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摘要: 电熔镁砂熔炼过程是以三相电机转动方向与频率为输入，以三相电极电流为输出的强非线性工业过程，其模型参数埋弧电阻率、熔池电阻率和熔池高度随熔炼过程和原矿颗粒长度及杂质成分的变化而变化.本文采用线性模型和未知高阶非线性项来描述电熔镁砂熔炼过程，其中未知高阶非线性项用已知的前一时刻高阶非线性项和其变化率来描述，采用线性模型设计PID控制器，并设计消除前一时刻高阶非线性项的补偿器和消除其变化率的补偿器，提出了带输出补偿的PID控制器，同时采用一步最优前馈控制律和一步最优调节律设计控制器参数.通过仿真实验和电熔镁炉的工业应用，表明当该过程的动态特性发生未知随机变化时，本文所提方法在所有运行时间内可以将电流跟踪误差控制在目标值范围内.
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关键词:
- 电熔镁炉 /
- 未知高阶非线性项 /
- 一步最优前馈控制律 /
- 一步最优调节律 /
- 带输出补偿的PID控制器
Abstract: The smelting process of fused magnesia is a strongly nonlinear industrial process with three-phase motor's rotating direction and frequency as input and three-phase electrode's current as output. Its model parameters such as submerged arc resistivity, molten pool resistivity and molten pool height vary with the change of smelting process and particle length of raw ore as well as its impurity compositions. In this paper, a linear model and an unknown high-order nonlinear term are adopted to describe the smelting process of fused magnesia, where the unknown high-order nonlinear term is described as known high-order nonlinear term at previous instant and its change rate. A linear model is used to design the PID controller, and compensators for eliminating both high-order nonlinear term at previous instant and its change rate are designed as well. Then the PID controller with output compensation is proposed. Meanwhile, the one-step optimal feedforward control law and one-step optimal regulation law are employed to design the controller parameters. Simulation experiment and industrial application in fused magnesium furnace show that the current tracking error can be controlled within its target range during all the operational time by the proposed method, when there occurs any unknown random variation of the dynamic characteristic of this process.1) 本文责任编委 阳春华 -
图 4 采用常规PID控制算法和本文控制算法时电极电流$y_1$的控制效果
Fig. 4 The control effects of electrode current $y_1$ using traditional PID control algorithm and the control algorithm of this paper
图 8 采用常规PID控制算法时电熔镁炉三相电极电流平均值$y$的控制效果
Fig. 8 The control effects of the average value $y$ of three phase electrode currents of fused magnesium furnace using traditional PID control algorithm
图 9 采用带输出补偿的PID控制算法时电熔镁炉三相电极电流平均值$y$的控制效果
Fig. 9 The control effects of the average value $y$ of three phase electrode currents of fused magnesium furnace using PID control algorithm with output compensation
图 10 采用常规PID控制算法和本文控制算法时三相电极电流跟踪误差平均值的经验概率分布
Fig. 10 Experienced probability distribution of the average value of three phase electrode currents$'$ tracking errors using traditional PID control algorithm and the control algorithm of this paper
表 1 采用PID控制器和本文所述控制器控制电流$y_1$时的性能评价表
Table 1 The performance evaluating table of current $y_1$ controlled with PID controller and the proposed controller in this paper
MSE IAE PID控制器 $2.3386\times10^6$ $0.6431\times10^6$ 本文所述控制器 $0.4502\times10^6$ $0.2787\times10^6$ 降低 $80.75\, \%$ $56.66\, \%$ 
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表 2 生产设备和工艺参数
Table 2 Parameters of production equipment and technology
参数 数值 电极直径 250 mm 电极长度 1 500 mm 炉体直径 2.5 m 熔炼电压 100 $\sim$ 150 V 熔炼时间 10 h
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表 3 采用常规PID控制器和本文所述带输出补偿的PID控制器时三相电极电流平均值$y$的性能评价表
Table 3 The performance evaluating table of the average value $y$ of three phase electrode currents using traditional PID controller and the proposed PID controller with output compensation in this paper
MSE IAE 常规PID $1.3083\times10^6$ $1.3503\times10^6$ 本文方法 $0.4260\times10^6$ $0.7743\times10^6$ 降低 $67.44\, \%$ $42.66\, \%$
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