A Minor Correction to “A New Algorithm for Discrete-Time Sliding Mode Control Using Fast Output Sampling Feedback”

Sliding mode control strategies are well known for ensuring robustness of the system with respect to disturbance and model uncertainties. For continuous-time plants, they achieve this property by confining the system state to a particular hyperplane in the state space. Contrary to this, discrete-time sliding mode control (DSMC) strategies only drive the system representative point to a certain vicinity of that hyperplane. In established literature on DSMC, the width of this vicinity has always been strictly greater than zero in the presence of uncertainties. Thus, ideal sliding motion was considered impossible for discrete-time systems. In this paper, a new approach to DSMC design is presented with the aim of driving the system representative point exactly onto the sliding hyperplane even in the presence of uncertainties. As a result, the quasi-sliding mode band width is effectively reduced to zero and ideal discrete-time sliding motion is ensured. This is achieved with the proper selection of the sliding hyperplane, using the unique properties of relative degree two sliding variables. It is further demonstrated that, even in cases where selection of a relative degree two sliding variable is impossible, one can use the proposed technique to significantly reduce the quasi-sliding mode band width.

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Performance Optimization Methodology for Discrete-Time Sliding Mode Control in Industrial Servo Systems Under Control Input Saturation and Disturbance

IFAC-PapersOnLine ◽

10.1016/j.ifacol.2020.12.2149 ◽

2020 ◽

Vol 53 (2) ◽

pp. 9112-9117

Author(s):

Ji-Seok Han ◽

Tae-Ho Oh ◽

Young-Seok Kim ◽

Hyun-Taek Lim ◽

Dae-Young Yang ◽

...

Keyword(s):

Sliding Mode Control ◽

Discrete Time ◽

Performance Optimization ◽

Sliding Mode ◽

Input Saturation ◽

Control Input ◽

Servo Systems ◽

Mode Control ◽

Optimization Methodology

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Reaching Law Based Sliding Mode Control of Sampled Time Systems

Energies ◽

10.3390/en14071882 ◽

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.

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