Robust model predictive control of Hammerstein systems

Abstract

There are very few controller design techniques that can be proven to stabilize processes in the presence of nonlinearities and constraints. Model predictive control (MPC) is one of these techniques. For this reason, there has been much interest in nonlinear model-based control within the process engineering community. A critical step in the application of these methods is the development of a suitable model for the process dynamics. In this sense, block-oriented models have proved to be useful as simple nonlinear models for a vast number of applications. They are described as a cascade of linear dynamic and nonlinear staticblocks. They have emerged as an appealing proposal due to their simplicity and the property of being valid over a larger operating region than a linear time invariant (LTI) model. A typical block-oriented model found in the literature is the Hammerstein model. In this structure a nonlinear memoryless block is followed by a linear dynamics. A broad type of dynamic processes can be described by such representations consisting of these two simple elements usually referred to as subsystems. This chapter deals withrobust control for uncertain Hammerstein models. The starting point for the controller design is a Hammerstein model which describes the systems dynamics in the presence of uncertainty. This model is employed to design a model based predictive controller. The mathematical problem involved in the development of the algorithm is stated in the context of Linear Matrix Inequalities (LMI) theory. The straightforward use of Hammerstein models for designing the Model Predictive controller would lead to a nonlinear optimization problem due to the static nonlinearity. From the point of view of the implementation, this could result in high computationalcomplexity and be a very time-consuming process. This can be avoided by exploiting the structure of the Hammerstein model, which is a novel approach. This strategy developed in this chapter takes advantage of the static nature of the nonlinearity which allows being transformed into polytopic representation and, therefore, to solve the control problem by focusing only in the linear dynamics. This formulation results in a simplified design procedure, because the original nonlinear Model Predictive Control problem turns into a linear one. At the end of the chapter, different simulation examples are presented to illustrate the controller design procedure.