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For this network, the controller saturated while attempting to clamp network firing at 10 Hz/unit, resulting in a control failure (grey trace).
For a target rate of 6 Hz/unit, the controller saturated at the maximal frequency of 10 Hz at around 7 hr into the control epoch, and target tracking failed as a result.
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This controller is saturated outside a domain of interest and a reduced-order observer is designed to estimate the substrate concentration in the bioreactor.
Two approaches are proposed based on: (i) ensuring that the controller never saturates: the obtained controller is linear time invariant (LTI), (ii) ensuring absolute stability against the saturations: the controller is then linear time varying (LTV).
Sufficient conditions are thus established that guarantee the closed-loop stability and the fact that both the actuator and the controller stop saturating after a finite transient period, implying perfect tracking of the output reference signal provided this is compatible with the actuator constraint.
The linear OF saturated controller: (i) recovers, in a practical stability sense, the behavior of a globally stabilizing nonlinear robust SF saturated controller, and (ii) becomes a linear PI controller in the absence of saturation.
The results show controller performance in single wheel motion without saturation and overall controller performance under saturated pump flow.
The consideration of the problem as an interlaced observer-control design leads to a saturated PI controller that recovers (up to observer convergence) the behavior of a detailed model-based robust nonlinear state-feedback (SF) globally stabilizing saturated controller.
Among advantages of this anti-windup protection scheme are its improved performance while the nominal controller is mildly saturated and its applicability to open-loop unstable plants.
For a special choice of the controller parameters, our controller reduces to a finely tuned saturated PI/PID type controller with an anti-windup structure.
The controllers have several nonlinearities: firstly, in all the controllers, the integrators are saturated at a particular value, and secondly, the speed controller has a dead zone to ensure smooth braking.
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