Reaching Law Based Sliding Mode Control of Sampled Time Systems

Abstract

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.

Reduction of the reaching time with adaptive slope sliding mode control

“…One of the weaknesses of this method is the lack of time limits for reaching the equilibrium point, which was solved by developing methods based on nonlinear surfaces such as the terminal sliding mode method. [5][6][7][8] Fast terminal sliding mode control methods were also proposed to improve the reaching speed by using a nonlinear surfaces. 9 The other weakness related to the use of sliding surfaces is the existence of the chattering phenomenon in the above-mentioned methods, which can be solved by changing the surface equations directly or switching between surfaces and so on.…”

“…One of the weaknesses of this method is the lack of time limits for reaching the equilibrium point, which was solved by developing methods based on nonlinear surfaces such as the terminal sliding mode method 5–8 . Fast terminal sliding mode control methods were also proposed to improve the reaching speed by using a nonlinear surfaces 9 .…”

Sliding Mode Controllers in Energy Systems and Other Applications

“…In another work, Lesniewski and Bartoszewicz [15] consider the sliding mode control of sampled data systems. This is a highly relevant topic, as virtually all control algorithms are applied digitally with no continuous states in the controller.…”