Integral Sliding Manifold Design for Linear Systems With Additive Unmatched Disturbances

Abstract

This note offers an integral sliding manifold design method for linear systems that minimizes the impact of unmatched constant external disturbances. System sensitivity upon an unmatched disturbance vector is assessed by the steadystate dependent criterion function. The derived procedure easily finds a unique integral sliding manifold that minimizes a quadratic optimization criterion. Applicability of this method in case of slowly-varying disturbances is supported by determining disturbance frequency limit that guarantees satisfactory performance. The proposed approach has been demonstrated on a numerical example and verified by simulations.

Tuning and Feasibility Analysis of Classical First-Order MIMO Non-Linear Sliding Mode Control Design for Industrial Applications

“…However, these parameters cannot be chosen deliberately, indeed they have to satisfy Equation (22) in order to verify Equation (18). For Equation (30) conditions, Equation (22) can be written as:…”

“…Many studies have been developed on SM, each one addressing a particular limitation, such as chattering [26], asymptotical convergence of the state variables to the desired value [27], insensitivity with respect to matched uncertainties [28], higher order derivative requirements for sliding surface design [29], and so on. Many other approaches can be found; for instance, a method to design integral sliding manifolds in the presence of additive unmatched uncertainties was discussed in Reference [30], while an adaptive second order sliding mode was proposed in Reference [31] in order to avoid the necessity of any a priori knowledge of the uncertainty upper bounds. In Reference [32] a peculiar approach was presented, where the physical model of the controlled system is not needed for the controller design, and the chattering behavior (determined by SM control) affecting the inverter switching frequency was analyzed and successfully addressed in Reference [33].…”

Passivity analysis and disturbance observer‐based adaptive integral sliding mode control for uncertain singularly perturbed systems with input non‐linearity

“…Sliding mode control (SMC) has been extensively investigated for its particular ability to suppress the disturbances [13], which enables the systems have strong robustness against matched disturbances [14], but sensitive to mismatched ones that may not satisfy the so‐called matching condition [15]. To this end, for disturbances, the integral SMC (ISMC) has been proved to be an alternative approach to guarantee the robustness throughout the closed‐loop system response [16–18].…”

Consensus Protocols for Heterogeneous Multiagent Systems with Disturbances via Integral Sliding Mode Control

“…It was regarded to have easy implementation and high robustness against uncertain but bounded disturbance. Numerous successful applications and theoretical extension of SMC have taken place in the last decades which include integral SMC (ISMC) [19][20][21]. Thus in this paper, we aim to study ISMC for heterogeneous MAS with disturbances.…”