Abstract
The paper addresses the problem of chattering elimination in sliding mode control for sampled data dynamical systems and proposes an innovative control scheme. The key to the proposed control method is utilizing a pregenerated nonswitching type reference sliding variable profile to control the disturbed plant. As sampled data systems contain sample-and-hold devices in their input and output channels, we carry out a discrete time analysis. We consider the discretization effects on the controller in two aspects: the pace of convergence of the system and the ultimate band width. Consequently, in the reference sliding variable generator, we analyse two reaching laws, differently adapting to changes of the controller’s frequency. We prove that this approach not only minimizes the chattering phenomenon but also provides a reduction of the quasi-sliding mode band width, which in general case remains of O(T) order. Furthermore, the proposed control method incorporates a disturbance compensation algorithm, which results in the ultimate band width of O(T2) order. Finally, we also show that a certain selection of the sliding plane guarantees limitation of all the state variables’ errors to O(T2) order as well. Therefore, the proposed control algorithm significantly improves the system’s robustness.
Highlights
Nowadays, it is hard to imagine any control implementation without microprocessors, digital sensors, and actuators
Once the representative point of the system becomes confined to the sliding plane, it slides along it to the equilibrium point. erefore, the stability of the system depends on the choice of the sliding plane only. e idea of sliding mode control has quickly gained popularity [4,5,6,7]; thanks to continuous updates of the control signal, it ensures insensitivity to matched external disturbance and model uncertainties [8]
We have shown that the proposed control strategy results in the ultimate band width of O (T2) order
Summary
It is hard to imagine any control implementation without microprocessors, digital sensors, and actuators. Continuous time sliding mode is a comparably new control idea, it has been thoroughly studied since the 1970s [1,2,3] It assumes continuous switching of the structure of the controller depending on the position of the representative point of the system relative to the chosen sliding plane so that the system’s states are always driven onto the plane. Is study takes into account a sampled data system, presents the control design, and discusses the influence of the choice of the discretization period T on the properties of the achieved quasi-sliding mode. In order to improve its robustness, we eliminate the chattering problem with the application of the nonswitching type reaching law and incorporate a disturbance compensation algorithm, which reduces the ultimate band width and the maximum errors of all state variables to O(T2) order.
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