湿法炼锌净化过程建模及基于控制参数化的优化方法
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摘要
湿法炼锌净化过程是除去硫酸锌溶液中杂质金属离子的一个重要生产环节,在该过程中,根据每小时化验检测的净化反应槽入口和出口的杂质金属离子浓度,添加锌粉置换溶液中的杂质离子,为后续电解过程提供合格的电解液。锌粉作为沉淀除杂的主要原料,是一个十分重要的控制条件。由于净化过程具有长流程、时滞、非线性、动态变化等特性,过程工况参数的改变要经过一段时间才能反映到出口杂质金属离子浓度的变化；另外,杂质金属离子浓度在生产现场中没有实现在线检测,人工化验检测和净化反应的滞后,使得操作工不能准确地根据离子浓度的变化情况来调整锌粉的添加量。同时,由于净化反应复杂,反应环境恶劣,操作工通常采用过量添加锌粉的方法来保证生产出合格的硫酸锌溶液。这种做法,虽然保证了溶液净化的质量,但却极大地增加了生产成本和能耗。
硫酸锌溶液净化过程采用三段净化工序,其中Ⅱ段净化工序主要是除去溶液中的杂质钴和镉离子,是整个净化过程中最关键的一道工序。论文在深入研究净化过程工艺和反应机理的基础上,首先依据生产过程数据,建立Ⅱ段净化过程出口杂质离子浓度的智能预测模型；其次,根据锌粉颗粒与金属离子间的置换沉淀反应机理,结合生产工况的特点,建立净化除杂的动态反应模型,并提出基于控制参数化技术的优化控制方法,最后,将其运用到锌粉添加量的优化控制方案中,取得了明显的成效。本文主要研究工作及创新性成果如下：
(1)在对硫酸锌溶液净化过程深入分析的基础上,针对Ⅱ段净化过程出口杂质金属离子浓度的重要性,根据生产过程中的大量工况数据,建立Ⅱ段净化过程出口钴离子和镉离子浓度的在线支持向量回归预测模型。由于在线支持向量回归算法中存在复杂的矩阵运算,提出采用分块矩阵的迭代更新法求解,以提高计算效率。基于生产数据的仿真分析说明模型具有良好的预测性能,明显提高计算速度,能为生产操作提供参考,进一步指导锌粉添加量的优化控制。
(2)研究金属离子的置换反应机理,其中发生的主要化学反应为锌粉颗粒置换沉淀钴和镉离子的反应过程,结合硫酸锌溶液净化过程的特点,以连续搅拌反应釜模型为基础,分别以钻离子和镉离子浓度作为状态变量,提出锌粉净化除杂质离子的非线性时滞关联动态反应模型。
(3)提出基于控制参数化的数值优化方法,解决非线性时滞关联动态反应模型中的参数计算问题。其基本思想是把控制量表示成分段常数函数形式,整个时间域内的非线性动态方程则被转化为与各个控制参数相应子区间内的线性动态方程。为求解最优动态模型参数,依据采样点,即特征时间点上的实际离子浓度检测数据,提出基于多特征时间点的优化参数选择方法,以确定动态模型中的未知参数。通过把该类优化参数选择问题转化为数学规划问题,每个模型参数与控制参数都被当作是决策变量,并推导出目标函数对于这些决策变量的梯度计算公式。给定参数初始值的情况下,利用序列二次规划优化方法来求解最优参数选择问题。针对求解时滞微分方程的特殊性,提出采用三次方样条插值拟合函数,依据采样时刻的离子浓度检测值,建立初始时刻以前的离子浓度状态函数。通过采用基于多特征时间点的时滞优化参数选择问题的数值计算方法,可以有效求得最优的动态系统模型参数。
(4)针对实际生产中锌粉总是被过量添加的情况,提出基于连续状态不等式约束的时滞优化控制方法,解决锌粉添加量的最优控制问题。通过采用局部光滑技术的约束转换方法,将连续状态不等式约束转化为一系列规范型的不等式约束,这些不等式约束的形式和目标函数保持一致。控制函数依然被表示成分段常数函数形式,每个控制参数都被认为是决策变量,并推导出目标函数和约束函数对于决策变量的梯度计算公式。最后,采用基于梯度的序列二次规划优化方法来求解该优化控制问题,数值仿真表明锌粉添加量可以有效地被减少。
(5)基于梯度的序列二次规划方法是一种局部优化算法,针对优化计算过程中容易陷入局部最优值的问题,提出采用基于填充函数全局优化的锌粉量时滞优化控制方法,解决后续时段锌粉添加量的最优控制问题。作为表示锌粉添加量的控制函数依然采用分段常数函数形式,以离线优化计算得到的最优控制参数作为在线优化控制的参数初始值,可以有效提高寻优效率。以基于生产数据的在线支持向量回归模型预测出的杂质金属离子浓度值作为时滞动态方程的状态参考值,期望时滞动态方程的状态解跟踪该参考轨迹,并在该种情况下在线优化控制锌粉添加量。数值仿真表明,采用该方法可以有效求解出后续时段内的最优锌粉添加量,为生产操作提供指导。
本文提出的基于控制参数化的优化控制方法具有较强的实用性,可以在类似的冶金生产过程中推广应用。
The purification process of zinc hydrometallurgy, in which metallic ion impurities are removed from a zinc sulphate solution, is an important industrial process.In this process, the zinc powder is added into the solution to remove the impurities based on the measured concentration of metallic ion impurities at the inlet and outlet of the reaction tank. Then, the eligible solution is fed to the electrolysis process. In addition, zinc powder is the primary material for inducing the deposition of the metallic ion impurities, and hence it is crucial that the amount used be controlled appropriately. Because the purification process has the characteristic of long flow, time delay, nonlinear and dynamic,it usually takes a period of time for the variation in the process parameters reflecting the alteration in the concentration of metallic ion impurities.Besides, the concentration of the metallic ion impurities is not detected online in the process.The operator can not regulate the amount of zinc powder added according to the variation in the concentration of impurities correctly due to the time delay in the chemical test and purification reaction.Meanwhile, there are many disturbances and uncertainties affecting the purification reaction, the amount of zinc powder added is always much more than required.The operator does this based on their experience and judgement, to ensure that the zinc sulphate solution produced is of a sufficiently high purity. However, this way of ensuring the purification quality is expensive and consumes significant amounts of energy.
There are three stages in the purification process of zinc sulphate solution.The cobalt and cadmium ions are removed mainly in the second stage, which is the most crucial stage in the whole purification process.On the basis of our research findings into the zinc sulphate purification process and reaction mechanism, an intelligent prediction model describing the concentration of metallic ion impurities in the second purification process outlet is established using the process data. Then, by taking into account the specific characteristics of the process, a mathematical model for the dynamic reaction of the purification process is constructed according to the deposition reaction mechanism between zinc powder particles and metallic ion impurities.An optimal control method based on the control parameterization technique is then proposed to obtain the optimal amount of zinc powder that should be added to the purification process at each time.The simulation results are very promising.The main research work and innovative achievements are listed as follows:
(1)The purification process of zinc sulphate solution is thoroughly investigated and analysed. Then, because of the significance of the concentrations of the metallic ion impurities in the second purification process outlet, an online support vector regression prediction model for the concentration of the cobalt and cadmium ions is constructed using the process data. As the matrix computation in the online support vector regression algorithm is very complicated, an iterative updating method of matrix blocking partition is developed so that the computation efficiency can be improved. The simulation results of the process data show that the prediction model performs quickly and gives good results. This model can serve as a reference for the production process, which indicates the optimal amount of zinc powder that should be added in the purification process.
(2)The replacement reaction mechanism of the metallic ions is also studied. The main chemical reaction includes the replacement deposition reaction between zinc powder particles and the cobalt or cadmium ions. By taking into account the characteristics of the purification process, the concentration of cobalt and cadmium ions are taken as state variables, a nonlinear time delay interactive dynamic reaction model is proposed for the metallic ion impurities deposition process, which is based on the continuous stirred tank reactor model.
(3)The numerical optimization method based on control parameterization is proposed to obtain the optimal parameters in the nonlinear time delay interactive dynamic reaction model.The main idea is that the control takes the form of piecewise constant function, then the nonlinear dynamic equation in the whole time domain can be transformed to linear dynamic equation in the subinterval corresponding to each control parameter. Based on the measured concentration of metallic ion impurities on the sampling point, i.e.characteristic time point, we formulate an optimal parameter selection method with multiple characteristic time points, in which the underlying dynamic system is a system of time delay differential equations, to obtain the optimal parameters in the dynamic model.This kind of optimal parameter selection problem can be transformed to mathematical programming problem. Each model parameter and control parameter can be taken as decision variable.Then, formulae for computing the gradient of the cost function with respect to these decision variables are derived.Given the initial parameters, the sequential quadratic programming method can be used to solve the optimal parameter selection problem. For solving the time delay differential system, a cubic spline interpolation function method is adopted to construct the function of metallic ion concentration prior to the initial time by using the measured values of the concentrations of the metallic ion at the sampling points.The optimal parameters of the dynamic system model can be obtained by using the computational method for the time delay optimal parameter selection problem with multiple characteristic time points mentioned above.We observe from numerical simulations that this method is highly effective.
(4) Since the zinc powder used is always more than required, we formulate the minimization of the zinc powder usage as a time delay optimal control problem with continuous state inequality constraints. By using the constraint transcription method together with a local smoothing technique, the continuous state inequality constraints are approximated by a sequence of canonical inequality constraints, which are of the same form as the cost function.Once again, the control is approximated by a piecewise constant function whose heights are taken as decision variables.Then, formulae for computing the gradient of the cost and constraint functions are derived. On this basis, the optimal control can be obtained by using a gradient-based optimization method, such as the sequential quadratic programming method. The numerical simulation shows that the amount of zinc powder added can be decreased efficiently.
(5)The gradient-based sequential quadratic programming method is a local optimization method. Due to the calculation can easily be trapped into the local optimal value, on the basis of a global optimization approach with filled function, the time delay optimal control method can be used to calculate the amount of zinc powder at the subsequent time. The control function, which represents the amount of zinc powder added, still is of the form of a piecewise constant function. The optimal control parameters solved from the offline optimization are taken as the initial values for the online optimization so that the computation efficiency can be improved. The predicted concentration of the metallic ion impurities obtained from the online support vector regression model is used as the reference state to be tracked by the solution of the underlying dynamics of the time delay optimal control problem. The optimal amount of zinc powder to be added at each subsequent time can be optimized effectively.
In conclusion, the optimal control method developed in this thesis, which is based on the control parameterization technique, has enormous practical relevance, particularly for metallurgical processes.
硫酸锌溶液净化过程采用三段净化工序,其中Ⅱ段净化工序主要是除去溶液中的杂质钴和镉离子,是整个净化过程中最关键的一道工序。论文在深入研究净化过程工艺和反应机理的基础上,首先依据生产过程数据,建立Ⅱ段净化过程出口杂质离子浓度的智能预测模型；其次,根据锌粉颗粒与金属离子间的置换沉淀反应机理,结合生产工况的特点,建立净化除杂的动态反应模型,并提出基于控制参数化技术的优化控制方法,最后,将其运用到锌粉添加量的优化控制方案中,取得了明显的成效。本文主要研究工作及创新性成果如下：
(1)在对硫酸锌溶液净化过程深入分析的基础上,针对Ⅱ段净化过程出口杂质金属离子浓度的重要性,根据生产过程中的大量工况数据,建立Ⅱ段净化过程出口钴离子和镉离子浓度的在线支持向量回归预测模型。由于在线支持向量回归算法中存在复杂的矩阵运算,提出采用分块矩阵的迭代更新法求解,以提高计算效率。基于生产数据的仿真分析说明模型具有良好的预测性能,明显提高计算速度,能为生产操作提供参考,进一步指导锌粉添加量的优化控制。
(2)研究金属离子的置换反应机理,其中发生的主要化学反应为锌粉颗粒置换沉淀钴和镉离子的反应过程,结合硫酸锌溶液净化过程的特点,以连续搅拌反应釜模型为基础,分别以钻离子和镉离子浓度作为状态变量,提出锌粉净化除杂质离子的非线性时滞关联动态反应模型。
(3)提出基于控制参数化的数值优化方法,解决非线性时滞关联动态反应模型中的参数计算问题。其基本思想是把控制量表示成分段常数函数形式,整个时间域内的非线性动态方程则被转化为与各个控制参数相应子区间内的线性动态方程。为求解最优动态模型参数,依据采样点,即特征时间点上的实际离子浓度检测数据,提出基于多特征时间点的优化参数选择方法,以确定动态模型中的未知参数。通过把该类优化参数选择问题转化为数学规划问题,每个模型参数与控制参数都被当作是决策变量,并推导出目标函数对于这些决策变量的梯度计算公式。给定参数初始值的情况下,利用序列二次规划优化方法来求解最优参数选择问题。针对求解时滞微分方程的特殊性,提出采用三次方样条插值拟合函数,依据采样时刻的离子浓度检测值,建立初始时刻以前的离子浓度状态函数。通过采用基于多特征时间点的时滞优化参数选择问题的数值计算方法,可以有效求得最优的动态系统模型参数。
(4)针对实际生产中锌粉总是被过量添加的情况,提出基于连续状态不等式约束的时滞优化控制方法,解决锌粉添加量的最优控制问题。通过采用局部光滑技术的约束转换方法,将连续状态不等式约束转化为一系列规范型的不等式约束,这些不等式约束的形式和目标函数保持一致。控制函数依然被表示成分段常数函数形式,每个控制参数都被认为是决策变量,并推导出目标函数和约束函数对于决策变量的梯度计算公式。最后,采用基于梯度的序列二次规划优化方法来求解该优化控制问题,数值仿真表明锌粉添加量可以有效地被减少。
(5)基于梯度的序列二次规划方法是一种局部优化算法,针对优化计算过程中容易陷入局部最优值的问题,提出采用基于填充函数全局优化的锌粉量时滞优化控制方法,解决后续时段锌粉添加量的最优控制问题。作为表示锌粉添加量的控制函数依然采用分段常数函数形式,以离线优化计算得到的最优控制参数作为在线优化控制的参数初始值,可以有效提高寻优效率。以基于生产数据的在线支持向量回归模型预测出的杂质金属离子浓度值作为时滞动态方程的状态参考值,期望时滞动态方程的状态解跟踪该参考轨迹,并在该种情况下在线优化控制锌粉添加量。数值仿真表明,采用该方法可以有效求解出后续时段内的最优锌粉添加量,为生产操作提供指导。
本文提出的基于控制参数化的优化控制方法具有较强的实用性,可以在类似的冶金生产过程中推广应用。
The purification process of zinc hydrometallurgy, in which metallic ion impurities are removed from a zinc sulphate solution, is an important industrial process.In this process, the zinc powder is added into the solution to remove the impurities based on the measured concentration of metallic ion impurities at the inlet and outlet of the reaction tank. Then, the eligible solution is fed to the electrolysis process. In addition, zinc powder is the primary material for inducing the deposition of the metallic ion impurities, and hence it is crucial that the amount used be controlled appropriately. Because the purification process has the characteristic of long flow, time delay, nonlinear and dynamic,it usually takes a period of time for the variation in the process parameters reflecting the alteration in the concentration of metallic ion impurities.Besides, the concentration of the metallic ion impurities is not detected online in the process.The operator can not regulate the amount of zinc powder added according to the variation in the concentration of impurities correctly due to the time delay in the chemical test and purification reaction.Meanwhile, there are many disturbances and uncertainties affecting the purification reaction, the amount of zinc powder added is always much more than required.The operator does this based on their experience and judgement, to ensure that the zinc sulphate solution produced is of a sufficiently high purity. However, this way of ensuring the purification quality is expensive and consumes significant amounts of energy.
There are three stages in the purification process of zinc sulphate solution.The cobalt and cadmium ions are removed mainly in the second stage, which is the most crucial stage in the whole purification process.On the basis of our research findings into the zinc sulphate purification process and reaction mechanism, an intelligent prediction model describing the concentration of metallic ion impurities in the second purification process outlet is established using the process data. Then, by taking into account the specific characteristics of the process, a mathematical model for the dynamic reaction of the purification process is constructed according to the deposition reaction mechanism between zinc powder particles and metallic ion impurities.An optimal control method based on the control parameterization technique is then proposed to obtain the optimal amount of zinc powder that should be added to the purification process at each time.The simulation results are very promising.The main research work and innovative achievements are listed as follows:
(1)The purification process of zinc sulphate solution is thoroughly investigated and analysed. Then, because of the significance of the concentrations of the metallic ion impurities in the second purification process outlet, an online support vector regression prediction model for the concentration of the cobalt and cadmium ions is constructed using the process data. As the matrix computation in the online support vector regression algorithm is very complicated, an iterative updating method of matrix blocking partition is developed so that the computation efficiency can be improved. The simulation results of the process data show that the prediction model performs quickly and gives good results. This model can serve as a reference for the production process, which indicates the optimal amount of zinc powder that should be added in the purification process.
(2)The replacement reaction mechanism of the metallic ions is also studied. The main chemical reaction includes the replacement deposition reaction between zinc powder particles and the cobalt or cadmium ions. By taking into account the characteristics of the purification process, the concentration of cobalt and cadmium ions are taken as state variables, a nonlinear time delay interactive dynamic reaction model is proposed for the metallic ion impurities deposition process, which is based on the continuous stirred tank reactor model.
(3)The numerical optimization method based on control parameterization is proposed to obtain the optimal parameters in the nonlinear time delay interactive dynamic reaction model.The main idea is that the control takes the form of piecewise constant function, then the nonlinear dynamic equation in the whole time domain can be transformed to linear dynamic equation in the subinterval corresponding to each control parameter. Based on the measured concentration of metallic ion impurities on the sampling point, i.e.characteristic time point, we formulate an optimal parameter selection method with multiple characteristic time points, in which the underlying dynamic system is a system of time delay differential equations, to obtain the optimal parameters in the dynamic model.This kind of optimal parameter selection problem can be transformed to mathematical programming problem. Each model parameter and control parameter can be taken as decision variable.Then, formulae for computing the gradient of the cost function with respect to these decision variables are derived.Given the initial parameters, the sequential quadratic programming method can be used to solve the optimal parameter selection problem. For solving the time delay differential system, a cubic spline interpolation function method is adopted to construct the function of metallic ion concentration prior to the initial time by using the measured values of the concentrations of the metallic ion at the sampling points.The optimal parameters of the dynamic system model can be obtained by using the computational method for the time delay optimal parameter selection problem with multiple characteristic time points mentioned above.We observe from numerical simulations that this method is highly effective.
(4) Since the zinc powder used is always more than required, we formulate the minimization of the zinc powder usage as a time delay optimal control problem with continuous state inequality constraints. By using the constraint transcription method together with a local smoothing technique, the continuous state inequality constraints are approximated by a sequence of canonical inequality constraints, which are of the same form as the cost function.Once again, the control is approximated by a piecewise constant function whose heights are taken as decision variables.Then, formulae for computing the gradient of the cost and constraint functions are derived. On this basis, the optimal control can be obtained by using a gradient-based optimization method, such as the sequential quadratic programming method. The numerical simulation shows that the amount of zinc powder added can be decreased efficiently.
(5)The gradient-based sequential quadratic programming method is a local optimization method. Due to the calculation can easily be trapped into the local optimal value, on the basis of a global optimization approach with filled function, the time delay optimal control method can be used to calculate the amount of zinc powder at the subsequent time. The control function, which represents the amount of zinc powder added, still is of the form of a piecewise constant function. The optimal control parameters solved from the offline optimization are taken as the initial values for the online optimization so that the computation efficiency can be improved. The predicted concentration of the metallic ion impurities obtained from the online support vector regression model is used as the reference state to be tracked by the solution of the underlying dynamics of the time delay optimal control problem. The optimal amount of zinc powder to be added at each subsequent time can be optimized effectively.
In conclusion, the optimal control method developed in this thesis, which is based on the control parameterization technique, has enormous practical relevance, particularly for metallurgical processes.
引文
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