On the Effects of Tunable Parameters of Model Predictive Control on the Locations of Closed-Loop Eigenvalues

Abstract

This paper presents an analytical study of the effects of model predictive control (MPC) tunable parameters on the closed-loop performance quantified in terms of the location(s) of closed-loop eigenvalue(s) of several common, single-input single-output, linear plants with inactive constraints. Symbolic manipulation capabilities of MATHEMATICA are used to obtain analytical expressions describing the dependence of closed-loop eigenvalues on the tunable parameters. This work is first to investigate how MPC tuning parameters affect the locations of the eigenvalues of the closed-loop system of a plant in the discrete-time setting. It provides theoretical basis/justification for several existing qualitative MPC tuning rules and proposes new tuning guidelines. For example, as the prediction horizon is increased while other tunable parameters remain constant, a subset of the closed-loop eigenvalues (poles) move toward the open-loop eigenvalues (poles) of the plant, if the plant is asymptotically stable. If a pred...