The industrial thermal and medical thermal processes under investigation, such as the snap curing oven, the semiconductor diffusion furnace, and the high intensity focused ultrasound therapy process for terminal cancers, are a kind of nonlinear distributed parameter system (DPS) described by partial differential equations (PDEs) with multi-heating zones and special boundary conditions. A good modeling is critical to control of the complex DPSs. However, it is very difficult to model this kind of process because of the following reasons: 1) the process response varies versus location due to time-space coupled nature of the process; 2) the process dynamics varies at different working conditions due to the strong nonlinearity; 3) uncertainties exist in the process; 4) only a few sensors and actuators are available in most of the DPSs, which makes the accurate modeling more difficult.
Since these thermal processes' dependence on historical inputs decreases rapidly with time, their I/O relationship can be expressed by Volterra series. Using the orthonormal functional series (OFS) to approximate each order Volterra kernel, we design an OFS-Volterra modeling methodology to separate the time/space variables of nonlinear DPSs, and then yield a more effective DPS model. The model developed from this methodology can serve as an internal model for the model predictive control (MPC). The control objective is to make the output distribution of the DPS (temperature field of the curing oven) evenly distributed with limited sensors and actuators. A relatively simple modelling method is presented to develop a realistic process model that is able to handle more complex time/space coupling nature and uncertainty. Using the developed process model as the internal model, three more properties (model prediction, moving horizon optimization, feedback rectification) of the nonlinear-MPC can be applied to suppress the model mismatching, uncertainty and external disturbances, so that a required output distribution can be achieved and maintained.
Back to Control Seminars Page.