1. O f S l I d I n g M o d e C o n t r o l
R e c e n t A d v a n t a g e s
O f S l I d I n g M o d e C o n t r o l
Europian Embedded Control Insttitute
SUPELEC March 19-23, 2012

2. - Introduction (prehistory) - Discrete-time sliding modes Observers and estimators Chattering problem High order sliding modes

10. Introduction of Sliding Mode Control
First Stage – Control in Canonical Space

11. Introduction of Sliding Mode Control
■ Concept of Sliding Mode ( Second order relay system )
Upper semi-plane :
Lower semi-plane :
• State trajectories are towards the line switching line s=0
• State trajectories cannot leave and belong to the switching line s=0
: sliding mode
• After sliding mode starts, further motion is governed by
: sliding mode equation
Sliding Mode n m
In sliding mode,
the system motion is
governed by 1st order equation (reduced order).
depending only on ‘c’ not plant dynamics.
Sliding Mode Equation

12. Trajectories should be oriented towards the switching surface

15. 15

16. Introduction of Sliding Mode Control
■ Concept of Sliding Mode ( Variable Structures System ) 1 2 1 2
State planes of two unstable structures

17. State planes of Variable Structure System
Introduction of Sliding Mode Control
• If c<c0, the state trajectories are towards the line switching line s=0
• State trajectories cannot leave and belong to the switching line s=0
: sliding mode
• After sliding mode starts, further motion is governed by
: sliding mode equation
State planes of Variable Structure System 1 2
In sliding mode,
the system motion is
governed by 1st order equation (reduced order).
depending only on ‘c’ not plant dynamics.

25. Dubrovnik 1964
IFAC Sensitivity Conference

26. Dubrovnik 1964
IFAC Sensitivity
Conference

27. Dubrovnik 1964
IFAC Sensitivity
Conference