The Modeling,Control And Application Research For The Output Probability Density Function

Stochastic distribution control system is an important branch of control theory and its applications. There are many random inputs, such as noise of sensors, random variation of parameters or random disturbance, existed in actual industrial processes. So far, extensive researches have been done for the control of stochastic systems, for example, the minimum variance control, self-tuning control and step parameter Markov system, etc. Most of these researches are for Gaussian system, however, for those non-Gaussian systems, the parameters of mean and variance can’t contain all the information of the systems. For such problem, the output probability density function (PDF) control theory, proposed by Professor Wang can solve this problem efficiently.So far, a complete theoretical system has been established for modeling and control of the2-dimensional (2D) PDF. Similar with the methods of modeling and control for2D PDF, the modeling and control strategy for the Three-dimensional PDF are studied in this thesis and then simulation researches are made for every method. The main content of this thesis are summarized as follows:Firstly, the methods of modeling and controller design for the2D PDF system, the necessity of modeling methods and control strategy for3D stochastic distribution systems and the application area of PDF are reviewed respectively in this part.Secondly, based on the analysis of selection for the Multi-variable B-spline, a static model of the3D output PDF is established through the recursive least squares algorithm which is used to identify parameters, and then a controller is designed, a simulation result shows the effective of the designed controlled.Thirdly, through the recursive least square algorithm, the linear B-spline model and square-root dynamic model of3D PDF are set up with the output and input data of the system respectively, then based on the contrasted3D square-root dynamic model, a regular and a square-root performance index are used for controller design, at last the simulation results verify the effectiveness of the presented controller.Fourthly, this part transfers the linear B-spline into a prediction model, and then a predictive control algorithm is designed for3D output PDF system to improve the control performance.At last, further research directions are discussed according to the research result and difficulties met in the research process.