Inverse tangent based switching type reaching law for discrete time sliding mode control systems

2015 ◽  
Author(s):  
Piotr Lesniewski ◽  
Andrzej Bartoszewicz
Keyword(s):  
Sliding Mode Control ◽  
Control Systems ◽  
Discrete Time ◽  
Sliding Mode ◽  
Reaching Law ◽  
Mode Control ◽  
Switching Type

An implicit discretization-based adaptive reaching law for discrete-time sliding mode control systems

2022 ◽  
pp. 107754632110576
Author(s):  
Cong Wang ◽  
Hongwei Xia ◽  
Shunqing Ren
Keyword(s):  
Sliding Mode Control ◽  
Control Systems ◽  
Discrete Time ◽  
Sliding Mode ◽  
Power Parameter ◽  
Reaching Law ◽  
Mode Control ◽  
Adaptive Power ◽  
High Control ◽  
Complexity Of Algorithm

In conventional reaching law approaches, the disturbance suppression is achieved at the cost of high-frequency chattering or increasing the complexity of algorithm such as adding a high-order disturbance compensator. This paper presents the design and analysis of a novel implicit discretization-based adaptive reaching law for discrete-time sliding mode control systems. First, the implicit Euler technique is introduced into the design of discrete reaching laws, and it is proved to be able to eliminate numerical chattering completely. By using a self-adaptive power term, the newly designed reaching law can obtain an arbitrarily small boundary layer of sliding surface, and at the different phases of sliding mode motion, the adaptive power parameter can automatically regulate its value to guarantee globally fast convergence without destroying the accuracy of sliding variable. Then, based on a predefined trajectory of sliding variable, the discrete-time sliding mode control law is developed to realize high control accuracy without additional design. Compared with previous methods, the main contribution of proposed reaching law lies in that it can acquire high-precision sliding mode motion and simultaneously eliminate numerical chattering in spite of complex uncertainties only by adjusting the adaptive power parameter. Finally, a simulation example on the piezomotor-driven linear stage is provided to verify the theoretical results.

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.

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
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