Stochastic distribution control (SDC) systems are known to have the 2-D characteristics regarding time and probability space of a random variables, respectively. A double closed-loop structure, which includes iterative learning modeling (ILM) and iterative learning control (ILC), is proposed for non-Gaussian SDC systems. The ILM is arranged in the outer loop, which takes a longer period for each cycle termed as a BATCH. Each BATCH is divided into a modeling period and a number of control intervals, called batches, being arranged in the inner loop for ILC. The output probability density functions (PDFs) of the system are approximated by a radial basis function neural network (RBFNN) model, whose parameters are updated via ILM in each BATCH. Based on the RBFNN approximation of the output PDF, a state-space model is constructed by employing the subspace parameter estimation method. An IL optimal controller is then designed by decreasing the PDF tracking errors from batch to batch. Model simulations are carried out on a forth-order numerical example to examine the effectiveness of the proposed algorithm. To further assess its application feasibility, a flame shape distribution control simulation platform for a combustion process in a coal-fired gate boiler system is constructed by integrating WinCC interface, MATLAB simulation programs, and OPC communication together. The simulation study over this industrial simulation platform shows that the output PDF tracking performance can be efficiently achieved by this double closed-loop iterative learning strategy.
- optimal tracking control
- subspace identification
- probability density function
- stochastic distribution control