solution for a wider range of systems an approximate approach is employed. The ISE problem is formulated as an optimal control problem such that the ISE optimal closed-loop response for a nonlinear nonminimum phase process is determined. This method recovers the solutions found analytically for a case study. It has the advantage of being applicable to processes with input multiplicities. The process inherent limitations of a fermentation process example with input multiplicities are thus studied. The evaluation approach is extended towards a design method for optimal switch ability and demonstrated for a reactor-separator process.

Type: Thesis (Doctoral)
Qualification: Ph.D
Title: Studies on Controllability Evaluation of Nonminimum Phase Processes
Open access status: An open access version is available from UCL Discovery
Language: English
Additional information: Thesis digitised by ProQuest
Keywords: Applied sciences; Integral square error
URI: https://discovery.ucl.ac.uk/id/eprint/10101441
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