On the Choice of Norm in Finite Control Set Model Predictive Control

In power electronics, the <inline-formula><tex-math notation="LaTeX">$\ell _1$</tex-math></inline-formula>-norm (instead of the squared <inline-formula><tex-math notation="LaTeX">$\ell _2$</tex-math></inline-formula>-norm) is often used in the objective function of model predictive controllers (MPCs) with reference tracking. Although the <inline-formula><tex-math notation="LaTeX">$\ell _1$</tex-math></inline-formula>-norm is preferred for its computational simplicity, it might lead to a performance deterioration and closed-loop instability. This paper analyzes the root cause for this and discusses the benefits of using the <inline-formula><tex-math notation="LaTeX"> $\ell _2$</tex-math></inline-formula>-norm instead. Given the theoretical nature of this paper, a power electronics-oriented case study is employed to visualize and exemplify—through examples and simulations—the mathematical concepts and arguments presented. To this end, a variable speed drive system with a three-level voltage-source inverter serves as an illustrative example to clearly demonstrate the effectiveness of using the <inline-formula><tex-math notation="LaTeX">$\ell _2$</tex-math></inline-formula>-norm.