A Study On Nonlinear System Modeling And Predictive Control

Model Predictive Control (MPC) refers to a class of control strategies, in which a dynamic process model is used to predict and optimize process performance. Linear MPC based on the linear predictive model can be used to control the dynamic process with weak non-linearity or working near the equilibrium point, and has been applied extensively into various constrained multivariable industrial processes. However, linear predictive model can not be used to approximate and predict the performance of the complicated process which is highly nonlinear and operates in a wide range, so nonlinear dynamic model and the relevant MPC strategy are necessary. The purpose of this paper is to study the nonlinear modeling method and the corresponding multi-step predictive control strategy for a family of complex plants with strong nonlinearity.Three nonlinear empirical modeling methods, including on-line fuzzy modeling, off-line fuzzy-neural modeling with on-line modification and off-line Least Squares Support Vector Machines(LS-SVM) based modeling are presented, and two strategies for optimizing the control action including a discrete optimization method and the Generalized Predictive Control (GPC) are studied in this paper. In addition, a receding horizon optimal control law is developed for a Stable Generalized Predictive Controller (SGPC), and the closed-loop stability condition is given and proved. The main contents are depicted as follows:1. Based on a SGPC configuration, a receding horizon optimal control law which can track constant set point free-offset is developed by optimizing the objective function over the future reference signals. The closed-loop stability condition is given and proved, and then the performance of SGPC is compared with that of GPC by numerical simulations. The simulation results show that SGPC is applicable not only to the nonminimum-phase, open-loop unstable plant with unknown dead-time and unknown order, but also to the plant with zeros and poles which can be nearly cancelled.2. A non-linear predictive control algorithm based on the fuzzy model is presented for a class of complex systems with severe nonlinearity. In order to implement nonlinear predictive control for the controlled plant, a T-S fuzzy predictive model is built on-line by using fuzzy clustering and linear identification, and discrete optimization of the control action is carried out according to the principle of Branch and Bound method. In the process of fuzzy modeling, the unsupervised fuzzy competitive learning algorithm and a discarding criteria are introduced to ensure that the system dynamics can be tracked in-time by the fuzzy model. The presented algorithm is also generalized to the multivariable system. The presented algorithm is applied to two SISO models which possess various degree of non-linearity, and a MIMO non-linear model. The simulation results demonstrate the effectiveness and merits of the obtained algorithm.3. Two predictive control algorithms based on T-S fuzzy model are presented for a family of complex systems with strong non-linearity. Using the sampling data set of the controlled plant, the model parameters are initialized by fuzzy clustering, learned using back-propagation algorithm off-line, and if necessary they can be rectified on-line to improve the predictive precision in the process of real-time control. Based on the obtained fuzzy model, the first algorithm optimizes the control action using the B&B method. In the second algorithm, the fuzzy model is locally and dynamically linearized to obtain a linear transfer function model of the controlled plant at current sampling instant, and then, the GPC strategy is employed to implement optimization of the control action. The presented algorithms are compared with each other on a pH neutralization process model and the simulation results show the effectiveness and merits of both the algorithms.4. Used for industrial process with different degree of non-linearity, two predictive control algorithms based on LS-SVM model are presented. For the weakly...