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摘要: 浮选过程是利用矿物本身的亲水或疏气性质或经药剂处理得到的亲水或疏气性质进行矿物分离的物理过程.本文通过建立以矿浆液位和矿浆流量为输入，以浮选过程的精矿品位与尾矿品位为输出的多变量、强耦合、非线性、时变的运行过程模型，利用未建模动态前一拍可测的特点，提出了包括矿物品位运行过程控制器驱动模型、PID控制器、反馈解耦控制器、未建模动态补偿器的数据驱动的一步最优未建模动态补偿PID解耦控制方法，实现了消除稳态误差、静态解耦与未建模动态的补偿，通过浮选过程运行反馈控制仿真实验验证了本文所提方法的有效性.Abstract: The flotation process is a mineral separating physical process by taking advantage of the hydrophilic or hydrophobic properties of the mineral or the hydrophilic or hydrophobic properties obtained by treatment. In this paper, firstly, a multivariable, strong coupling, nonlinear and time-varying operational process model is established with the input and output of the pulp level and feed flow as its inputs and the concentrate grade and tailing grade as its outputs. Secondly, by taking the advantage that the unmodeled dynamics at last sampling point can be measured, a scheme of one-step optimal unmodeled dynamic compensation PID decoupling control is proposed including the ore grade operational process controller driven model, PID controller, feedback decoupling controller and unmodeled dynamic compensator, to guarantee zero steady-state error, static decoupling, and unmodeled dynamics compensation. Finally, a simulation experiment on the operational feedback control in an industrial flotation process is conducted to demonstrate the effectiveness of the proposed method.
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Key words:
- Data-driven /
- flotation processes /
- operational control /
- decoupling
1) 本文责任编委 侯忠生 -
图 2 数据驱动一步最优未建模动态补偿PID解耦控制结构图
Fig. 2 Structure diagram of data driven one-step optimal unmodeled dynamic compensation PID decoupling control
图 3 线性模型下PID解耦控制的矿物品位跟踪曲线
Fig. 3 Ore grade tracking curve with PID decoupling control under linear model
图 4 线性模型下PID解耦控制的控制输入
Fig. 4 Control input curve with PID decoupling control under linear model
图 5 线性模型下模型预测控制控制的矿物品位跟踪曲线
Fig. 5 Ore grade tracking curve with MPC under linear model
图 8 非线性模型下数据驱动一步最优未建模动态补偿的PID解耦控制的矿物品位跟踪曲线
Fig. 8 Ore grade tracking curve with data driven one step optimal unmolded dynamic compensation PID decoupling control under nonlinear model
图 9 非线性模型下数据驱动一步最优未建模动态补偿的PID解耦控制的控制输入
Fig. 9 Control input curve with data driven one step optimal unmolded dynamic compensation PID decoupling control under nonlinear model
图 11 非线性模型下模型预测控制的矿物品位跟踪曲线
Fig. 11 Ore grade tracking curve with MPC under nonlinear model
表 1 浮选过程符号表
Table 1 Flotation process symbol table
符号 物理含义 $k_p^1$ 黄铜矿浮选率 $k_e^1$ 黄铜矿排放率 $g_{a}$ 原矿浆黄铜矿品位 $X_a^2$ 脉石矿浆浓度 $H$ 浮选槽高度 $L_{cu}$ 黄铜矿矿物品位 $g_{cp}^1$ 黄铜矿浆的 黄铜矿品位 $k_p^2$ 脉石浮选率 $k_e^2$ 脉石排放率 $X_a^1$ 黄铜矿浆浓度 $A$ 浮选槽底面积 ${q_T}$ 尾矿流量 ${q_c}$ 精矿流量 $g_{cp}^2$ 脉石矿浆的 黄铜矿品位 
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表 2 对比实验评价指标
Table 2 Performance index of comparison experiment
IAE MSE 本文$r_1$ 0.2078 $3.3073\times10^{-5}$ 本文$r_2$ 0.1803 $2.396\times10^{-5}$ MPC $r_1$ 18.1797 0.0601 MPC $r_2$ 37.4461 0.2563
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