Modeling And Predictive Control For Spatially Distributed System Based On Input/Output Data

The spatially-distributed system (SDS) has strong spatial variations that the states, controls and outputs depend on spatial position. The spatial-temporal coupling and infinite dimensionality of the systems make them very difficult for analysis, modeling and control. Usually the ordinary differential equations (ODEs) is obtained from patial differential equations (PDEs) and the traditional control methods developed for lumped parameter systems are used in the actual application. Classical control methods for spatially distributed systems need not only the precise mathematical models of the systems to be controlled, but also the designers to grasp plentiful, complicated mathematical knowledge involved in control theory of spatially distributed systems. In real-world systems, the spatial state of the system can be obtained by finite sensors and acutuator. The structure of data based model is easy. And it is easy for controldesign too. Few publications are focus on the modeling and control design based on the input and output data sets. Thus, in this dissertation, research on modeling and control design for SDS are studied based on input/output data.Considering that SDS can be classified into hyperbolic SDS and parabolic SDS according to the property of their spatial differential operators, the modeling and control design for two kinds of SDSs (parabolic SDS and hyperbolic SDS) are dertermined based on input and output data sets.The main contents are as follows:A new time/space separation modeling method based on interval type-2 fuzzy set is proposed for parabolic spatially-distributed system. Firstly, principal component analysis (PCA) is used for the time /space separation and the dimension reduction, as the first finite terms can provide a good approximation for most industrial processes due to their slow/fast separation properties. Subsequently, the low-dimensional model is obtained from the temporal coefficients using interval type-2 T-S fuzzy model. Combination of PCA method for the construction of interval type-2 T-S fuzzy model for the nonlinear parabolic spatially distributed system is employed for the modeling which is arbitrarily close, up to a desired accuracy, to the original infinite-dimensional system. Finally, the simulations based on parabolic rod reactor show that the proposed approach can achieve a better performance.Two kinds of MPC strategies based on low-dimensional model are presented for parabolic spatially-distributed systems (SDSs). Firstly, applying the PCA method to obtain spatial basis function and low-dimensional model. Then the control of the spatial outputs can be transform to control the low-dimensional model. As the state of the low-dimensional temporal model can not be measured directly, based on the state estimation the MPC strategy is designed and closed-loop stability analysis are presented and proven. Secondly, the infinite horizon MPC stratety is proposed based on low-dimensional model, in which the terminal constraints are used to transform the cost function along an infinite prediction horizon into finite prediction horizon.The simulations demonstrated show the accuracy and efficiency of the proposed methodologies.A local modeling approach based on interval type-2 T-S fuzzy sets is proposed for hyperbolic spatially-distributed system. The simulated annealing method based on PCA approach is proposed for region division. The interval type-2 T-S fuzzy model is developed to the local dynamics in consideration of the mutual influence of neighbor regions. The parameters and the proper fuzzy rules of the local models are obtained by using interval type-2 fuzzy satisfactory clustering algorithm. Then the global models can be determined by constructing the local models by smooth interpolation. The simulations based on heat exchanger show that the proposed approach can achieve a better performance. A model predictive control strategy for hyperbolic spatially-distributed system is proposed. The local modeling approach based on interval type-2 T-S fuzzy sets is used to predict hyperbolic spatially-distributed system based on the input-output data. Then, the multiple local models are implemented in Model Predictive Control (MPC) procedure. The simulations demonstrated show the accuracy and efficiency of the proposed methodologies.