Modelling And Optimization Method Based On Control Parameterization In Purification Process Of Zinc Hydrometallurgy

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.