Dynamic Simulation and Model-based Control System Design for Comminution Circuits - Advanced Control and Supervision of Mineral Processing Plants - page 232

⎡
⎣

⎤
⎦

− Gu min − f + r

− Gu min + f − r

y max − Gu min − f

− y max + Gu min + f

−

u min
u min
u max

b = (5.65)

− u min

u max − T u min − 1 · u ( k − 1 )

− u min + T u min + 1 · u ( k − 1 )

0

where matrix T is a lower triangular matrix whose entries are ones, O is a matrix
whose entries are zeros, I is the identity matrix and 1 is a vector composed of ones.

5.6 Model-based Control Strategies for Grinding Circuits

Developing a control strategy for a grinding circuit is an extremely complex task.
This is due to the large number of variables involved in the process, the high degree
of interaction between them, highly nonlinear and time-varying dynamics, long time
delays and strong non-measured disturbances such as ore hardness. Two examples
illustrate the use of a simulator for designing and testing model-based control strate-
gies for grinding circuits.

5.6.1 Regulatory Control of a Conventional Grinding Circuit

Control of conventional grinding circuits has been widely studied, through both nu-
merical simulation and plant experiments. Proposals for grinding control strategies
include, for instance, PID regulators [20, 21]; multivariable control systems [21-
23]; adaptive control [24, 25] and optimal control [26]. Most of these strategies
try to maintain tight level control over the sump box by manipulating pump speed.
This approach results in a highly coupled system, as inlet flow disturbances of the
sump box are propagated towards the battery of hydrocyclones, producing undesir-
able transient dynamics, which can affect the recovery of valuable minerals in the
rougher flotation stage.
This section describes a constrained model-predictive control system formulated
as a LP problem. This dynamically optimizes the operation of the grinding circuit,
enabling the incorporation of some operational practices usually seen at grinding
plants, such as maximization of production at a constant fineness [27]. Furthermore,
under this formulation, inlet flow disturbances from the sump box towards the hy-
drocyclones are decoupled in a natural way, achieving a smoother grinding circuit
operation. The solution to the optimization problem results in a control strategy sim-
ilar to the stabilizing strategy at Amax's Buick Mine, as described by Herbst [20].