A steel hot strip finishing mill presents significant interactions between variables that considerably reduce performance. Traditionally, the control techniques implemented are based on classical approaches assuming an ideal model. Modelling interactions would allow the opportunity to suppress them by the application of modern multivariable control techniques. In this paper the derivation of a linearized multivariable model of a real-life hot strip mill based on previous schemes is presented as a case study. Linearization of the nonlinear static relations around an operating point is performed. The operating conditions are the mill set-up calculations obtained from rolling schedules and non-linear relations used in the plant. Some useful details for practitioners are given. Simulations and experimental model validation are also presented. Since the mill in the real hot rolling line is in closed loop, it is not possible to carry out an experimental validation of the plant itself (i.e. in open loop); therefore, the model was experimentally validated in closed loop. As an example of the use of the multivariable model an H ' multivariable optimal controller to attain nominal performance is designed for the looper system and results are presented.

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The problem of coordinating directional overcurrent relay is one of the most important in electrical power system planning and operation. In this paper, a new objective function, based on genetic algorithms of Chu-Beasley, to carry out an optimal coordination of directional overcurrent relay is presented. The characteristics of the genetic algorithms of Chu-Beasley and some modifications, having taken into account inherent constraints to the problem, were used in order to properly solve the problem. A case study including 11 nodes and 22 directional relays was conducted to validate the performance of the proposed technique. Finally, a methodology to obtain a directional overcurrent relay coordination is proposed, including an expert (human) criterion. Detailed results are presented and discussed.

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In hot strip mills, estimation of rolling variables is of crucial importance to setting up the finishing mill and meeting dimensional control requirements. although the use of physics-based models is preferred by the specialists to keep the fundamental knowledge of the underlying phenomena, many times a purely empirical model, such as an artificial neural network, will provide better predictions although at the cost of losing such fundamental knowledge. This paper presents the application of physics-based and artificial neural networks-based hybrid models for scale breaker entry temperature prediction in a real hot strip mill. The idea behind combining these two types of models is to capitalize in what are often portrayed as their main advantages: (i) keeping the physics knowledge of the process and (ii) providing better predictions. Temperature prediction schemes with different hybrid levels between a pure heat transfer model and an artificial neural network alone were evaluated and compared showing promising results in this case study. Using an artificial neural network together with the heat transfer model helped to achieve better temperature predictions than using the heat transfer model alone in every instance, thereby proving the hybrid schemes attractive to the industry. In this work, three different hybrid schemes combining the knowledge imbedded in a heat transfer model and the prediction capabilities of an artificial neural network in temperature prediction in a hot strip mill were tried. The hybrid models came out quite competitive in this case study. The results support the use of empirical models to foster the prediction ability of physics-based models; that is, they make the case for their joint use as opposed to their exclusive use.