This chapter summarizes the basic concepts used in the design of sliding mode controllers, from the definition of conventional sliding set, and the main concept of sliding motion, to the design of the advanced robust exact high-order sliding modes differentiator. These pages describe the basis on which the methodologies presented along the book are designed, with this aim a short historical background is presented in Section 1.1, the main concepts related to the sliding mode theory are presented in Section 1.2. Section 1.3 describes the design process applied to the manifold, which restricts the movement of the state trajectories during the sliding motion. The basis of the design of standard sliding mode controllers are presented in Section 1.4. The main second-order sliding-mode algorithms are presented in Section 1.5 and the robust-exact high-order sliding-mode differentiator is described in Section 1.6.

Chapter Contents:

• 1.1 Historical background
• 1.2 Definitions of solutions
• 1.2.1 Filippov definition
• 1.2.2 Equivalent control
• 1.3 Sliding manifold design
• 1.4 First-order sliding-modes
• 1.4.1 Conventional sliding-modes
• 1.4.2 Integral sliding mode
• 1.4.3 Integral sliding modes for linear systems
• 1.5 Second-order sliding-modes
• 1.5.1 The concept of high order sliding-mode
• 1.5.2 Twisting second-order sliding-modes algorithm
• 1.5.3 Super-twisting second-order sliding-modes algorithm
• 1.5.4 Suboptimal second-order sliding-mode algorithm
• 1.6 Robust exact arbitrary order differentiator
• 1.7 Conclusions
• Acknowledgments
• References

Inspec keywords: robust control; variable structure systems; control system synthesis

Other keywords: state trajectories; sliding mode theory; conventional sliding set; advanced robust exact high-order sliding modes differentiator; sliding mode controller design; second-order sliding-mode algorithms; sliding motion

Subjects: Stability in control theory; Control system analysis and synthesis methods; Multivariable control systems