Compensation Signal Based Adaptive PID Control Method For Currents Of Fused Magnesium Furnace

Fused magnesia has characteristics such as high melting point,oxidation resistance,strong insulation and so on.It is an important strategic resource in China,which is mainly used in metallurgy,chemical engineering,and aerospace,etc.Fused magnesia is smelted with fused magnesium furnace(FMF),the raw ore of which is magnesite.FMF is a kind of typical high energy-consuming equipment.The smelting temperature of FMF is above 2850℃,which is far higher than 1700℃ required by the steel-making electric arc furnace.Therefore FMF takes the manner of submerged arc.In the smelting process,the raw ore is smelted and new raw ore is added to the furnace at the same time.Consequenlty,the dynamical characteristics of FMF change with the addition of raw ore and the variation of smelting process.Therefore,the optimal smelting current to ensure the qualified product quality and minimal electric power consumption changes accordingly.By adjusting the distance between the three phase electrodes and molten pool with current control system in the smelting process,the three phase electrode currents are controlled to track the optimal smelting current.Only by controlling the electrode currents within the optimal smelting current range and reducing the current fluctuation to the greatest extent all the time under different working conditions such as the normal smelting and feeding,the qualified product quality and low energy consumption can be ensured.Under the two kinds of working conditions,normal smelting and feeding of FMF,the current model parameters embedded arc resistivity,molten pool resistivity and molten pool height are unknown nonlinear functions and change along with the variation of smelting process and particle size as well as impurity composition of raw ore.The current model parameter arc column length frequently changes under feeding condition.Thus,the dynamical characteristic of the controlled object is in variation all the time,which leads to the controller’s integral function invalid.It is difficult to control the electrode current within target range with existing control methods.Therefore,to guarantee the electrode currents track the optimal smelting current very well,this paper analyzes the dynamical characteristics of the fused magnesia smelting process under normal smelting condition and feeding condition,and then proposes the compensation signal based current’s adaptive PID control algorithms for the two conditions.The proposed control algorithms’ stability and convergence analysis is built and their validity is verified with simulation experiments and industrial application.The results of this paper are as follows:(1)Compensation signal based current’s adaptive PID control algorithms under normal smelting and feeding conditionsBy analyzing the smelting mechanisms of normal smelting and feeding conditions,this paper establishes the current mechanism models for the two conditions respectively.By using the characteristic that FMF operates nearby the smelting current setpoint,the dynamical current models under normal smelting and feeding conditions are all expressed as an acuurate linear model and an unknown high-order nonlinear term.The high-order nonlinear term can be experessed with the high-order nonlinear term at previous instant and its change rate.By designing the linear model based PID controller,the compensator for eliminateing the high-order nonlinear term at previous instant and compensator for eliminating its change rate,the compensation signal based current’s adaptive PID control algorithms for the two conditions are proposed respectively.In the proposed algorithms,the PID controller and compensator for eliminating the high-order nonlinear term at previous instant are all designed employing one-step optimal feedforward control law.The compensator of the change rate of high-order nonlinear term is designed employing one-step optimal regulation law under normal smelting condition.The compensator of the change rate of high-order nonlinear term is designed employing one-step optimal control law under feeding condition so as to restrain the fluctuation of compensation signal.The simulation comparison of the proposed control algorithms and the self-tuning PID control algorithm in literature is carried out.The result shows that the control effect of the proposed algorithms is better than that of self-tuning PID control algorithm when the model parameters are unknown or changing.(2)Analysis of stability and convergenceAs to the proposed two control algorithms for normal smelting condition and feeding condition,this paper establishes the analysis of stability and convergence of them.The analysis proves that when the model parameters randomly changes,there is no need for the proposed algorithms in this paper to tune controller’s parameters using parameter estimation.Instead,they change the controllers’ outputs with compensation signals and let the controllers have strong robust adaptive function.Thus the proposed algorithms can ensure the current’s control effect all along under the normal smelting condition and feeding condition.(3)Verification with semi-physical simulationThe unknown changing nonlinear functions in current mechanism models under the two conditions are expressed with unknown constants,and the resulting model error is represented with unmodeled dynamics.Consequently the current simulation models are established respectively,each of which consists of an approximation model whose model parameters are unknown and unmodeled dynamics.The alternating identification algorithm based on recursive least square method and BP neural network is adopted to identify the model parameters and unmodeled dynamics.Based on the two established simulation models,the semi-physical simulation system of fused magnesia smelting process is employed to carry through the semi-physical simulation experiments for the proposed algorithms in this paper.The control effects of the proposed algorithms and the existing self-tuning PID control method are compared.Experimental results show that both of the proposed algorithms in this paper can make the electrode currents track the smelting curret setpoint very well,and the fluctuation of controller’s output signal can be restrained effectively under feeding condition,which is better than the existing self-tuning PID control method.(4)Industrial applicationThe proposed algorithms in this paper are carried out with induatrial application into a practical smelting process of some enterprise for fused magnesia production in Dashiqiao tity,Liaoning province.The two algorithms proposed in this paper are switched based on different working conditions in the application process.Application effects show that the compensation signal based current’s adaptive PID control methods proposed in this paper can make the electrode currents track the smelting curret setpoint very well under different working conditions including normal smelting and feeding.Consequently the energy consumption of per-ton qualified product is reduced.