b. Derive an expression for a non switching based sliding mode control of a discrete time
SISO system subjected to parametric variations in system matrix and is also subjected to

external disturbances. (4)

Part C (Modules VI)

7) 4.Briefly explain the design of an Utkin observer for an LTI system.
b. Explain the term relative degree and order w.r.t to sliding mode control system. (4)

௦. For ೩ 8751017 described by

and assume a sliding surface = CIXI + c2x2 + .13 is designed. Find the reative degree
w.r.t for the above system. Is it possible to design a classical SMC for the above system
with the above sliding surface if not why?. (2)

8) a. Prove that in an Utkin's sliding mode observer sliding mode will takes place in finite time.
(6) b. Explain in detail design ofa second order sliding mode controller that will provide

acontinuous control. (6)

9) a. Explain the need of an observer. Also, compare the features of a sliding mode observer and
Leunberger observer. Also mention their respective observer dynamics and error dynamics.

(6) b. Explain in detail design of a super-twisting based differentiator. (6)

3
b. Derive an expression for a non switching based sliding mode control of a discrete time
SISO system subjected to parametric variations in system matrix and is also subjected to

external disturbances. (4)