A Constrained Dynamic Optimization Method For Flotation Process

The goal of floatation process control is not only making the pulp level and the feed flow tracking level and flow rate setting value,but making the flotation process terminal concentrate grade tracking the optimal concentrate grade.Meanwhile the economic index related to flotation process such as concentrate grade,tailing grade,the pulp level and the feed flow should be kept in the constraint range.In conventional flotation process control,the process engineers give concentrate grade and tailing grade target range,operation personnel gives set-points of flotation process pulp level and feed flow according to the target range of the concentrate grade and tailing grade by experience.However,when the pulp concentration and mineral granularity boundary conditions change frequently,artificial control cannot adjust the set-points of pulp level and feed flow of flotation process timely and accurately.It is difficult to control economic indicators,the concentrate grade and tail grade within the target range,and it will even result in the failure condition.Based on the analysis of dynamic mechanism model whose pulp level and feed flow are input,and concentrate grade and tail grade are output,using the characteristics of the flotation process is running near the working point,this paper established the state space model of flotation process,whose inputs are pulp level and feed flow,concentrate grade and tailings grade are output and the quality of ore and mud in the pulp layer and foam layer are states,meanwhile we formulated the optimization problem where the optimal concentrate grade tracking error is the objective function,feed flow and pulp level are decision variables,maximum and minimum bounds of concentrate grade,tail grade,feed flow and pulp level are the constraints.Then we analyzed difficulties of the nonlinear optimization problem with functional inequality constraints.In view of this class of optimization problem with functional inequality constraints,we proposed an integral method which can address the functional inequality constraints,to transform them to traditional inequality constraint.Then the original nonlinear programming problem(NLP)can be reformulated as a standard NLP problem.To solve the reformulated NLP problem,we use the sequential quadratic programming method,which is an approach of sequential method.Still the optimal concentrate grade tracking error is the objective function,feed flow and pulp level are decision variables,maximum and minimum bounds of concentrate grade,tail grade,feed flow and pulp level are the constraints.Finally a simulation is finished and the results show that through the proposed method in this paper,the tracking error between actual concentrate grade and optimal concentrate grade is 0.007,and feed flow,pulp level,concentrate grade and tail grade satisfy their own constraints strictly.