Offset-free Tracking: There and Back Again

Feedback is necessary to reduce the effect of disturbances and to cope with unavoidable modeling errors. Nonetheless, the way in which feedback is used to achieve offset-free tracking in the presence of persistent errors or non-zero mean disturbances appears to be often a question of personal preference among possible different, sometimes ad-hoc, methods. As a matter of fact, this aspect of controller design is typically overlooked in academic papers but is often fundamental for successful implementation. After a preliminary introduction to linear offset-free Model Predictive Control (MPC) design principles based on disturbance models, explaining how the integral action is achieved in spite of modeling errors, we address the following results. 1. We propose an observer-based Internal Model Control (IMC) struc- ture which extends the simple IMC design principles to integrating and unstable plants, showing the conditions for internal stability and offset-free property. A connection with the Youla-Kucera parameter- ization is also established as a special case. 2. We show that several known alternative offset-free MPC algorithms (using velocity models) are special cases of the general disturbance models. 3. We extend the concepts of offset-free estimation to design an eco- nomic MPC algorithm that is able to cope with persistent errors while still achieving the optimal ultimate economic performance.