Robust tube-based MPC for tracking of constrained linear systems with additive disturbances

This paper is devoted to solve the problem that the predictive controllers may present when the target operation point changes. Model predictive controllers (MPC) are capable to steer an uncertain system to a given target operation point fulfilling the constraints. But if the target changes significantly the controller may not success due to the loss of feasibility of the optimization problem and the inadequacy of the terminal conditions.This paper presents a novel formulation of a robust model predictive controller (MPC) for tracking changing targets based on a single optimization problem. The plant is assumed to be modelled as a linear system with additive uncertainties confined to a bounded known polyhedral set. Under mild assumptions, the proposed MPC is feasible under any change of the target and steers the uncertain system to (a neighborhood of) the target if this is admissible. If the target is not admissible, and hence unreachable, the system is steered to the closest admissible operating point.The controller formulation has some parameters which provide extra degrees of freedom. These new parameters allow control objectives such as disturbance rejection, output offset prioritization or enlargement of the domain of attraction to be dealt with. The paper shows how these parameters can be calculated off-line.In order to demonstrate the benefits of the proposed controller, it has been tested on a real plant: the four tanks plant which is a multivariable nonlinear system configured to exhibit non-minimum phase transmission zeros. Experimental results show the robust stability and offset-free tracking of the controlled plant.