Conditions for offset elimination in state space receding horizon controllers: A tutorial analysis

An offset-free control is one that drives the controlled outputs to their desired targets at steady state. In the linear model predictive control (MPC) framework, the elimination of steady-state offset may seem a little obscure, since the closed-loop optimization tends to hide the integral action. Theoretically, implementing a well-posed optimization problem and having unbiased steady-state predictions are sufficient conditions to eliminate the output offset. However, these basic conditions are not always achieved in practical applications, especially when state-space models are used to perform the output predictions. This paper presents a detailed practical analysis of the existing strategies to eliminate offset when using linear state-space models with moderated uncertainties. The effectiveness of these strategies is demonstrated by simulating three different control problems: a linear SISO system where the effect of using the estimation of the control variable is highlighted, a continuous stirred tank reactor (CSTR) with non-linear dynamics and the consequent model uncertainty and, a 2 × 2 system representing a distillation column that verifies the consistency of previous results and extends the conclusions to higher dimension systems.