Model predictive control of hybrid systems.
Hybrid systems combine the continuous behavior evolution specified by differential equations with discontinuous changes specified by discrete event logic. Usually these systems in the processing industry can be identified as having to depend on discrete decisions regarding their operation. In process control there therefore is a challenge to automate these decisions. A model predictive control (MPC) strategy was proposed and verified for the control of hybrid systems. More specifically, the dynamic matrix control (DMC) framework commonly used in industry for the control of continuous variables was modified to deal with mixed integer variables, which are necessary for the modelling and control of hybrid systems. The algorithm was designed and commissioned in a closed control loop comprising a SCADA system and an optimiser (GAMS). GAMS (General Algebraic Modelling System) is an optimisation package that is able to solve for integer/continuous variables given a model of the system and an appropriate objective function. Online and offline closed loop tests were undertaken on a benchmark interacting tank system and a heating/cooling circuit. The algorithm was also applied to an industrial problem requiring the optimal sequencing of coal locks in real time. To complete the research concerning controller design for hybrid behavior, an investigation was undertaken regarding systems that have different modes of operation due to physicochemical (inherent) discontinuities e.g. a tank with discontinuous cross sectional area, fitted with an overflow. The findings from the online tests and offline simulations reveal that the proposed algorithm, with some system specific modification, was able to control each of the four hybrid systems under investigation. Based on which hybrid system was being controlled, by modifying the DMC algorithm to include integer variables, the mixed integer predictive controller (MIPC) was employed to initiate selections, switchings and determine sequences. Control of the interacting tank system was focused on an optimum selection in terms of operating positions for process inputs. The algorithm was shown to retain the usual features of DMC (i.e. tuning and dealing with multivariable interaction). For a system with multiple modes of operation i.e. the heating/cooling circuit, the algorithm was able to switch the mode of operation in order to meet operating objectives. The MPC strategy was used to good effect when getting the algorithm to sequence the operation of several coal locks. In this instance, the controller maintained system variables within certain operating constraints. Furthermore, soft constraints were proposed and used to promote operation close to operating constraints without the danger of computational failure due to constraint violations. For systems with inherent discontinuities, a MPC strategy was proposed that predicted trajectories which crossed discontinuities. Convolution models were found to be inappropriate in this instance and state space equations describing the dynamics of the system were used instead.
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