Trickett, KJ; (1995) Quantification of inverse response for controllability assessment of nonlinear processes. Doctoral thesis , University of London.

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Abstract

The challenge of process design is to develop an economically viable processing plant and control system which can be operated safely, reliably and with an acceptable environmental impact. The controllability assessment of a process deals with the assessment of its dynamic performance and its ability to cope with disturbances and uncertainties. One of the characteristics which limits the achievable process and control performances, independent of the controller design, is the presence of inverse response behaviour in the process. A system subject to inverse response has its initial response in the opposite direction from its final steady state. In a given linear process, the inherent characteristic that causes initial inverse response is the presence of RHP zeros in its transfer function. In this work, qualitative and quantitative indexes are presented to assess the effect of inverse response characteristics in linear processes. However, most industrial processes are nonlinear, and linear models may not describe these industrial processes with sufficient rigour. One novel approach to detect the presence of RHP zeros in the nonlinear setting is proposed in this work: By globally linearizing the nonlinear system into a system linear in input-output sense by feedback, the nonlinear expressions of the zero dynamics are extracted. This work shows that the zero dynamics and the zeros are equivalent for linear systems. Also, by analysing the stability of these zero dynamics, the inverse response characteristics of the nonlinear system can be identified directly in the nonlinear setting. Lyapunov's Second Method, and in particular Krasovskii's method, is employed to determine the stability characteristics of the zero dynamics. However, due to limitations associated with these stability tests, the zero dynamics may have to be linearized in order to fully quantify the inverse response characteristics of the nonlinear system. The proposed methodology is applied to two examples of Single Input Single Output systems, an industrial evaporator and an isothermal CSTR, and will be extended to the model of a Multi Input Multi Output non-isothermal CSTR with second-order kinetics. Throughout these examples, the methodology identifies which system is not affected by inverse response, and which system is. And for these systems, the effect of the inverse response in the nonlinear system is quantified over the given operating range.

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