Adaptive Fuzzy Control Design for Nonlinear Distributed Parameter Systems with Application to Semiconductor Industry

Most industrial processes are inherently distributed in space and time. They are usually described by nonlinear partial differential equations (PDEs) with mixed or homogeneous boundary conditions. Due to infinite-dimensional nature of these distributed parameter systems (DPSs), it is very difficult to apply directly the design methods of lamped parameter systems (LPSs) for their controller design that can be readily implemented in real-time with reasonable computing power. Therefore, the study of modeling and control of DPSs is of theoretical and practical importance. The goal of this project is to develop an adaptive fuzzy control design for nonlinear parabolic PDE systems using the Takagi-Sugeno (T-S) fuzzy model and adaptive bounding technique, and apply it to temperature profile control for a curing process in semiconductor packaging industry. By using model reduction techniques for the parabolic PDEs, a model of finite-dimensional nonlinear ordinary differential equations (ODEs) can be derived. These ODEs are subsequently represented or approximated by a T-S fuzzy linear model. As a consequence, the original PDE system can be described by a T-S fuzzy model with uncertainties including parameter uncertainties (if they exist in the original PDEs), finite-dimensional approximation error and fuzzy modeling error. So, the fruitful and powerful linear control theory and techniques can be applied to design a nominal control law, and adaptive bounding technique can be used to design a corrective control law such that the augmented control law can stabilize the PDE system subject to these uncertainties. Besides the stabilization problem, performance enhancing goals including such things as quadratic cost, disturbance attenuation, and tracking are also desirable. Moreover, successful application of the proposed design method to the selected industrial process will have a great impact on both academia and industry.