11.2 Cost Function Classification
Although the cost function's main objective is to keep track of a particular variable and control the system, it is not limited to this, as explained in the previous chapter. In fact, one of the main advantages of MPC is that the cost function admits any necessary term that could represent a prediction for another system variable, system constraint, or system requirement. Since these terms most likely can be of a different physical nature (current, voltage, reactive power, switching losses, torque, flux, etc.) their units and magnitudes can also be very different. This issue has been commonly dealt with in MPC by including weighting coefficients or weighting factors λ, for each term of the cost function
Depending on the nature of the different terms involved in the formulation of the cost function, they can be classified in different groups. This classification is necessary in order to facilitate the definition of a weighting factor adjustment procedure that could be applied to similar types of cost functions or terms.
11.2.1 Cost Functions without Weighting Factors
In this kind of cost function, only one, or the components of one variable, are controlled. This is the simplest case, and since only one type of variable is controlled, no weighting factors are necessary. Some representative examples of this type of cost function are obtained for: ...