Constraining State Variables and Control Signal via Sliding Mode Control Approach

Abstract

In this paper the issue of constraining the control input and the state variables in continuoustime systems via sliding mode control was considered. The sliding mode controller was designed using the reaching law technique. Further, the time-varying convergence rate was selected so that the fastest, finitetime, monotonic convergence of the state to the predefined sliding hyperplane simultaneously satisfying both control input and state limitations is ensured. Sufficient condition that guarantees these properties was presented and proved. INDEX TERMS continuous-time systems, control input constraint, sliding mode control, state constraint

Sliding Mode Control With Limits on the Control Signal and Linear State Combinations

“…Therefore, in this paper we examine this issue upon the perturbed continuous time system with time-varying model uncertainties and external disturbances (which do not need to satisfy the matching conditions). We propose a reaching law that ensures the fastest, monotonic and finite-time convergence of the representative point to the predefined switching hyperplane, simultaneously limiting state constraints and control input, extending results obtained in [37]. The novelty of this paper consists of considering the state constraints in the forms of linear combinations, fully eliminating the chattering effect on the boundaries of the admissible set and increasing the convergence speed by taking into account maximal impact of model uncertainties at every time instant.…”

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

“…Theorem 5. If the control strategy for plant (2) is defined by (13) with sliding hyperplane selected according to (16), then system output rate of change is bounded in the following way for all k ≥ n…”

“…It has been demonstrated that, if the sliding variable rate of change is bounded, then the output rate of change will also be proportionally limited. Furthermore, its bound strictly depends on coefficient 𝜆 from sliding hyperplane (16) and parameter 𝜀 from reaching law (8). Consequently, any constraints (4) placed on the system can be satisfied with the proper choice of these parameters.…”

“…We first consider the case in which current values of all four state variables of the considered plant are always known. For such systems, we define the sliding hyperplane according to (16) with parameter 𝜆 = −0.5. Then, according to Theorem 5, output rate of change will satisfy inequality…”

“…This can create a barrier in practical implementation of sliding mode control, since in many systems these variables may need to satisfy particular constraints. Although the issue of state constraints has been considered in literature on continuous-time sliding mode control, [14][15][16][17] few similar results exist for discrete-time plants.…”