In general, industrial processes are nonlinear, but, as has been shown in this book, most MPC applications are based on the use of linear models. There are two main reasons for this: on one hand, the identification of a linear model based on process data is relatively easy and, on the other hand, linear models provide good results when the plant is operating in the neighbourhood of the operating point. In the process industries, where linear MPC is widespread, the objective is to keep the process around the stationary state rather than perform frequent changes from one operation point to another and, therefore, a precise linear model is enough. Besides, the use of a linear model together with a quadratic objective function gives rise to a convex problem (Quadratic Programming) whose solution is well studied with many commercial products available. The existence of algorithms that can guarantee a convergent solution in a time shorter than the sampling time is crucial in processes where a great number of variables appear.However, the dynamic response of the resulting linear controllers is unacceptable when applied to processes that are nonlinear to varying degrees of severity. Although in many situations the process will be operating in the neighbourhood of a steady state, and therefore a linear representation will be adequate, there are some very important situations where this does not occur. On one hand, there are processes for which the nonlinearities are so severe (even in the vicinity of steady states) and so crucial to the closed-loop stability that a linear model is not sufficient. On the other hand, there are some processes that experience continuous transitions (startups, shutdowns, etc.) and spend a great deal of time away from a steady-state operating region or even processes which are never in steady-state operation, as is the case of batch processes, where the whole operation is carried out in transient mode. For these processes a linear control law will not be very effective, so nonlinear controllers will be essential for improved performance or stable operation.Although the number of applications of Nonlinear Model Predictive Control (NMPC) is still very limited (see [14], [171]), its potential is really E. F. Camacho et al., Model Predictive Control

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This chapter describes the elements that are common to all Model Predictive controllers, showing the various alternatives used in the different implementations. Some of the most popular methods will later be reviewed to demonstrate their most outstanding characteristics. MPC ElementsAll the MPC algorithms possess common elements, and different options can be chosen for each element giving rise to different algorithms. These elements are:• prediction model, • objective function and • obtaining the control law. Prediction ModelThe model is the cornerstone of MPC; a complete design should include the necessary mechanisms for obtaining the best possible model, which should be complete enough to fully capture the process dynamics and allow the predictions to be calculated, and at the same time to be intuitive and permit theoretic analysis. The use of the process model is determined by the necessity to calculate the predicted output at future instantsŷ(t + k | t). The different strategies of MPC can use various models to represent the relationship between the outputs and the measurable inputs, some of which are manipulated variables and others can be considered to be measurable disturbances which can be compensated for by feedforward action. A disturbance model can also be taken into account to describe the behaviour not reflected by the process model, including the effect of nonmeasurable inputs, E. F. Camacho et al., Model Predictive Control

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