Model predictive control with nonlinear state space models

Abstract

This paper presents a model predictive control scheme based on nonlinear state space models. The considered class of systems is supposed to be separable into a linear part and a nonlinear feedback path. Therefore, the overall discrete-time dynamic system is nonlinear. Most of the existing model predictive control algorithms for nonlinear systems require the solution of a nonconvex nonlinear optimization problem within the interval of one sample time step. This seems to be practically impossible in systems with fast sample rates as they occur in electrical drive systems. In order to facilitate the predictive control algorithm for real-time applications, the nonlinear feedback path is linearized along a reference trajectory within the prediction horizon. This results in a linear time-variant model, where the nonlinearity is mapped to the time variance of the model. The trajectory for linearization can either be the reference trajectory in the prediction horizon or must be generated based on other available information of the system. The prediction j steps ahead and the control law in analogy to generalized predictive control can be calculated analytically in absence of constraints. However, the system's nonlinearity is taken into account by the linearization along a trajectory at every integration and prediction step. The inclusion of constraints in the optimization problem results in a quadratic program for which efficient solution methods exist. This leads to a computationally more practical predictive control concept for nonlinear systems applicable to fast processes even in the presence of constraints.