A generalized reaching law for discrete time sliding mode control

Automatica ◽  
2015 ◽  
Vol 52 ◽  
pp. 83-86 ◽  
Author(s):  
Sohom Chakrabarty ◽  
Bijnan Bandyopadhyay
Keyword(s):  
Sliding Mode Control ◽  
Discrete Time ◽  
Sliding Mode ◽  
Reaching Law ◽  
Mode Control

scholarly journals Reaching Law Based Sliding Mode Control of Sampled Time Systems

Energies ◽  
2021 ◽  
Vol 14 (7) ◽  
pp. 1882
Author(s):  
Piotr Leśniewski ◽  
Andrzej Bartoszewicz
Keyword(s):  
Sliding Mode Control ◽  
Discrete Time ◽  
Sliding Mode ◽  
Rate Of Change ◽  
Reaching Law ◽  
Mode Control ◽  
Sliding Motion ◽  
Control Precision ◽  
Continuous Time Systems ◽  
Time Systems

In this paper, discrete time reaching law-based sliding mode control of continuous time systems is considered. In sliding mode control methods, usually the assumption of bounded absolute values of disturbances is used. However in many cases, the rate of change of the disturbance is also bounded. In the presented approach, this knowledge is used to improve the control precision and reduce the undesirable chattering. Another advantage of the proposed method is that the disturbance does not have to satisfy the matching conditions. In the paper two new reaching laws are analyzed, one of them ensures the switching quasi-sliding motion and the other the non-switching motion. For both of them, the robustness is assessed by calculating the quasi-sliding mode band width, as well as the greatest possible state error values. Specifically, the state errors are not considered only at the sampling instants, as is usual for discrete time systems, but the bounds on the continuous values “between” the sampling instants are also derived. Then, the proposed approaches are compared and analyzed with respect to energy expenditure of the control signal.

scholarly journals Multi-Power Reaching Law Based Discrete-Time Sliding-Mode Control

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 49822-49829 ◽  
Author(s):  
Haifeng Ma ◽  
Yangmin Li
Keyword(s):  
Sliding Mode Control ◽  
Discrete Time ◽  
Sliding Mode ◽  
Reaching Law ◽  
Mode Control

scholarly journals A Reference Trajectory Based Discrete Time Sliding Mode Control Strategy

2019 ◽  
Vol 29 (3) ◽  
pp. 517-525 ◽  
Author(s):  
Andrzej Bartoszewicz ◽  
Katarzyna Adamiak
Keyword(s):  
Sliding Mode Control ◽  
Discrete Time ◽  
Control Strategy ◽  
Control Method ◽  
Sliding Mode ◽  
Reference Trajectory ◽  
State Variables ◽  
Reaching Law ◽  
Mode Control ◽  
Sliding Motion

Abstract This study presents a new, reference trajectory based sliding mode control strategy for disturbed discrete time dynamical systems. The desired trajectory, which is generated externally according to an existing switching type reaching law, determines the properties of the emerging sliding motion of the system. It is proved that an appropriate choice of the trajectory generator parameters ensures the existence of the quasi-sliding motion of the system according to the definition by Gao et al. (1995) in spite of the influence of disturbances. Moreover, the paper shows that the application of the desired trajectory based reaching law results in a significant reduction in the quasi-sliding mode band width and errors of all state variables. Therefore, in comparison with Gao’s control method, the system’s robustness is increased. The paper also presents an additional modification of the reaching law, which guarantees a further reduction in the quasi-sliding mode band in the case of slowly varying disturbances. The results are confirmed with a simulation example.

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