A stable real-time implementation model predictive control for fast nonlinear systems

Abstract

This dissertation presents two novel approaches for real-time implementation of robust Model Predictive Control (MPC) for fast complex nonlinear systems. These approaches use a linearization step of the model of the system by two different strategies depending on the nature of the nonlinear system. Linear Parameter Varying (LPV) modeling and Differential Flatness representation are the strategies chosen to develop the Model Predictive Controller. LPV modeling consists of the embedding of the nonlinear terms of the system into a series of scheduling parameters. Therefore, the Model Predictive Control is designed using a linear model being a function of the scheduling parameter to predict the behavior of the states of the system along the prediction horizon. The future values of the scheduling parameters are estimated using a recursive least squares algorithm. Both stability and robustness conditions are ensured using Linear Matrix Inequalities (LMI) constraints included in the optimization problem of the MPC. Finally, terminal ellipsoidal sets are introduced in the cost function to improve the performance of the controller. On the other hand, Differential Flatness representation is used to build a linear MPC to exploit the flatness property of some nonlinear systems. In this approach, the nonlinear model is solved as a function of the flat outputs of the system and its derivatives. Thus, a linear optimization problem is solved to predict the future behavior of the flat output and its derivatives as a function of an auxiliary control variable. Afterward, a feedforward controller is designed to define the optimal control action to be inputted into the system as a function of the auxiliary control variable. Finally, the performance of both control strategies is tested with several simulations of complex nonlinear systems using the Matlab-Simulink environment