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03000EE304052001

PART C
Answer any two full questions, each carries10 marks.

Obtain the state model of the system whose transfer function is given by
Y(s)/U(s)= 10/(5 4452541]
Obtain the state model of a field controlled DC motor.
A discrete time system is described by the difference equation
y(k+2)+5 y(k+1)+6y(k)=u(k)
y(0)=y(1)=0; T=1 sec.
(a) Determine state model in a canonical form (b) Find the state transition matrix
Check the stability of the sampled data control system with the following characteristic
equation using Jury’s stability test. z*-1.7z*+1.04z7-0.268z+0.024=0
PART D

Answer any two full questions, each carries 10 marks.

Derive the Describing function of saturation with deadzone.

Construct the phase trajectory for the system
⋅ ⋅ 1 20 ⋅
∍∊⋅↥−−⊼≳∣∂∁∎≳−−−≤⇂⇪⊺⇂∊∝↕⊃∥↗∣⇂∊⊺∊≤⇂∙⇪⊺⇂↻∊↥⋟−− | 7 < 0 starting from (2,0)
− ಹೆ

Test the stability of the system using Lyapunov stability theorem

−⋅ 2 −⋅
وا = 2 , 212 + ≖↧−−↥↥↺≗≼

(b) x4 = 2८2, 22 = —sin(x,) — 2

(5)

(5)
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