| An optimal equilibrium control system for an ore concentration plant has been developed using an approach which may be considered global from three different points of view: (i)The control system and the model have been treated in close relation to each other. Thus, the model incorporates features which are important in the control problem, and serves for detecting plant characteristics which contribute to simplify the optimal equilibrium control system. On the other hand, once a detailed model has been derived, it has been simplified, according to the way in which the plant is to operate under the proposed control system. (ii)The opinions, attitudes, and points of view found in the process industry medium--concerning what characteristics innovative control systems should have, in order to be accepted by industry--have been brought into the general problem, in order that the control system may be eventually applied to an actual plant. This approach has lead to the development of an optimal equilibrium control system which is largely independent of the plant model. In particular, all plant parameters may be unknown, the performance measure in equilibrium need not be a smooth function of the optimizing control, and no convexity (or concavity) conditions are required. However, the control system does require asymptotic stability of a unique plant equilibrium state. But this is proved to be a property of the concentration plant model when adequate variables--defined as "secondary controls"--are used to control the plant. (iii) The optimal control problem is in itself global, because it deals with the joint equilibrium optimal control of two different plants: the grinding, and the rougher flotation plant. The overall performance measure for the combined plants is taken as the price per minute of the concentrate produced at the flotation plant. This performance measure is maximized, when equilibrium is reached, by means of the grinding plant controls. Local objectives concerning what the output of the grinding plant should be (e.g., concerning fineness of grind, and total ore flow) are, thus, rendered irrelevant by the global approach.;An algorithm, based on a theorem stated and proved here, forms the basis of the optimal equilibrium control system. A control sequence is generated which converges to a close neighborhood of the optimal control. This control sequence, in turn, produces a succession of step controls such that optimal equilibrium is reached. The optimal equilibrium state is shown to be unique, and quasi-asymptotically stable with respect to a region of physically significant plant states.;A prediction scheme is proposed to estimate in advance the equilibrium output with which the control sequence is determined. The resulting overall system is, then, interpreted as a Hammerstein model, having as a static nonlinear part the detailed equilibrium model of the plant. The linear part is an approximation which is constantly being identified, but the nonlinear part need not be identified except at a single point.;Examples of the system operation are given through simulation, both for the case of the concentration plant, and for simple examples. |
