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In this paper, we develop a state space model of semi-autogenous (SAG) mill systems, which is of great significance to the mineral processing control. According to the practical enterprise production condition, the model is composed of two main parts. One is the ore circuit model. Compared with other models of ore circuit, the present model is simple and efficient. Another part is the SAG subsystem model where the state space model is utilized to depict the grinding mechanism. Furthermore, the grinding process of holdups are analyzed and presented with the common outputs such as power draw, pulp density and pulp flow. We consider the mass of rocks, granules and water as states and analyze the observability of the SAG subsystem model. For the ore circuit system and the SAG subsystem established respectively, unknown parameters of these models are identified by appropriate parameter estimation methods. Verified by the actual plant data, the result shows that the SAG mill system works well. INDEX TERMS SAG mill system, dynamic model, parameter identification.

This paper investigates distributed Nash equilibrium (NE) seeking problems.A bilateral bounded gradient approach, a novel optimization algorithm, is utilized to solve strongly convex problems. Furthermore, for a strongly monotone game, the NE can be obtained in finite time by the bilateral bounded gradient algorithm. In the distributed manner, two types of algorithms are proposed for seeking the NE: consensus-based strategy and passivity-based strategy. For each player, nonlinear protocols are proposed to estimate the actions of their rivals, enabling these estimations to converge to the actual actions in fixed time.To solve the optimization problem, the bilateral bounded gradient algorithm is employed, ensuring that all players' actions converge to the NE in finite time.Moreover, to reduce the communication consumption, event-triggered schemes are introduced in the information exchange of players. Finally, swarm roundup behavior is analyzed by a non-cooperative game in which the proposed algorithms drive all tanks to hunt the target in finite time. The roundup effectiveness is verified by the simulations.

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