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Structured total least norm for MISO ARX system identification

Larkowski T., Vinsonneau B., Burnham K. J.

Systems Science

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2007

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Vol. 33, no 4

73-83

EN

The errors-in-variables (EIV) identification framework concerns the identification of dynamic models of systems where all the variables are corrupted by noise. The total least squares (TLS) is one of the most prominent techniques that has proven to be both robust and reliable. The structured total least norm (STLN) can be seen as a natural extension to TLS that preserves any affine structure of the joint data matrix, which is mostly the case in identification schemes. In contrast to the least squares (LS), TLS or mixed LS-TLS problems, the STLN solution cannot be expressed in a closed form, therefore, an optimization procedure is required. Note that STLN allows different norms to be considered other than the usual square norm (or 2 norm). This paper describes a direct application of the STLN approach for systems that can be represented by auto-regressive with exogenous input (ARX) multi-input single-output (MISO) models. The performance of the proposed STLN algorithm (in the case of the square norm) is compared to the LS, the bias-eliminating LS (BELS), the extended matrix LS (EMLS), the instrumental variables (IV), TLS and the compensated TLS (CTLS) methods when applied to a simulated MISO ARX system. Results, obtained from Monte Carlo simulation, show that, under the conditions considered here, STLN surpasses all other investigated techniques, attaining the best estimates of the true system parameters.

2

A goal oriented approach to model identification of an industrial furnace system combining a priori knowledge and optimal estimation

Vinsonneau B., Martineau S., Goodall D. P., Burnham K. J.

Systems Science

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2007

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Vol. 33, no 4

103-110

EN

Prompted by the need to determine a unique tuning parameter, the paper proposes a conceptual model for a high temperature industrial furnace in which the notion of an unmeasurable "global temperature" plays a key role. The developed approach is designed to accommodate a priori knowledge of system nonlinearities, as well as the effects of an externally triggered burner firing cycle which gives rise to an oscillatory response present on the locally measured zone temperature. It is assumed that the variation in the global temperature is lower than that observed at the locally measured temperature at a point. The developed model is able to accommodate, and effectively separate, the effects of the combustion burner firing cycle and the underlying bilinear characteristic behaviour relating fuel combustion and temperature of each zone. It is assumed that these physical phenomena can be represented by a linear model, modelling the effects of the combustion burner firing cycle, cascaded with a bilinear model, where an intermediate variable is the global temperature. The result of employing a regularisation technique together with the cascade multiple model produces an optimal value for the tuning parameter of a four-term bilinear PID control system.

3

Goal oriented estimation of an industrial furnace to be controlled using bilinear PID

Vinsonneau B., Martineau S., Burnham K. J.

Systems Science

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2005

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Vol. 31, no 1

53-61

EN

PID control systems are tunable devices which provide acceptable performances and are widespread in many industries. However, it is assumed that local linearity holds for the plant to be controlled, with the tuning being valid around a particular operating point only. Extending the performance over a wider range usually involves an in-depth local understanding of plant nonlinearities. In some cases, this can be approximately expressed as a bilinearity. To illustrate the approach, appropriate system modelling and design of a bilinear control strategy for a high-temperature industrial furnace system is presented.