Model Reduction And Control Of Cross Direction Basis Weight On Paper Machine

An industrial paper machine produces a wide sheet of paper which is required to be of uniform quality in terms of basis weight, moisture, and caliper. Basis weight which means the mass of a unit area is a fundamental property of paper. It needs to be controlled precisely. The goal of basis weight control is to make the paper as uniform as possible.It is also one of the most complicated control targets in the paper making processes. Due to the changes in raw materials and the complicated pulping process prior to the paper machines, variations will undoubtedly exist in the formed paper sheet. The controlling problem on paper machines is becoming more and more difficult because of the increase in sheet width and machine speed.Paper machine cross direction processes are large two-dimensional systems. In order to make the online computational load feasible in real time, it is necessary to reduce the dimensions of the model. Due to the very large dimension and ill-conditioning of the process, the plant model can be effectively reduced by wavelet matrices based on a modified wavelet packet method. The reduced model captures the controllable spatial components of CD processes. After model reduction, MPC based on the reduced model is implemented in the wavelet domain. Meanwhile, the constrains can be exactly represented in the wavelet domain. The main benefit of implementing MPC in the reduced domain is that the on-line computational time for solving the quadratic programming problem can be greatly reduced while good performance is preserved.The main content of this thesis is listed as fellows:(1) The paper manufacture process is researched. Then the developing history, current situation of cross direction control is thoroughly studied, including the main problems which make cross direction control difficult;(2) wavelet theory is researched including its application in signal processing and system modeling;(3) Developing a new method for model reduction using modified wavelet packet. The thesis first makes a thoroughly study of the property of the cross direction process then points out that the key of good performance is achieved by controlling the controllable contents of the system. A method based on the modified wavelet packet is used in model reduction, followed by a set of indices which are used to evaluate the performance of the method; (4) MPC method based on reduced model is implemented in wavelet domain. Through some experiments we conclude that the method is useful, it can preserve the controllable components of the system while reducing computational time.Finally, the conclusions are drawn, and the challenges and problems which may appear in the future are discussed.