In this paper we propose an anti-windup strategy to counteract directionality effects arising in saturated MIMO systems in which independent dynamical subsystems are coupled through a static mixing of the inputs. Since such systems are affected by undesired input cross-couplings when saturation occurs, we propose an anti-windup augmentation scheme built on top of the baseline controller and tailored to achieve satisfactory timedomain performance for reference signals of interest. Motivated by the quadrotor application, in which position control has higher priority over yaw control for safety reasons, we embed in the antiwindup synthesis procedure the possibility to prioritize the level of performance degradation during saturation for the different system outputs.

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In this paper we present and validate an anti-windup control design suitable to deal with saturated discrete-time linear plants. Following the modern approach to anti-windup design, the proposed synthesis procedure is based on the compensator paradigm in which the anti-windup controller acts on top of a baseline one, tuned to achieve desirable performance in the unsaturated regime. After extending existing ideas for continuoustime plants to their discrete-time counterparts, the design of the anti-windup compensator is carried out with a focus on computational efficiency and optimized performance in practical operating scenarios. The proposed approach allows one to design fixed-dynamics anti-windup compensators for possibly open-loop unstable plants using generalized sector conditions. Then, the synthesis procedure is applied to tune a fixed-dynamics compensator having the structure of a static compensator cascaded with a unit delay to avoid algebraic loops. Finally, the benefits of such anti-windup augmentation are assessed experimentally to counteract windup effects arising in the position control of multirotor UAVs when pitch limitations are imposed.

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