A Hybrid Automaton Model of the Cement Mill Control

Cement milling circuits are controlled by linear quadratic strategies with the purpose of retaining the circuit stability. Generally, the controlled variables of milling circuits present discontinuities over the range of values they take during the plant operation. The design of linear quadratic control algorithms is based on linear approximations of the nonlinear differential equations that hold over the continuous time ranges of the controlled variables. These approximations make the practical implementation of these algorithms less effective than expected and for this reason there is the need to verify the range of the variable values over which the algorithms can retain the circuit stability before commissioning them. In this paper, an alternative model to that of the nonlinear differential equations is developed for the verification of the milling circuit stability. The model is based on the rectangular hybrid automata formalism. This formalism provides a more systematic and formal way of modeling the plant operation over different ranges of variables presenting discontinuities and does not require to develop informal textual description of the conditions under which different sets of differential equations model the plant operation within the different continuous ranges of the variables. In order to use this model for verifying the circuit stability, the requirements for the circuit stability are expressed in the form of a logical proposition of the ranges of the values within which certain variables of the cement milling circuit must remain. The circuit stability is verified by finding whether the states that are defined by the logical proposition are included in the state space of the automaton. There are, however, cases in which existing algorithms that search into the state space either do not terminate or take very long times in identifying the existence or not of the desired state. After the elapse of a significant portion of time the analyst does not kn- - ow whether this long time is due to algorithm termination problem or to the very large number of remaining computations. In this paper, a new algorithm was developed which does not search into the state space of the automaton as most of the other algorithms do, but computes the number of automaton iterations required for reaching a state. If this is a finite number one can conclude that the desired state is reachable. This algorithm was used in verifying the circuit stability.