The output distribution control of stochastic systems is very important because it is widely required in industries. For the stochastic systems whose noise inputs satisfy the Gaussian distribution, the statistical parameters of the output can be controlled so as to control the output probability density function(PDF),but for non-Gaussian stochastic systems, this kind of control methods can not be used and the whole shape of the output PDF should be controlled instead. For this problem, Professor Wang proposed a new control method in 1998 which aims to control the output PDF of bounded stochastic systems. In this thesis, new modelling and controller design based on Wang's PDF control methods are proposed, and the main parts of the thesis are summarized as follows 1 The modelling and control methods of the output PDF for non-Gaussian stochastic systems are introduced, and the modelling and control of molecular weight distribution (MWD) in polymerization are reviewed. 2 New modelling methods are proposed for both the single input single output and the multi-input single output stochastic systems to overcome the disadvantages of the existing modelling method. Both the old and the new modelling methods and the controller design are studied with the simulation of MWD control in styrene polymerization process. 3 The dynamic modelling and control of the output PDF is discussed. The existing method can't perform the perfect tracking of the output PDF to the desired distribution, therefore the predictive control algorithm is developed for the PDF shaping problem. 4 Model adaptive control method is studied to improve the accuracy of the modelling so as to achieve a good tracking performance of the output PDF to its desired shape. 5 The iterative learning control (ILC) is incorporated in batch operation stochastic systems. By tuning the basis functions and model parameters batch by batch, the dimension of the model is kept low and the modelling accuracy is improved asymptotically. It is supposed to make the output PDF of the stochastic system obtain a perfect tracking to the desire PDF. The above ILC algorithm is time-consuming as it needs to tune the basis function and re-identify the model parameters. A new ILC law is proposed to tune the control input directly, and makes the output PDF of the system to trace the desired shape in several control periods. The predictive control algorithm, the parameter adaptive control algorithm and the iterative learning control algorithm are all applied to the simulation study of MWD control in styrene polymerization process. In summary, signi¯cant progresses on output PDF modelling and control have been made and the results are applied to the MWD modelling and control of a polymerization process.
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