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An Approximate Differentiation Method of Inverse Simulation based on a Continuous System Simulation Approach David J. Murray-Smith University of Glasgow, School of Engineering, Rankine Building, Oakfield Avenue, Glasgow G12 8LT, United Kingdom; [email protected]

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Abstract. Inverse simulation techniques allow inverse solutions to be found for a range of problems involving dynamic systems described by sets of linear or nonlinear ordinary differential equations. Techniques in common use generally involve iterative solutions based on discretised descriptions but continuous system simulation tools can also provide solutions and are often simpler to apply and computationally more efficient. This paper presents a method of inverse simulation which involves use of a very simple, but effective, approximation for derivative terms within the model. Discussion of results for linear and non-linear examples leads to the conclusion that this technique can be applied to a wide range of dynamic models that are of practical importance for engineering applications.

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Figure 2: The upper trace shows the input found from inverse simulation of the linear SISO system of Equations (2) and (3). The lower traces (superimposed) show the demanded output

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Figure 5: Flow rates determined by inverse simulation for the first case considered.

Figure 6: Differences between reference liquid level time histories and liquid levels found by applying inputs from inverse simulation to the forward simulation model.

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Figure 9: Differences between the desired levels and the levels found from forward simulation of the coupled-tanks model for the case defined by the inputs of Figure 8.

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Figure 7: Required liquid levels for second case involving a larger difference between final levels in Tank 1 and Tank2 resulting in a required flow rate for Tank 1 that exceeds the maximum.

Figure 8: Input flow rates found using inverse simulation

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for level variations defined in Figure 7.



SNE 23(3-4) – 12/2013 115

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An Approximate Differentiation Method of Inverse Simulation

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