The main objective of tracking model predictive control is to stabilize the plant satisfying the constraints and steering the tracking error, that is, the difference between the reference and the output, to zero. In order to predict the expected evolution of the tracking error, some assumptions on the future values of the reference must be considered. Since the reference may differ from expected, the tracking problem is inherently uncertain.
The most common case is to assume that the reference will remain constant along the prediction horizon. These predictive control schemes are typically based on a two-layer control structure in which, provided the value of the reference, first an appropriate target equilibrium point is computed, and then an MPC is designed to regulate the system to this target. Under certain assumptions, closed-loop stability can be guaranteed if the initial state is inside the feasibility region of the MPC. However, if the value of the reference is changed, then there is no guarantee that feasibility and stability properties of the resulting control law hold. Specialized predictive controllers have been designed to deal with this problem. Particularly interesting is the so-called MPC for tracking, which ensures recursive feasibility and asymptotic stability of the setpoint when the value of the reference is changed.
The presence of exogenous disturbances or model mismatches may lead to the controlled system to exhibit offset error. Offset-free control can be achieved by using disturbance models and disturbance estimators together with the tracking predictive controller.
Reference tracking Loss of recursive feasibility MPC for tracking Offset-free control
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The authors would like to thank the support received by the MINECO-Spain and FEDER Funds under project DPI2016-76493-C3-1-R.
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