Nonlinear model predictive control of fast system

Abstract

Nonlinear model predictive control (NMPC) has been considered as a promising control algorithm which is based on a real-time solution of a nonlinear dynamic optimization problem [1]. Nonlinear model equations and control as well as state restrictions are treated as equality and inequality constraints of the optimal control problem. However, NMPC has been applied mostly in relatively slow processes until now [2], due to its high computational expense. Therefore, computation time needed for the solution of NMPC leads to a bottleneck in its application to fast systems such as mechanical and/or electrical processes. In this work, a new solution strategy to efficiently solve NMPC problems is proposed so that it can be applied to fast systems. It is a combination of the multiple shooting and the collocation method. The multiple shooting method is used for discretizing the dynamic model, through which the optimal control problem is converted to a nonlinear programming (NLP) problem. To solve this NLP problem, the values of state variables and their gradients at the end of each shooting need to be computed. We use collocation on finite elements to carry out this task. As a result, the advantages of both the multiple shooting and the collocation method can be employed and therefore the computation efficiency can be considerably enhanced [3].