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1. Introduction

     Recently, customers require increasingly better quality for hotrolled strip products, such as automotive companies expect to gain an advantage from thinner but still very strong types of steel sheeting which makes their vehicles more efficient and more environmentally compatible. In addition to the alloying elements, the cooling section is crucial for the quality of products [1]. Hot-rolled strip laminar cooling process (HSLC) is used to cool a strip from an initial temperature of roughly 820–920 C down to a coiling temperature of roughly 400–680 C, according to the steel grade and geometry. The mechanical properties of the corresponding strip are determined by the time–temperature-course (or cooling curve) when strip is cooled down on the run-out table [1,2]. The preciseand highly flexible control of the cooling curve in the cooling section is therefore extremely important.

        Most of the control methods (e.g. Smith predictor control [3],element tracking control [4], self-learning strategy [6] and adaptive control [5]) pursue the precision of coiling temperature and care less about the evolution of strip temperature. In these methods, the control problem is simplified so greatly that only the coiling temperature is controlled by the closed-loop part of the controller. However, it is necessary to regulate the whole evolution procedure of striptemperature if better properties of strip are required. This is a nonlinear, large-scale, MIMO, parameter distributed complicated system. Therefore, the problem is how to control the whole HSLC process online precisely with the size of
HSLC process and the computational efforts required.

         Model predictive control (MPC) is widely recognized as a practical control technology with high performance, where a control action sequence is obtained by solving, at each sampling instant, a finite horizon open-loop receding optimization problem and the first control action is applied to the process [7]. An attractive attribute of MPC technology is its ability to systematically account for process constraints. It has been successfully applied to many various linear [7–12], nonlinear [13–17] systems in the process industries and is becoming more widespread [7,10]. For large-scale and relatively fast systems, however, the on-line implementation of centralized MPC is impractical due to its excessive on-line computation demand. With the development of DCS, the field-bus technology and the communication network, centralized MPC has been gradually replaced by decentralized or distributed MPC in large-scale systems [21,22] and [24]. DMPC accounts for the interactions among subsystems. Each subsystem-based MPC in DMPC, in addition to determining the optimal current response, also generates a prediction of future subsystem behaviour. By suitably leveraging this prediction of future subsystem behaviour, the various subsystem-based MPCs can be integrated and therefore the overall system performance is improved. Thus the DMPC is a good method to control HSLC. 

        Some DMPC formulations are available in the literatures [18–25]. Among them, the methods described in [18,19] are proposed for a set of decoupled subsystems, and the methoddescribed in [18] is extended in [20] recently, which handles systems with weakly interacting subsystem dynamics. For arge-scale linear time-invariant (LTI) systems, a DMPC scheme is proposed in [21]. In the procedure of optimization of each subsystem-based MPC in this method, the states of other subsystems are approximated to the prediction of previous instant. To enhance the efficiency of DMPC solution, Li et al. developed an iterative algorithm for DMPC based on Nash optimality for large-scale LTI processes in [22]. The whole system will arrive at Nash equilibrium if the convergent condition of the algorithm is satisfied. Also, in [23], a DMPC method with guaranteed feasibility properties is presented. This method allows the practitioner to terminate the distributed MPC algorithm at the end of the sampling interval, even if convergence is not attained. However, as pointed out by the authors of [22–25], the performance of the DMPC framework is, in most cases, different from that of centralized MPC. In order to guarantee performance improvement and the appropriate communication burden among subsystems, an extended scheme based on a so called ‘‘neighbourhood optimization” is proposed in [24], in which the optimization objective of each subsystem-based MPC considers not only the performance of the local subsystem, but also those of its neighbours.

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