Model Reference DSMC With a Relative Degree Two Switching Variable

Abstract

Reaching-law-based discrete sliding mode controllers are well known to be easy to tune and robust with respect to disturbance. In recent years, it has been demonstrated that their robustness can be further enhanced with the use of arbitrary relative degree sliding variables. However, reaching laws using such variables only ensure a good sliding mode performance of the system when the perturbations affecting the plant are matched, which is a very restrictive assumption. To address this issue and to further improve robustness of the plant, in this article, we propose a new model reference approach for strategies with relative degree two sliding variables. In the proposed approach, the reaching law is first used to control the evolution of a disturbance-free model of the plant, and then, the original system state is driven toward that of the model with a secondary controller. It will be shown that the proposed approach ensures better system robustness compared to the conventional reaching law approach and that it does not require the assumption about matched uncertainties.

Constraining the output of discrete‐time systems using sliding mode control with a novel sliding hyperplane

“…In order to simplify notation, the disturbance affecting the plant is assumed to satisfy matching conditions. It is possible to omit this assumption in discrete‐time sliding mode control, 20 but that is not the main objective of this article. The objective of the control strategy for such a system is to drive its state from the initial value of $$$ \boldsymbol{x}(0)\ne 0 $$$ to zero.…”

Integral sliding mode predictive control with disturbance attenuation for discrete‐time systems

“…Since u sw (k) is designed to deal with the disturbance, 𝛽 is chosen as a constant of O(h 2 ) magnitude and satisfying 𝛽 > 𝛿 1 . By combining (16) and (17), the overall control law u(k) is presented:…”

“…A reaching condition of QSM with fast convergence rate and a generalized discrete reaching method with adjustable convergence rate were proposed in [15] for the discrete-time sliding mode control. For the system where the perturbations affecting the plant were unmatched, a new reaching law based discrete sliding mode control law with relative degree two sliding variables was presented in [16].…”

Disturbance supression improved discrete sliding mode fast current tracking control of experimental advanced superconducting tokamak fast control power supply

“…A DSMC for disturbance compensation based on switching function is proposed in Haifeng et al, 13 achieving good disturbance suppression performance in the magnetic lever system, but it is difficult to achieve both optimization in rapidity and chattering suppression performance. To improve the robustness of SMC, a model reference DSMC combining two related switching variables is proposed in Latosinski and Bartoszewicz, 14 which solves the control problem of parameter mismatch and has good robustness, but the sliding mode surface design is too complex. To solve the disturbance problem of discrete systems, a degradation disturbance observer based on adaptive reaching law is designed in Wang et al, 15 achieving good disturbance suppression effect, but the adaptive process requires much computation.…”