1. Sliding Mode : An Introduction
S. Janardhanan

2. Outline
What is this ‘Sliding mode’ and how did its study start?

3. Primitive Examples - Electrical

4. Primitive Examples-Mechanical

5. First ‘Formal’ Steps
The first steps of sliding mode control ‘theory’ originated in the early 1950’s initiated by S. V. Emel’yanov.
Started as VSC – Variable Structure Control
Varying system structure for stabilization.

6. Variable Structure Control – Constituent Systems
Both systems have their eigenvalues on the imaginary axis. Neither system is asymptotically stable.
Mode 2
Mode 1

7. Piecing together …

8. Properties of VSC
Both constituent systems were oscillatory and were not asymptotically stable.
‘Combined’ system is asymptotically stable.
Property not present in any of the constituent system is obtained by VSC

9. Another Example – Unstable Constituent Systems
Zeta and alpha are both positive. In both cases, the system is unstable.

10. Analysis … Both systems are unstable
Only stable mode is one mode of system
IF the following VSC is employed

11. Combined ..

12. In this case,…
Again, property not present in constituent systems is found in the combined system.
A stable structure can be obtain by varying between two unstable structures.
However, a more interesting behaviour can be observed if we use a different ‘switching’ logic.

13. The regions

14. Sliding Mode
New trajectory that was not present in any of the two original systems

15. Sliding Mode ?
Defined : Motion of the system trajectory along a ‘chosen’ line/plane/surface of the state space.
Sliding Mode Control : Control designed with the aim to achieve sliding mode.
Is usually of VSC type
Eg : Previous problem can be perceived as

16. Sliding Mode Control and Controller Design for Continuous time Systems
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Sliding Mode Control and Controller Design for Continuous time Systems